Package org.joml

Interface Matrix4dc

All Known Implementing Classes:

Matrix4d, Matrix4dStack

public interface Matrix4dc

Interface to a read-only view of a 4x4 matrix of double-precision floats.

Author:

Kai Burjack

Field Summary

Fields

Modifier and Type	Field	Description
static final int	CORNER_NXNYNZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, -1) when using the identity matrix.
static final int	CORNER_NXNYPZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, 1) when using the identity matrix.
static final int	CORNER_NXPYNZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, -1) when using the identity matrix.
static final int	CORNER_NXPYPZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, 1) when using the identity matrix.
static final int	CORNER_PXNYNZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, -1) when using the identity matrix.
static final int	CORNER_PXNYPZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, 1) when using the identity matrix.
static final int	CORNER_PXPYNZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, -1) when using the identity matrix.
static final int	CORNER_PXPYPZ	Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, 1) when using the identity matrix.
static final int	PLANE_NX	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=-1 when using the identity matrix.
static final int	PLANE_NY	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=-1 when using the identity matrix.
static final int	PLANE_NZ	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=-1 when using the identity matrix.
static final int	PLANE_PX	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=1 when using the identity matrix.
static final int	PLANE_PY	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=1 when using the identity matrix.
static final int	PLANE_PZ	Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=1 when using the identity matrix.
static final byte	PROPERTY_AFFINE	Bit returned by properties() to indicate that the matrix represents an affine transformation.
static final byte	PROPERTY_IDENTITY	Bit returned by properties() to indicate that the matrix represents the identity transformation.
static final byte	PROPERTY_ORTHONORMAL	Bit returned by properties() to indicate that the upper-left 3x3 submatrix represents an orthogonal matrix (i.e.
static final byte	PROPERTY_PERSPECTIVE	Bit returned by properties() to indicate that the matrix represents a perspective transformation.
static final byte	PROPERTY_TRANSLATION	Bit returned by properties() to indicate that the matrix represents a pure translation transformation.

Method Summary

Modifier and Type	Method	Description
Matrix4d	add(Matrix4dc other, Matrix4d dest)	Component-wise add this and other and store the result in dest.
Matrix4d	add4x3(Matrix4dc other, Matrix4d dest)	Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.
Matrix4d	add4x3(Matrix4fc other, Matrix4d dest)	Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.
Matrix4d	arcball(double radius, double centerX, double centerY, double centerZ, double angleX, double angleY, Matrix4d dest)	Apply an arcball view transformation to this matrix with the given radius and center (centerX, centerY, centerZ) position of the arcball and the specified X and Y rotation angles, and store the result in dest.
Matrix4d	arcball(double radius, Vector3dc center, double angleX, double angleY, Matrix4d dest)	Apply an arcball view transformation to this matrix with the given radius and center position of the arcball and the specified X and Y rotation angles, and store the result in dest.
Matrix3d	cofactor3x3(Matrix3d dest)	Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest.
Matrix4d	cofactor3x3(Matrix4d dest)	Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest.
double	determinant()	Return the determinant of this matrix.
double	determinant3x3()	Return the determinant of the upper left 3x3 submatrix of this matrix.
double	determinantAffine()	Return the determinant of this matrix by assuming that it represents an affine transformation and thus its last row is equal to (0, 0, 0, 1).
boolean	equals(Matrix4dc m, double delta)	Compare the matrix elements of this matrix with the given matrix using the given delta and return whether all of them are equal within a maximum difference of delta.
Matrix4d	fma4x3(Matrix4dc other, double otherFactor, Matrix4d dest)	Component-wise add the upper 4x3 submatrices of this and other by first multiplying each component of other's 4x3 submatrix by otherFactor, adding that to this and storing the final result in dest.
Matrix4d	frustum(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	frustum(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)	Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Vector3d	frustumCorner(int corner, Vector3d point)	Compute the corner coordinates of the frustum defined by this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given point.
Matrix4d	frustumLH(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	frustumLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)	Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Vector4d	frustumPlane(int plane, Vector4d dest)	Calculate a frustum plane of this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given dest.
Vector3d	frustumRayDir(double x, double y, Vector3d dir)	Obtain the direction of a ray starting at the center of the coordinate system and going through the near frustum plane.
double[]	get(double[] arr)	Store this matrix into the supplied double array in column-major order.
double[]	get(double[] arr, int offset)	Store this matrix into the supplied double array in column-major order at the given offset.
float[]	get(float[] arr)	Store the elements of this matrix as float values in column-major order into the supplied float array.
float[]	get(float[] arr, int offset)	Store the elements of this matrix as float values in column-major order into the supplied float array at the given offset.
double	get(int column, int row)	Get the matrix element value at the given column and row.
ByteBuffer	get(int index, ByteBuffer buffer)	Store this matrix in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
DoubleBuffer	get(int index, DoubleBuffer buffer)	Store this matrix in column-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.
FloatBuffer	get(int index, FloatBuffer buffer)	Store this matrix in column-major order into the supplied FloatBuffer starting at the specified absolute buffer position/index.
ByteBuffer	get(ByteBuffer buffer)	Store this matrix in column-major order into the supplied ByteBuffer at the current buffer position.
DoubleBuffer	get(DoubleBuffer buffer)	Store this matrix in column-major order into the supplied DoubleBuffer at the current buffer position.
FloatBuffer	get(FloatBuffer buffer)	Store this matrix in column-major order into the supplied FloatBuffer at the current buffer position.
Matrix4d	get(Matrix4d dest)	Get the current values of this matrix and store them into dest.
Matrix3d	get3x3(Matrix3d dest)	Get the current values of the upper left 3x3 submatrix of this matrix and store them into dest.
Matrix4x3d	get4x3(Matrix4x3d dest)	Get the current values of the upper 4x3 submatrix of this matrix and store them into dest.
ByteBuffer	get4x3Transposed(int index, ByteBuffer buffer)	Store the upper 4x3 submatrix of this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
DoubleBuffer	get4x3Transposed(int index, DoubleBuffer buffer)	Store the upper 4x3 submatrix of this matrix in row-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.
ByteBuffer	get4x3Transposed(ByteBuffer buffer)	Store the upper 4x3 submatrix of this matrix in row-major order into the supplied ByteBuffer at the current buffer position.
DoubleBuffer	get4x3Transposed(DoubleBuffer buffer)	Store the upper 4x3 submatrix of this matrix in row-major order into the supplied DoubleBuffer at the current buffer position.
Vector3d	getColumn(int column, Vector3d dest)	Get the first three components of the column at the given column index, starting with 0.
Vector4d	getColumn(int column, Vector4d dest)	Get the column at the given column index, starting with 0.
Vector3d	getEulerAnglesXYZ(Vector3d dest)	Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of this and store the extracted Euler angles in dest.
Vector3d	getEulerAnglesZYX(Vector3d dest)	Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of this and store the extracted Euler angles in dest.
ByteBuffer	getFloats(int index, ByteBuffer buffer)	Store the elements of this matrix as float values in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
ByteBuffer	getFloats(ByteBuffer buffer)	Store the elements of this matrix as float values in column-major order into the supplied ByteBuffer at the current buffer position.
Quaterniond	getNormalizedRotation(Quaterniond dest)	Get the current values of this matrix and store the represented rotation into the given Quaterniond.
Quaternionf	getNormalizedRotation(Quaternionf dest)	Get the current values of this matrix and store the represented rotation into the given Quaternionf.
Vector3d	getRow(int row, Vector3d dest)	Get the first three components of the row at the given row index, starting with 0.
Vector4d	getRow(int row, Vector4d dest)	Get the row at the given row index, starting with 0.
double	getRowColumn(int row, int column)	Get the matrix element value at the given row and column.
Vector3d	getScale(Vector3d dest)	Get the scaling factors of this matrix for the three base axes.
Matrix4dc	getToAddress(long address)	Store this matrix in column-major order at the given off-heap address.
Vector3d	getTranslation(Vector3d dest)	Get only the translation components (m30, m31, m32) of this matrix and store them in the given vector xyz.
ByteBuffer	getTransposed(int index, ByteBuffer buffer)	Store this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
DoubleBuffer	getTransposed(int index, DoubleBuffer buffer)	Store this matrix in row-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.
FloatBuffer	getTransposed(int index, FloatBuffer buffer)	Store this matrix in row-major order into the supplied FloatBuffer starting at the specified absolute buffer position/index.
ByteBuffer	getTransposed(ByteBuffer buffer)	Store this matrix in row-major order into the supplied ByteBuffer at the current buffer position.
DoubleBuffer	getTransposed(DoubleBuffer buffer)	Store this matrix in row-major order into the supplied DoubleBuffer at the current buffer position.
FloatBuffer	getTransposed(FloatBuffer buffer)	Store this matrix in row-major order into the supplied FloatBuffer at the current buffer position.
ByteBuffer	getTransposedFloats(int index, ByteBuffer buffer)	Store this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
ByteBuffer	getTransposedFloats(ByteBuffer buffer)	Store this matrix as float values in row-major order into the supplied ByteBuffer at the current buffer position.
Quaterniond	getUnnormalizedRotation(Quaterniond dest)	Get the current values of this matrix and store the represented rotation into the given Quaterniond.
Quaternionf	getUnnormalizedRotation(Quaternionf dest)	Get the current values of this matrix and store the represented rotation into the given Quaternionf.
Matrix4d	invert(Matrix4d dest)	Invert this matrix and store the result in dest.
Matrix4d	invertAffine(Matrix4d dest)	Invert this matrix by assuming that it is an affine transformation (i.e.
Matrix4d	invertFrustum(Matrix4d dest)	If this is an arbitrary perspective projection matrix obtained via one of the frustum() methods, then this method builds the inverse of this and stores it into the given dest.
Matrix4d	invertOrtho(Matrix4d dest)	Invert this orthographic projection matrix and store the result into the given dest.
Matrix4d	invertPerspective(Matrix4d dest)	If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation, then this method builds the inverse of this and stores it into the given dest.
Matrix4d	invertPerspectiveView(Matrix4dc view, Matrix4d dest)	If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation and the given view matrix is affine and has unit scaling (for example by being obtained via lookAt()), then this method builds the inverse of this * view and stores it into the given dest.
Matrix4d	invertPerspectiveView(Matrix4x3dc view, Matrix4d dest)	If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation and the given view matrix has unit scaling, then this method builds the inverse of this * view and stores it into the given dest.
boolean	isAffine()	Determine whether this matrix describes an affine transformation.
boolean	isFinite()	Determine whether all matrix elements are finite floating-point values, that is, they are not NaN and not infinity.
Matrix4d	lerp(Matrix4dc other, double t, Matrix4d dest)	Linearly interpolate this and other using the given interpolation factor t and store the result in dest.
Matrix4d	lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a rotation transformation to this matrix to make -z point along dir and store the result in dest.
Matrix4d	lookAlong(Vector3dc dir, Vector3dc up, Matrix4d dest)	Apply a rotation transformation to this matrix to make -z point along dir and store the result in dest.
Matrix4d	lookAt(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.
Matrix4d	lookAt(Vector3dc eye, Vector3dc center, Vector3dc up, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.
Matrix4d	lookAtLH(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.
Matrix4d	lookAtLH(Vector3dc eye, Vector3dc center, Vector3dc up, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.
Matrix4d	lookAtPerspective(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.
Matrix4d	lookAtPerspectiveLH(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.
double	m00()	Return the value of the matrix element at column 0 and row 0.
double	m01()	Return the value of the matrix element at column 0 and row 1.
double	m02()	Return the value of the matrix element at column 0 and row 2.
double	m03()	Return the value of the matrix element at column 0 and row 3.
double	m10()	Return the value of the matrix element at column 1 and row 0.
double	m11()	Return the value of the matrix element at column 1 and row 1.
double	m12()	Return the value of the matrix element at column 1 and row 2.
double	m13()	Return the value of the matrix element at column 1 and row 3.
double	m20()	Return the value of the matrix element at column 2 and row 0.
double	m21()	Return the value of the matrix element at column 2 and row 1.
double	m22()	Return the value of the matrix element at column 2 and row 2.
double	m23()	Return the value of the matrix element at column 2 and row 3.
double	m30()	Return the value of the matrix element at column 3 and row 0.
double	m31()	Return the value of the matrix element at column 3 and row 1.
double	m32()	Return the value of the matrix element at column 3 and row 2.
double	m33()	Return the value of the matrix element at column 3 and row 3.
Matrix4d	mapnXnYnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXnYZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXnZnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXnZY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXYnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXZnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnXZY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYnXnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYnXZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYnZnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYnZX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYXnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYXZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYZnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnYZX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZnXnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZnXY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZnYnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZnYX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZXnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZXY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZYnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapnZYX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapXnYnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapXnZnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapXnZY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapXZnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapXZY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYnXnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYnXZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYnZnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYnZX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYXnZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYXZ(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYZnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapYZX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZnXnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZnXY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZnYnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZnYX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZXnY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZXY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZYnX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mapZYX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	mul(double r00, double r01, double r02, double r03, double r10, double r11, double r12, double r13, double r20, double r21, double r22, double r23, double r30, double r31, double r32, double r33, Matrix4d dest)	Multiply this matrix by the matrix with the supplied elements and store the result in dest.
Matrix4d	mul(Matrix3x2dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul(Matrix3x2fc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul(Matrix4dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul(Matrix4fc right, Matrix4d dest)	Multiply this matrix by the supplied parameter matrix and store the result in dest.
Matrix4d	mul(Matrix4x3dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul(Matrix4x3fc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul0(Matrix4dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix and store the result in dest.
Matrix4d	mul3x3(double r00, double r01, double r02, double r10, double r11, double r12, double r20, double r21, double r22, Matrix4d dest)	Multiply this matrix by the 3x3 matrix with the supplied elements expanded to a 4x4 matrix with all other matrix elements set to identity, and store the result in dest.
Matrix4d	mul4x3ComponentWise(Matrix4dc other, Matrix4d dest)	Component-wise multiply the upper 4x3 submatrices of this by other and store the result in dest.
Matrix4d	mulAffine(Matrix4dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix, both of which are assumed to be affine, and store the result in dest.
Matrix4d	mulAffineR(Matrix4dc right, Matrix4d dest)	Multiply this matrix by the supplied right matrix, which is assumed to be affine, and store the result in dest.
Matrix4d	mulComponentWise(Matrix4dc other, Matrix4d dest)	Component-wise multiply this by other and store the result in dest.
Matrix4d	mulLocal(Matrix4dc left, Matrix4d dest)	Pre-multiply this matrix by the supplied left matrix and store the result in dest.
Matrix4d	mulLocalAffine(Matrix4dc left, Matrix4d dest)	Pre-multiply this matrix by the supplied left matrix, both of which are assumed to be affine, and store the result in dest.
Matrix4d	mulOrthoAffine(Matrix4dc view, Matrix4d dest)	Multiply this orthographic projection matrix by the supplied affine view matrix and store the result in dest.
Matrix4d	mulPerspectiveAffine(Matrix4dc view, Matrix4d dest)	Multiply this symmetric perspective projection matrix by the supplied affine view matrix and store the result in dest.
Matrix4d	mulPerspectiveAffine(Matrix4x3dc view, Matrix4d dest)	Multiply this symmetric perspective projection matrix by the supplied view matrix and store the result in dest.
Matrix4d	mulTranslationAffine(Matrix4dc right, Matrix4d dest)	Multiply this matrix, which is assumed to only contain a translation, by the supplied right matrix, which is assumed to be affine, and store the result in dest.
Matrix4d	negateX(Matrix4d dest)	Multiply this by the matrix
Matrix4d	negateY(Matrix4d dest)	Multiply this by the matrix
Matrix4d	negateZ(Matrix4d dest)	Multiply this by the matrix
Matrix3d	normal(Matrix3d dest)	Compute a normal matrix from the upper left 3x3 submatrix of this and store it into dest.
Matrix4d	normal(Matrix4d dest)	Compute a normal matrix from the upper left 3x3 submatrix of this and store it into the upper left 3x3 submatrix of dest.
Matrix3d	normalize3x3(Matrix3d dest)	Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.
Matrix4d	normalize3x3(Matrix4d dest)	Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.
Vector3d	normalizedPositiveX(Vector3d dir)	Obtain the direction of +X before the transformation represented by this orthogonal matrix is applied.
Vector3d	normalizedPositiveY(Vector3d dir)	Obtain the direction of +Y before the transformation represented by this orthogonal matrix is applied.
Vector3d	normalizedPositiveZ(Vector3d dir)	Obtain the direction of +Z before the transformation represented by this orthogonal matrix is applied.
Matrix4d	obliqueZ(double a, double b, Matrix4d dest)	Apply an oblique projection transformation to this matrix with the given values for a and b and store the result in dest.
Vector3d	origin(Vector3d origin)	Obtain the position that gets transformed to the origin by this matrix.
Vector3d	originAffine(Vector3d origin)	Obtain the position that gets transformed to the origin by this affine matrix.
Matrix4d	ortho(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	ortho(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)	Apply an orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	ortho2D(double left, double right, double bottom, double top, Matrix4d dest)	Apply an orthographic projection transformation for a right-handed coordinate system to this matrix and store the result in dest.
Matrix4d	ortho2DLH(double left, double right, double bottom, double top, Matrix4d dest)	Apply an orthographic projection transformation for a left-handed coordinate system to this matrix and store the result in dest.
Matrix4d	orthoCrop(Matrix4dc view, Matrix4d dest)	Build an ortographic projection transformation that fits the view-projection transformation represented by this into the given affine view transformation.
Matrix4d	orthoLH(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an orthographic projection transformation for a left-handed coordiante system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	orthoLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)	Apply an orthographic projection transformation for a left-handed coordiante system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	orthoSymmetric(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply a symmetric orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	orthoSymmetric(double width, double height, double zNear, double zFar, Matrix4d dest)	Apply a symmetric orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	orthoSymmetricLH(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply a symmetric orthographic projection transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	orthoSymmetricLH(double width, double height, double zNear, double zFar, Matrix4d dest)	Apply a symmetric orthographic projection transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	perspective(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspective(double fovy, double aspect, double zNear, double zFar, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
double	perspectiveFar()	Extract the far clip plane distance from this perspective projection matrix.
double	perspectiveFov()	Return the vertical field-of-view angle in radians of this perspective transformation matrix.
Matrix4d	perspectiveFrustumSlice(double near, double far, Matrix4d dest)	Change the near and far clip plane distances of this perspective frustum transformation matrix and store the result in dest.
Vector3d	perspectiveInvOrigin(Vector3d dest)	Compute the eye/origin of the inverse of the perspective frustum transformation defined by this matrix, which can be the inverse of a projection matrix or the inverse of a combined modelview-projection matrix, and store the result in the given dest.
Matrix4d	perspectiveLH(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspectiveLH(double fovy, double aspect, double zNear, double zFar, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
double	perspectiveNear()	Extract the near clip plane distance from this perspective projection matrix.
Matrix4d	perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	perspectiveOffCenterFov(double angleLeft, double angleRight, double angleDown, double angleUp, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspectiveOffCenterFov(double angleLeft, double angleRight, double angleDown, double angleUp, double zNear, double zFar, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	perspectiveOffCenterFovLH(double angleLeft, double angleRight, double angleDown, double angleUp, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspectiveOffCenterFovLH(double angleLeft, double angleRight, double angleDown, double angleUp, double zNear, double zFar, Matrix4d dest)	Apply an asymmetric off-center perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Vector3d	perspectiveOrigin(Vector3d origin)	Compute the eye/origin of the perspective frustum transformation defined by this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given origin.
Matrix4d	perspectiveRect(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.
Matrix4d	perspectiveRect(double width, double height, double zNear, double zFar, Matrix4d dest)	Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
Matrix4d	pick(double x, double y, double width, double height, int[] viewport, Matrix4d dest)	Apply a picking transformation to this matrix using the given window coordinates (x, y) as the pick center and the given (width, height) as the size of the picking region in window coordinates, and store the result in dest.
Vector3d	positiveX(Vector3d dir)	Obtain the direction of +X before the transformation represented by this matrix is applied.
Vector3d	positiveY(Vector3d dir)	Obtain the direction of +Y before the transformation represented by this matrix is applied.
Vector3d	positiveZ(Vector3d dir)	Obtain the direction of +Z before the transformation represented by this matrix is applied.
Vector3d	project(double x, double y, double z, int[] viewport, Vector3d winCoordsDest)	Project the given (x, y, z) position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.
Vector4d	project(double x, double y, double z, int[] viewport, Vector4d winCoordsDest)	Project the given (x, y, z) position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.
Vector3d	project(Vector3dc position, int[] viewport, Vector3d winCoordsDest)	Project the given position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.
Vector4d	project(Vector3dc position, int[] viewport, Vector4d winCoordsDest)	Project the given position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.
Matrix4d	projectedGridRange(Matrix4dc projector, double sLower, double sUpper, Matrix4d dest)	Compute the range matrix for the Projected Grid transformation as described in chapter "2.4.2 Creating the range conversion matrix" of the paper Real-time water rendering - Introducing the projected grid concept based on the inverse of the view-projection matrix which is assumed to be this, and store that range matrix into dest.
int	properties()	Return the assumed properties of this matrix.
Matrix4d	reflect(double nx, double ny, double nz, double px, double py, double pz, Matrix4d dest)	Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in dest.
Matrix4d	reflect(double a, double b, double c, double d, Matrix4d dest)	Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the equation x*a + y*b + z*c + d = 0 and store the result in dest.
Matrix4d	reflect(Quaterniondc orientation, Vector3dc point, Matrix4d dest)	Apply a mirror/reflection transformation to this matrix that reflects about a plane specified via the plane orientation and a point on the plane, and store the result in dest.
Matrix4d	reflect(Vector3dc normal, Vector3dc point, Matrix4d dest)	Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in dest.
Matrix4d	rotate(double ang, double x, double y, double z, Matrix4d dest)	Apply rotation to this matrix by rotating the given amount of radians about the given axis specified as x, y and z components and store the result in dest.
Matrix4d	rotate(double angle, Vector3dc axis, Matrix4d dest)	Apply a rotation transformation, rotating the given radians about the specified axis and store the result in dest.
Matrix4d	rotate(double angle, Vector3fc axis, Matrix4d dest)	Apply a rotation transformation, rotating the given radians about the specified axis and store the result in dest.
Matrix4d	rotate(AxisAngle4d axisAngle, Matrix4d dest)	Apply a rotation transformation, rotating about the given AxisAngle4d and store the result in dest.
Matrix4d	rotate(AxisAngle4f axisAngle, Matrix4d dest)	Apply a rotation transformation, rotating about the given AxisAngle4f and store the result in dest.
Matrix4d	rotate(Quaterniondc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix and store the result in dest.
Matrix4d	rotate(Quaternionfc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix and store the result in dest.
Matrix4d	rotateAffine(double ang, double x, double y, double z, Matrix4d dest)	Apply rotation to this affine matrix by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.
Matrix4d	rotateAffine(Quaterniondc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this affine matrix and store the result in dest.
Matrix4d	rotateAffine(Quaternionfc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this affine matrix and store the result in dest.
Matrix4d	rotateAffineXYZ(double angleX, double angleY, double angleZ, Matrix4d dest)	Apply rotation of angleX radians about the X axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.
Matrix4d	rotateAffineYXZ(double angleY, double angleX, double angleZ, Matrix4d dest)	Apply rotation of angleY radians about the Y axis, followed by a rotation of angleX radians about the X axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.
Matrix4d	rotateAffineZYX(double angleZ, double angleY, double angleX, Matrix4d dest)	Apply rotation of angleZ radians about the Z axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleX radians about the X axis and store the result in dest.
Matrix4d	rotateAround(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.
Matrix4d	rotateAroundAffine(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this affine matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.
Matrix4d	rotateAroundLocal(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)	Pre-multiply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.
Matrix4d	rotateLocal(double ang, double x, double y, double z, Matrix4d dest)	Pre-multiply a rotation to this matrix by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.
Matrix4d	rotateLocal(Quaterniondc quat, Matrix4d dest)	Pre-multiply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix and store the result in dest.
Matrix4d	rotateLocal(Quaternionfc quat, Matrix4d dest)	Pre-multiply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix and store the result in dest.
Matrix4d	rotateLocalX(double ang, Matrix4d dest)	Pre-multiply a rotation around the X axis to this matrix by rotating the given amount of radians about the X axis and store the result in dest.
Matrix4d	rotateLocalY(double ang, Matrix4d dest)	Pre-multiply a rotation around the Y axis to this matrix by rotating the given amount of radians about the Y axis and store the result in dest.
Matrix4d	rotateLocalZ(double ang, Matrix4d dest)	Pre-multiply a rotation around the Z axis to this matrix by rotating the given amount of radians about the Z axis and store the result in dest.
Matrix4d	rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest)	Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local +Z axis with dir and store the result in dest.
Matrix4d	rotateTowards(Vector3dc direction, Vector3dc up, Matrix4d dest)	Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local +Z axis with direction and store the result in dest.
Matrix4d	rotateTowardsXY(double dirX, double dirY, Matrix4d dest)	Apply rotation about the Z axis to align the local +X towards (dirX, dirY) and store the result in dest.
Matrix4d	rotateTranslation(double ang, double x, double y, double z, Matrix4d dest)	Apply rotation to this matrix, which is assumed to only contain a translation, by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.
Matrix4d	rotateTranslation(Quaterniondc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix, which is assumed to only contain a translation, and store the result in dest.
Matrix4d	rotateTranslation(Quaternionfc quat, Matrix4d dest)	Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix, which is assumed to only contain a translation, and store the result in dest.
Matrix4d	rotateX(double ang, Matrix4d dest)	Apply rotation about the X axis to this matrix by rotating the given amount of radians and store the result in dest.
Matrix4d	rotateXYZ(double angleX, double angleY, double angleZ, Matrix4d dest)	Apply rotation of angleX radians about the X axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.
Matrix4d	rotateY(double ang, Matrix4d dest)	Apply rotation about the Y axis to this matrix by rotating the given amount of radians and store the result in dest.
Matrix4d	rotateYXZ(double angleY, double angleX, double angleZ, Matrix4d dest)	Apply rotation of angleY radians about the Y axis, followed by a rotation of angleX radians about the X axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.
Matrix4d	rotateZ(double ang, Matrix4d dest)	Apply rotation about the Z axis to this matrix by rotating the given amount of radians and store the result in dest.
Matrix4d	rotateZYX(double angleZ, double angleY, double angleX, Matrix4d dest)	Apply rotation of angleZ radians about the Z axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleX radians about the X axis and store the result in dest.
Matrix4d	scale(double x, double y, double z, Matrix4d dest)	Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
Matrix4d	scale(double xyz, Matrix4d dest)	Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor and store the result in dest.
Matrix4d	scale(Vector3dc xyz, Matrix4d dest)	Apply scaling to this matrix by scaling the base axes by the given xyz.x, xyz.y and xyz.z factors, respectively and store the result in dest.
Matrix4d	scaleAround(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest)	Apply scaling to this matrix by scaling the base axes by the given sx, sy and sz factors while using (ox, oy, oz) as the scaling origin, and store the result in dest.
Matrix4d	scaleAround(double factor, double ox, double oy, double oz, Matrix4d dest)	Apply scaling to this matrix by scaling all three base axes by the given factor while using (ox, oy, oz) as the scaling origin, and store the result in dest.
Matrix4d	scaleAroundLocal(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest)	Pre-multiply scaling to this matrix by scaling the base axes by the given sx, sy and sz factors while using the given (ox, oy, oz) as the scaling origin, and store the result in dest.
Matrix4d	scaleAroundLocal(double factor, double ox, double oy, double oz, Matrix4d dest)	Pre-multiply scaling to this matrix by scaling all three base axes by the given factor while using (ox, oy, oz) as the scaling origin, and store the result in dest.
Matrix4d	scaleLocal(double x, double y, double z, Matrix4d dest)	Pre-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.
Matrix4d	scaleLocal(double xyz, Matrix4d dest)	Pre-multiply scaling to this matrix by scaling all base axes by the given xyz factor, and store the result in dest.
Matrix4d	scaleXY(double x, double y, Matrix4d dest)	Apply scaling to this matrix by by scaling the X axis by x and the Y axis by y and store the result in dest.
Matrix4d	shadow(double lightX, double lightY, double lightZ, double lightW, double a, double b, double c, double d, Matrix4d dest)	Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation x*a + y*b + z*c + d = 0 as if casting a shadow from a given light position/direction (lightX, lightY, lightZ, lightW) and store the result in dest.
Matrix4d	shadow(double lightX, double lightY, double lightZ, double lightW, Matrix4dc planeTransform, Matrix4d dest)	Apply a projection transformation to this matrix that projects onto the plane with the general plane equation y = 0 as if casting a shadow from a given light position/direction (lightX, lightY, lightZ, lightW) and store the result in dest.
Matrix4d	shadow(Vector4dc light, double a, double b, double c, double d, Matrix4d dest)	Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation x*a + y*b + z*c + d = 0 as if casting a shadow from a given light position/direction light and store the result in dest.
Matrix4d	shadow(Vector4dc light, Matrix4dc planeTransform, Matrix4d dest)	Apply a projection transformation to this matrix that projects onto the plane with the general plane equation y = 0 as if casting a shadow from a given light position/direction light and store the result in dest.
Matrix4d	sub(Matrix4dc subtrahend, Matrix4d dest)	Component-wise subtract subtrahend from this and store the result in dest.
Matrix4d	sub4x3(Matrix4dc subtrahend, Matrix4d dest)	Component-wise subtract the upper 4x3 submatrices of subtrahend from this and store the result in dest.
boolean	testAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ)	Test whether the given axis-aligned box is partly or completely within or outside of the frustum defined by this matrix.
boolean	testPoint(double x, double y, double z)	Test whether the given point (x, y, z) is within the frustum defined by this matrix.
boolean	testSphere(double x, double y, double z, double r)	Test whether the given sphere is partly or completely within or outside of the frustum defined by this matrix.
Matrix4d	tile(int x, int y, int w, int h, Matrix4d dest)	This method is equivalent to calling: translate(w-1-2*x, h-1-2*y, 0, dest).scale(w, h, 1)
Vector4d	transform(double x, double y, double z, double w, Vector4d dest)	Transform/multiply the vector (x, y, z, w) by this matrix and store the result in dest.
Vector4d	transform(Vector4d v)	Transform/multiply the given vector by this matrix and store the result in that vector.
Vector4d	transform(Vector4dc v, Vector4d dest)	Transform/multiply the given vector by this matrix and store the result in dest.
Matrix4d	transformAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ, Vector3d outMin, Vector3d outMax)	Transform the axis-aligned box given as the minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ) by this affine matrix and compute the axis-aligned box of the result whose minimum corner is stored in outMin and maximum corner stored in outMax.
Matrix4d	transformAab(Vector3dc min, Vector3dc max, Vector3d outMin, Vector3d outMax)	Transform the axis-aligned box given as the minimum corner min and maximum corner max by this affine matrix and compute the axis-aligned box of the result whose minimum corner is stored in outMin and maximum corner stored in outMax.
Vector4d	transformAffine(double x, double y, double z, double w, Vector4d dest)	Transform/multiply the 4D-vector (x, y, z, w) by assuming that this matrix represents an affine transformation (i.e.
Vector4d	transformAffine(Vector4d v)	Transform/multiply the given 4D-vector by assuming that this matrix represents an affine transformation (i.e.
Vector4d	transformAffine(Vector4dc v, Vector4d dest)	Transform/multiply the given 4D-vector by assuming that this matrix represents an affine transformation (i.e.
Vector3d	transformDirection(double x, double y, double z, Vector3d dest)	Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=0, by this matrix and store the result in dest.
Vector3f	transformDirection(double x, double y, double z, Vector3f dest)	Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=0, by this matrix and store the result in dest.
Vector3d	transformDirection(Vector3d v)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.
Vector3d	transformDirection(Vector3dc v, Vector3d dest)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in dest.
Vector3f	transformDirection(Vector3f v)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.
Vector3f	transformDirection(Vector3fc v, Vector3f dest)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in dest.
Vector3d	transformPosition(double x, double y, double z, Vector3d dest)	Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=1, by this matrix and store the result in dest.
Vector3d	transformPosition(Vector3d v)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by this matrix and store the result in that vector.
Vector3d	transformPosition(Vector3dc v, Vector3d dest)	Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by this matrix and store the result in dest.
Vector3d	transformProject(double x, double y, double z, double w, Vector3d dest)	Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store (x, y, z) of the result in dest.
Vector4d	transformProject(double x, double y, double z, double w, Vector4d dest)	Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store the result in dest.
Vector3d	transformProject(double x, double y, double z, Vector3d dest)	Transform/multiply the vector (x, y, z) by this matrix, perform perspective divide and store the result in dest.
Vector3d	transformProject(Vector3d v)	Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
Vector3d	transformProject(Vector3dc v, Vector3d dest)	Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.
Vector4d	transformProject(Vector4d v)	Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
Vector3d	transformProject(Vector4dc v, Vector3d dest)	Transform/multiply the given vector by this matrix, perform perspective divide and store the x, y and z components of the result in dest.
Vector4d	transformProject(Vector4dc v, Vector4d dest)	Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.
Vector4d	transformTranspose(double x, double y, double z, double w, Vector4d dest)	Transform/multiply the vector (x, y, z, w) by the transpose of this matrix and store the result in dest.
Vector4d	transformTranspose(Vector4d v)	Transform/multiply the given vector by the transpose of this matrix and store the result in that vector.
Vector4d	transformTranspose(Vector4dc v, Vector4d dest)	Transform/multiply the given vector by the transpose of this matrix and store the result in dest.
Matrix4d	translate(double x, double y, double z, Matrix4d dest)	Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	translate(Vector3dc offset, Matrix4d dest)	Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	translate(Vector3fc offset, Matrix4d dest)	Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	translateLocal(double x, double y, double z, Matrix4d dest)	Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	translateLocal(Vector3dc offset, Matrix4d dest)	Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	translateLocal(Vector3fc offset, Matrix4d dest)	Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.
Matrix4d	transpose(Matrix4d dest)	Transpose this matrix and store the result into dest.
Matrix3d	transpose3x3(Matrix3d dest)	Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
Matrix4d	transpose3x3(Matrix4d dest)	Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
Vector3d	unproject(double winX, double winY, double winZ, int[] viewport, Vector3d dest)	Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
Vector4d	unproject(double winX, double winY, double winZ, int[] viewport, Vector4d dest)	Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
Vector3d	unproject(Vector3dc winCoords, int[] viewport, Vector3d dest)	Unproject the given window coordinates winCoords by this matrix using the specified viewport.
Vector4d	unproject(Vector3dc winCoords, int[] viewport, Vector4d dest)	Unproject the given window coordinates winCoords by this matrix using the specified viewport.
Vector3d	unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector3d dest)	Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
Vector4d	unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector4d dest)	Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
Vector3d	unprojectInv(Vector3dc winCoords, int[] viewport, Vector3d dest)	Unproject the given window coordinates winCoords by this matrix using the specified viewport.
Vector4d	unprojectInv(Vector3dc winCoords, int[] viewport, Vector4d dest)	Unproject the given window coordinates winCoords by this matrix using the specified viewport.
Matrix4d	unprojectInvRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest)	Unproject the given 2D window coordinates (winX, winY) by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.
Matrix4d	unprojectInvRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest)	Unproject the given window coordinates winCoords by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.
Matrix4d	unprojectRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest)	Unproject the given 2D window coordinates (winX, winY) by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.
Matrix4d	unprojectRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest)	Unproject the given 2D window coordinates winCoords by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.
Matrix4d	withLookAtUp(double upX, double upY, double upZ, Matrix4d dest)	Apply a transformation to this matrix to ensure that the local Y axis (as obtained by positiveY(Vector3d)) will be coplanar to the plane spanned by the local Z axis (as obtained by positiveZ(Vector3d)) and the given vector (upX, upY, upZ), and store the result in dest.
Matrix4d	withLookAtUp(Vector3dc up, Matrix4d dest)	Apply a transformation to this matrix to ensure that the local Y axis (as obtained by positiveY(Vector3d)) will be coplanar to the plane spanned by the local Z axis (as obtained by positiveZ(Vector3d)) and the given vector up, and store the result in dest.

Field Details

PLANE_NX

static final int PLANE_NX

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=-1 when using the identity matrix.

See Also:

• Constant Field Values

PLANE_PX

static final int PLANE_PX

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=1 when using the identity matrix.

See Also:

• Constant Field Values

PLANE_NY

static final int PLANE_NY

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=-1 when using the identity matrix.

See Also:

• Constant Field Values

PLANE_PY

static final int PLANE_PY

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=1 when using the identity matrix.

See Also:

• Constant Field Values

PLANE_NZ

static final int PLANE_NZ

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=-1 when using the identity matrix.

See Also:

• Constant Field Values

PLANE_PZ

static final int PLANE_PZ

Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=1 when using the identity matrix.

See Also:

• Constant Field Values

CORNER_NXNYNZ

static final int CORNER_NXNYNZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, -1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_PXNYNZ

static final int CORNER_PXNYNZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, -1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_PXPYNZ

static final int CORNER_PXPYNZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, -1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_NXPYNZ

static final int CORNER_NXPYNZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, -1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_PXNYPZ

static final int CORNER_PXNYPZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, 1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_NXNYPZ

static final int CORNER_NXNYPZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, 1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_NXPYPZ

static final int CORNER_NXPYPZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, 1) when using the identity matrix.

See Also:

• Constant Field Values

CORNER_PXPYPZ

static final int CORNER_PXPYPZ

Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, 1) when using the identity matrix.

See Also:

• Constant Field Values

PROPERTY_PERSPECTIVE

static final byte PROPERTY_PERSPECTIVE

Bit returned by properties() to indicate that the matrix represents a perspective transformation.

See Also:

• Constant Field Values

PROPERTY_AFFINE

static final byte PROPERTY_AFFINE

Bit returned by properties() to indicate that the matrix represents an affine transformation.

See Also:

• Constant Field Values

PROPERTY_IDENTITY

static final byte PROPERTY_IDENTITY

Bit returned by properties() to indicate that the matrix represents the identity transformation.

See Also:

• Constant Field Values

PROPERTY_TRANSLATION

static final byte PROPERTY_TRANSLATION

Bit returned by properties() to indicate that the matrix represents a pure translation transformation.

See Also:

• Constant Field Values

PROPERTY_ORTHONORMAL

static final byte PROPERTY_ORTHONORMAL

Bit returned by properties() to indicate that the upper-left 3x3 submatrix represents an orthogonal matrix (i.e. orthonormal basis). For practical reasons, this property also always implies PROPERTY_AFFINE in this implementation.

See Also:

• Constant Field Values

Method Details

properties

int properties()

Return the assumed properties of this matrix. This is a bit-combination of PROPERTY_IDENTITY, PROPERTY_AFFINE, PROPERTY_TRANSLATION and PROPERTY_PERSPECTIVE.

Returns:

the properties of the matrix

m00

double m00()

Return the value of the matrix element at column 0 and row 0.

Returns:

the value of the matrix element

m01

double m01()

Return the value of the matrix element at column 0 and row 1.

Returns:

the value of the matrix element

m02

double m02()

Return the value of the matrix element at column 0 and row 2.

Returns:

the value of the matrix element

m03

double m03()

Return the value of the matrix element at column 0 and row 3.

Returns:

the value of the matrix element

m10

double m10()

Return the value of the matrix element at column 1 and row 0.

Returns:

the value of the matrix element

m11

double m11()

Return the value of the matrix element at column 1 and row 1.

Returns:

the value of the matrix element

m12

double m12()

Return the value of the matrix element at column 1 and row 2.

Returns:

the value of the matrix element

m13

double m13()

Return the value of the matrix element at column 1 and row 3.

Returns:

the value of the matrix element

m20

double m20()

Return the value of the matrix element at column 2 and row 0.

Returns:

the value of the matrix element

m21

double m21()

Return the value of the matrix element at column 2 and row 1.

Returns:

the value of the matrix element

m22

double m22()

Return the value of the matrix element at column 2 and row 2.

Returns:

the value of the matrix element

m23

double m23()

Return the value of the matrix element at column 2 and row 3.

Returns:

the value of the matrix element

m30

double m30()

Return the value of the matrix element at column 3 and row 0.

Returns:

the value of the matrix element

m31

double m31()

Return the value of the matrix element at column 3 and row 1.

Returns:

the value of the matrix element

m32

double m32()

Return the value of the matrix element at column 3 and row 2.

Returns:

the value of the matrix element

m33

double m33()

Return the value of the matrix element at column 3 and row 3.

Returns:

the value of the matrix element

mul

Matrix4d mul(Matrix4dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the multiplication

dest - will hold the result

Returns:

dest

mul0

Matrix4d mul0(Matrix4dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

This method neither assumes nor checks for any matrix properties of this or right and will always perform a complete 4x4 matrix multiplication. This method should only be used whenever the multiplied matrices do not have any properties for which there are optimized multiplication methods available.

Parameters:

right - the right operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(double r00,
 double r01,
 double r02,
 double r03,
 double r10,
 double r11,
 double r12,
 double r13,
 double r20,
 double r21,
 double r22,
 double r23,
 double r30,
 double r31,
 double r32,
 double r33,
 Matrix4d dest)

Multiply this matrix by the matrix with the supplied elements and store the result in dest.

If M is this matrix and R the right matrix whose elements are supplied via the parameters, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

r00 - the m00 element of the right matrix

r01 - the m01 element of the right matrix

r02 - the m02 element of the right matrix

r03 - the m03 element of the right matrix

r10 - the m10 element of the right matrix

r11 - the m11 element of the right matrix

r12 - the m12 element of the right matrix

r13 - the m13 element of the right matrix

r20 - the m20 element of the right matrix

r21 - the m21 element of the right matrix

r22 - the m22 element of the right matrix

r23 - the m23 element of the right matrix

r30 - the m30 element of the right matrix

r31 - the m31 element of the right matrix

r32 - the m32 element of the right matrix

r33 - the m33 element of the right matrix

dest - the destination matrix, which will hold the result

Returns:

dest

mul3x3

Matrix4d mul3x3(double r00,
 double r01,
 double r02,
 double r10,
 double r11,
 double r12,
 double r20,
 double r21,
 double r22,
 Matrix4d dest)

Multiply this matrix by the 3x3 matrix with the supplied elements expanded to a 4x4 matrix with all other matrix elements set to identity, and store the result in dest.

If M is this matrix and R the right matrix whose elements are supplied via the parameters, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

r00 - the m00 element of the right matrix

r01 - the m01 element of the right matrix

r02 - the m02 element of the right matrix

r10 - the m10 element of the right matrix

r11 - the m11 element of the right matrix

r12 - the m12 element of the right matrix

r20 - the m20 element of the right matrix

r21 - the m21 element of the right matrix

r22 - the m22 element of the right matrix

dest - the destination matrix, which will hold the result

Returns:

this

mulLocal

Matrix4d mulLocal(Matrix4dc left,
 Matrix4d dest)

Pre-multiply this matrix by the supplied left matrix and store the result in dest.

If M is this matrix and L the left matrix, then the new matrix will be L * M. So when transforming a vector v with the new matrix by using L * M * v, the transformation of this matrix will be applied first!

Parameters:

left - the left operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mulLocalAffine

Matrix4d mulLocalAffine(Matrix4dc left,
 Matrix4d dest)

Pre-multiply this matrix by the supplied left matrix, both of which are assumed to be affine, and store the result in dest.

This method assumes that this matrix and the given left matrix both represent an affine transformation (i.e. their last rows are equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrices only represent affine transformations, such as translation, rotation, scaling and shearing (in any combination).

This method will not modify either the last row of this or the last row of left.

If M is this matrix and L the left matrix, then the new matrix will be L * M. So when transforming a vector v with the new matrix by using L * M * v, the transformation of this matrix will be applied first!

Parameters:

left - the left operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(Matrix3x2dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(Matrix3x2fc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(Matrix4x3dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

The last row of the right matrix is assumed to be (0, 0, 0, 1).

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(Matrix4x3fc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix and store the result in dest.

The last row of the right matrix is assumed to be (0, 0, 0, 1).

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication

dest - the destination matrix, which will hold the result

Returns:

dest

mul

Matrix4d mul(Matrix4fc right,
 Matrix4d dest)

Multiply this matrix by the supplied parameter matrix and store the result in dest.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the multiplication

dest - will hold the result

Returns:

dest

mulPerspectiveAffine

Matrix4d mulPerspectiveAffine(Matrix4dc view,
 Matrix4d dest)

Multiply this symmetric perspective projection matrix by the supplied affine view matrix and store the result in dest.

If P is this matrix and V the view matrix, then the new matrix will be P * V. So when transforming a vector v with the new matrix by using P * V * v, the transformation of the view matrix will be applied first!

Parameters:

view - the affine matrix to multiply this symmetric perspective projection matrix by

dest - the destination matrix, which will hold the result

Returns:

dest

mulPerspectiveAffine

Matrix4d mulPerspectiveAffine(Matrix4x3dc view,
 Matrix4d dest)

Multiply this symmetric perspective projection matrix by the supplied view matrix and store the result in dest.

If P is this matrix and V the view matrix, then the new matrix will be P * V. So when transforming a vector v with the new matrix by using P * V * v, the transformation of the view matrix will be applied first!

Parameters:

view - the matrix to multiply this symmetric perspective projection matrix by

dest - the destination matrix, which will hold the result

Returns:

dest

mulAffineR

Matrix4d mulAffineR(Matrix4dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix, which is assumed to be affine, and store the result in dest.

This method assumes that the given right matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrix only represents affine transformations, such as translation, rotation, scaling and shearing (in any combination).

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))

dest - the destination matrix, which will hold the result

Returns:

dest

mulAffine

Matrix4d mulAffine(Matrix4dc right,
 Matrix4d dest)

Multiply this matrix by the supplied right matrix, both of which are assumed to be affine, and store the result in dest.

This method assumes that this matrix and the given right matrix both represent an affine transformation (i.e. their last rows are equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrices only represent affine transformations, such as translation, rotation, scaling and shearing (in any combination).

This method will not modify either the last row of this or the last row of right.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))

dest - the destination matrix, which will hold the result

Returns:

dest

mulTranslationAffine

Matrix4d mulTranslationAffine(Matrix4dc right,
 Matrix4d dest)

Multiply this matrix, which is assumed to only contain a translation, by the supplied right matrix, which is assumed to be affine, and store the result in dest.

This method assumes that this matrix only contains a translation, and that the given right matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)).

This method will not modify either the last row of this or the last row of right.

If M is this matrix and R the right matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the transformation of the right matrix will be applied first!

Parameters:

right - the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))

dest - the destination matrix, which will hold the result

Returns:

dest

mulOrthoAffine

Matrix4d mulOrthoAffine(Matrix4dc view,
 Matrix4d dest)

Multiply this orthographic projection matrix by the supplied affine view matrix and store the result in dest.

If M is this matrix and V the view matrix, then the new matrix will be M * V. So when transforming a vector v with the new matrix by using M * V * v, the transformation of the view matrix will be applied first!

Parameters:

view - the affine matrix which to multiply this with

dest - the destination matrix, which will hold the result

Returns:

dest

fma4x3

Matrix4d fma4x3(Matrix4dc other,
 double otherFactor,
 Matrix4d dest)

Component-wise add the upper 4x3 submatrices of this and other by first multiplying each component of other's 4x3 submatrix by otherFactor, adding that to this and storing the final result in dest.

The other components of dest will be set to the ones of this.

The matrices this and other will not be changed.

Parameters:

other - the other matrix

otherFactor - the factor to multiply each of the other matrix's 4x3 components

dest - will hold the result

Returns:

dest

add

Matrix4d add(Matrix4dc other,
 Matrix4d dest)

Component-wise add this and other and store the result in dest.

Parameters:

other - the other addend

dest - will hold the result

Returns:

dest

sub

Matrix4d sub(Matrix4dc subtrahend,
 Matrix4d dest)

Component-wise subtract subtrahend from this and store the result in dest.

Parameters:

subtrahend - the subtrahend

dest - will hold the result

Returns:

dest

mulComponentWise

Matrix4d mulComponentWise(Matrix4dc other,
 Matrix4d dest)

Component-wise multiply this by other and store the result in dest.

Parameters:

other - the other matrix

dest - will hold the result

Returns:

dest

add4x3

Matrix4d add4x3(Matrix4dc other,
 Matrix4d dest)

Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.

The other components of dest will be set to the ones of this.

Parameters:

other - the other addend

dest - will hold the result

Returns:

dest

add4x3

Matrix4d add4x3(Matrix4fc other,
 Matrix4d dest)

Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.

The other components of dest will be set to the ones of this.

Parameters:

other - the other addend

dest - will hold the result

Returns:

dest

sub4x3

Matrix4d sub4x3(Matrix4dc subtrahend,
 Matrix4d dest)

Component-wise subtract the upper 4x3 submatrices of subtrahend from this and store the result in dest.

The other components of dest will be set to the ones of this.

Parameters:

subtrahend - the subtrahend

dest - will hold the result

Returns:

dest

mul4x3ComponentWise

Matrix4d mul4x3ComponentWise(Matrix4dc other,
 Matrix4d dest)

Component-wise multiply the upper 4x3 submatrices of this by other and store the result in dest.

The other components of dest will be set to the ones of this.

Parameters:

other - the other matrix

dest - will hold the result

Returns:

dest

determinant

double determinant()

Return the determinant of this matrix.

If this matrix represents an affine transformation, such as translation, rotation, scaling and shearing, and thus its last row is equal to (0, 0, 0, 1), then determinantAffine() can be used instead of this method.

Returns:

the determinant

See Also:

• determinantAffine()

determinant3x3

double determinant3x3()

Return the determinant of the upper left 3x3 submatrix of this matrix.

Returns:

the determinant

determinantAffine

double determinantAffine()

Return the determinant of this matrix by assuming that it represents an affine transformation and thus its last row is equal to (0, 0, 0, 1).

Returns:

the determinant

invert

Matrix4d invert(Matrix4d dest)

Invert this matrix and store the result in dest.

If this matrix represents an affine transformation, such as translation, rotation, scaling and shearing, and thus its last row is equal to (0, 0, 0, 1), then invertAffine(Matrix4d) can be used instead of this method.

Parameters:

dest - will hold the result

Returns:

dest

See Also:

• invertAffine(Matrix4d)

invertPerspective

Matrix4d invertPerspective(Matrix4d dest)

If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation, then this method builds the inverse of this and stores it into the given dest.

This method can be used to quickly obtain the inverse of a perspective projection matrix when being obtained via perspective().

Parameters:

dest - will hold the inverse of this

Returns:

dest

See Also:

• perspective(double, double, double, double, Matrix4d)

invertFrustum

Matrix4d invertFrustum(Matrix4d dest)

If this is an arbitrary perspective projection matrix obtained via one of the frustum() methods, then this method builds the inverse of this and stores it into the given dest.

This method can be used to quickly obtain the inverse of a perspective projection matrix.

If this matrix represents a symmetric perspective frustum transformation, as obtained via perspective(), then invertPerspective(Matrix4d) should be used instead.

Parameters:

dest - will hold the inverse of this

Returns:

dest

See Also:

• frustum(double, double, double, double, double, double, Matrix4d)
• invertPerspective(Matrix4d)

invertOrtho

Matrix4d invertOrtho(Matrix4d dest)

Invert this orthographic projection matrix and store the result into the given dest.

This method can be used to quickly obtain the inverse of an orthographic projection matrix.

Parameters:

dest - will hold the inverse of this

Returns:

dest

invertPerspectiveView

Matrix4d invertPerspectiveView(Matrix4dc view,
 Matrix4d dest)

If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation and the given view matrix is affine and has unit scaling (for example by being obtained via lookAt()), then this method builds the inverse of this * view and stores it into the given dest.

This method can be used to quickly obtain the inverse of the combination of the view and projection matrices, when both were obtained via the common methods perspective() and lookAt() or other methods, that build affine matrices, such as translate and rotate(double, double, double, double, Matrix4d), except for scale().

For the special cases of the matrices this and view mentioned above, this method is equivalent to the following code:

 dest.set(this).mul(view).invert();
 

Parameters:

view - the view transformation (must be affine and have unit scaling)

dest - will hold the inverse of this * view

Returns:

dest

invertPerspectiveView

Matrix4d invertPerspectiveView(Matrix4x3dc view,
 Matrix4d dest)

If this is a perspective projection matrix obtained via one of the perspective() methods, that is, if this is a symmetrical perspective frustum transformation and the given view matrix has unit scaling, then this method builds the inverse of this * view and stores it into the given dest.

This method can be used to quickly obtain the inverse of the combination of the view and projection matrices, when both were obtained via the common methods perspective() and lookAt() or other methods, that build affine matrices, such as translate and rotate(double, double, double, double, Matrix4d), except for scale().

For the special cases of the matrices this and view mentioned above, this method is equivalent to the following code:

 dest.set(this).mul(view).invert();
 

Parameters:

view - the view transformation (must have unit scaling)

dest - will hold the inverse of this * view

Returns:

dest

invertAffine

Matrix4d invertAffine(Matrix4d dest)

Invert this matrix by assuming that it is an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and write the result into dest.

Parameters:

dest - will hold the result

Returns:

dest

transpose

Matrix4d transpose(Matrix4d dest)

Transpose this matrix and store the result into dest.

Parameters:

dest - will hold the result

Returns:

dest

transpose3x3

Matrix4d transpose3x3(Matrix4d dest)

Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.

All other matrix elements are left unchanged.

Parameters:

dest - will hold the result

Returns:

dest

transpose3x3

Matrix3d transpose3x3(Matrix3d dest)

Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

getTranslation

Vector3d getTranslation(Vector3d dest)

Get only the translation components (m30, m31, m32) of this matrix and store them in the given vector xyz.

Parameters:

dest - will hold the translation components of this matrix

Returns:

dest

getScale

Vector3d getScale(Vector3d dest)

Get the scaling factors of this matrix for the three base axes.

Parameters:

dest - will hold the scaling factors for x, y and z

Returns:

dest

get

Matrix4d get(Matrix4d dest)

Get the current values of this matrix and store them into dest.

Parameters:

dest - the destination matrix

Returns:

the passed in destination

get4x3

Matrix4x3d get4x3(Matrix4x3d dest)

Get the current values of the upper 4x3 submatrix of this matrix and store them into dest.

Parameters:

dest - the destination matrix

Returns:

the passed in destination

get3x3

Matrix3d get3x3(Matrix3d dest)

Get the current values of the upper left 3x3 submatrix of this matrix and store them into dest.

Parameters:

dest - the destination matrix

Returns:

the passed in destination

getUnnormalizedRotation

Quaternionf getUnnormalizedRotation(Quaternionf dest)

Get the current values of this matrix and store the represented rotation into the given Quaternionf.

This method assumes that the first three column vectors of the upper left 3x3 submatrix are not normalized and thus allows to ignore any additional scaling factor that is applied to the matrix.

Parameters:

dest - the destination Quaternionf

Returns:

the passed in destination

See Also:

• Quaternionf.setFromUnnormalized(Matrix4dc)

getNormalizedRotation

Quaternionf getNormalizedRotation(Quaternionf dest)

Get the current values of this matrix and store the represented rotation into the given Quaternionf.

This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.

Parameters:

dest - the destination Quaternionf

Returns:

the passed in destination

See Also:

• Quaternionf.setFromNormalized(Matrix4dc)

getUnnormalizedRotation

Quaterniond getUnnormalizedRotation(Quaterniond dest)

Get the current values of this matrix and store the represented rotation into the given Quaterniond.

This method assumes that the first three column vectors of the upper left 3x3 submatrix are not normalized and thus allows to ignore any additional scaling factor that is applied to the matrix.

Parameters:

dest - the destination Quaterniond

Returns:

the passed in destination

See Also:

• Quaterniond.setFromUnnormalized(Matrix4dc)

getNormalizedRotation

Quaterniond getNormalizedRotation(Quaterniond dest)

Get the current values of this matrix and store the represented rotation into the given Quaterniond.

This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.

Parameters:

dest - the destination Quaterniond

Returns:

the passed in destination

See Also:

• Quaterniond.setFromNormalized(Matrix4dc)

get

DoubleBuffer get(DoubleBuffer buffer)

Store this matrix in column-major order into the supplied DoubleBuffer at the current buffer position.

This method will not increment the position of the given DoubleBuffer.

In order to specify the offset into the DoubleBuffer at which the matrix is stored, use get(int, DoubleBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix in column-major order at its current position

Returns:

the passed in buffer

See Also:

• get(int, DoubleBuffer)

get

DoubleBuffer get(int index,
 DoubleBuffer buffer)

Store this matrix in column-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given DoubleBuffer.

Parameters:

index - the absolute position into the DoubleBuffer

buffer - will receive the values of this matrix in column-major order

Returns:

the passed in buffer

get

FloatBuffer get(FloatBuffer buffer)

Store this matrix in column-major order into the supplied FloatBuffer at the current buffer position.

This method will not increment the position of the given FloatBuffer.

In order to specify the offset into the FloatBuffer at which the matrix is stored, use get(int, FloatBuffer), taking the absolute position as parameter.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

Parameters:

buffer - will receive the values of this matrix in column-major order at its current position

Returns:

the passed in buffer

See Also:

• get(int, FloatBuffer)

get

FloatBuffer get(int index,
 FloatBuffer buffer)

Store this matrix in column-major order into the supplied FloatBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given FloatBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

Parameters:

index - the absolute position into the FloatBuffer

buffer - will receive the values of this matrix in column-major order

Returns:

the passed in buffer

get

ByteBuffer get(ByteBuffer buffer)

Store this matrix in column-major order into the supplied ByteBuffer at the current buffer position.

This method will not increment the position of the given ByteBuffer.

In order to specify the offset into the ByteBuffer at which the matrix is stored, use get(int, ByteBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix in column-major order at its current position

Returns:

the passed in buffer

See Also:

• get(int, ByteBuffer)

get

ByteBuffer get(int index,
 ByteBuffer buffer)

Store this matrix in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given ByteBuffer.

Parameters:

index - the absolute position into the ByteBuffer

buffer - will receive the values of this matrix in column-major order

Returns:

the passed in buffer

getToAddress

Matrix4dc getToAddress(long address)

Store this matrix in column-major order at the given off-heap address.

This method will throw an UnsupportedOperationException when JOML is used with `-Djoml.nounsafe`.

This method is unsafe as it can result in a crash of the JVM process when the specified address range does not belong to this process.

Parameters:

address - the off-heap address where to store this matrix

Returns:

this

getFloats

ByteBuffer getFloats(ByteBuffer buffer)

Store the elements of this matrix as float values in column-major order into the supplied ByteBuffer at the current buffer position.

This method will not increment the position of the given ByteBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given ByteBuffer.

In order to specify the offset into the ByteBuffer at which the matrix is stored, use getFloats(int, ByteBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the elements of this matrix as float values in column-major order at its current position

Returns:

the passed in buffer

See Also:

• getFloats(int, ByteBuffer)

getFloats

ByteBuffer getFloats(int index,
 ByteBuffer buffer)

Store the elements of this matrix as float values in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given ByteBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given ByteBuffer.

Parameters:

index - the absolute position into the ByteBuffer

buffer - will receive the elements of this matrix as float values in column-major order

Returns:

the passed in buffer

get

double[] get(double[] arr,
 int offset)

Store this matrix into the supplied double array in column-major order at the given offset.

Parameters:

arr - the array to write the matrix values into

offset - the offset into the array

Returns:

the passed in array

get

double[] get(double[] arr)

Store this matrix into the supplied double array in column-major order.

In order to specify an explicit offset into the array, use the method get(double[], int).

Parameters:

arr - the array to write the matrix values into

Returns:

the passed in array

See Also:

• get(double[], int)

get

float[] get(float[] arr,
 int offset)

Store the elements of this matrix as float values in column-major order into the supplied float array at the given offset.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given float array.

Parameters:

arr - the array to write the matrix values into

offset - the offset into the array

Returns:

the passed in array

get

float[] get(float[] arr)

Store the elements of this matrix as float values in column-major order into the supplied float array.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given float array.

In order to specify an explicit offset into the array, use the method get(float[], int).

Parameters:

arr - the array to write the matrix values into

Returns:

the passed in array

See Also:

• get(float[], int)

getTransposed

DoubleBuffer getTransposed(DoubleBuffer buffer)

Store this matrix in row-major order into the supplied DoubleBuffer at the current buffer position.

This method will not increment the position of the given DoubleBuffer.

In order to specify the offset into the DoubleBuffer at which the matrix is stored, use getTransposed(int, DoubleBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix in row-major order at its current position

Returns:

the passed in buffer

See Also:

• getTransposed(int, DoubleBuffer)

getTransposed

DoubleBuffer getTransposed(int index,
 DoubleBuffer buffer)

Store this matrix in row-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given DoubleBuffer.

Parameters:

index - the absolute position into the DoubleBuffer

buffer - will receive the values of this matrix in row-major order

Returns:

the passed in buffer

getTransposed

ByteBuffer getTransposed(ByteBuffer buffer)

Store this matrix in row-major order into the supplied ByteBuffer at the current buffer position.

This method will not increment the position of the given ByteBuffer.

In order to specify the offset into the ByteBuffer at which the matrix is stored, use getTransposed(int, ByteBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix in row-major order at its current position

Returns:

the passed in buffer

See Also:

• getTransposed(int, ByteBuffer)

getTransposed

ByteBuffer getTransposed(int index,
 ByteBuffer buffer)

Store this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given ByteBuffer.

Parameters:

index - the absolute position into the ByteBuffer

buffer - will receive the values of this matrix in row-major order

Returns:

the passed in buffer

getTransposed

FloatBuffer getTransposed(FloatBuffer buffer)

Store this matrix in row-major order into the supplied FloatBuffer at the current buffer position.

This method will not increment the position of the given FloatBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

In order to specify the offset into the FloatBuffer at which the matrix is stored, use getTransposed(int, FloatBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix in row-major order at its current position

Returns:

the passed in buffer

See Also:

• getTransposed(int, FloatBuffer)

getTransposed

FloatBuffer getTransposed(int index,
 FloatBuffer buffer)

Store this matrix in row-major order into the supplied FloatBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given FloatBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

Parameters:

index - the absolute position into the FloatBuffer

buffer - will receive the values of this matrix in row-major order

Returns:

the passed in buffer

getTransposedFloats

ByteBuffer getTransposedFloats(ByteBuffer buffer)

Store this matrix as float values in row-major order into the supplied ByteBuffer at the current buffer position.

This method will not increment the position of the given ByteBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

In order to specify the offset into the ByteBuffer at which the matrix is stored, use getTransposedFloats(int, ByteBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of this matrix as float values in row-major order at its current position

Returns:

the passed in buffer

See Also:

• getTransposedFloats(int, ByteBuffer)

getTransposedFloats

ByteBuffer getTransposedFloats(int index,
 ByteBuffer buffer)

Store this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given ByteBuffer.

Please note that due to this matrix storing double values those values will potentially lose precision when they are converted to float values before being put into the given FloatBuffer.

Parameters:

index - the absolute position into the ByteBuffer

buffer - will receive the values of this matrix as float values in row-major order

Returns:

the passed in buffer

get4x3Transposed

DoubleBuffer get4x3Transposed(DoubleBuffer buffer)

Store the upper 4x3 submatrix of this matrix in row-major order into the supplied DoubleBuffer at the current buffer position.

This method will not increment the position of the given DoubleBuffer.

In order to specify the offset into the DoubleBuffer at which the matrix is stored, use get4x3Transposed(int, DoubleBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of the upper 4x3 submatrix in row-major order at its current position

Returns:

the passed in buffer

See Also:

• get4x3Transposed(int, DoubleBuffer)

get4x3Transposed

DoubleBuffer get4x3Transposed(int index,
 DoubleBuffer buffer)

Store the upper 4x3 submatrix of this matrix in row-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given DoubleBuffer.

Parameters:

index - the absolute position into the DoubleBuffer

buffer - will receive the values of the upper 4x3 submatrix in row-major order

Returns:

the passed in buffer

get4x3Transposed

ByteBuffer get4x3Transposed(ByteBuffer buffer)

Store the upper 4x3 submatrix of this matrix in row-major order into the supplied ByteBuffer at the current buffer position.

This method will not increment the position of the given ByteBuffer.

In order to specify the offset into the ByteBuffer at which the matrix is stored, use get4x3Transposed(int, ByteBuffer), taking the absolute position as parameter.

Parameters:

buffer - will receive the values of the upper 4x3 submatrix in row-major order at its current position

Returns:

the passed in buffer

See Also:

• get4x3Transposed(int, ByteBuffer)

get4x3Transposed

ByteBuffer get4x3Transposed(int index,
 ByteBuffer buffer)

Store the upper 4x3 submatrix of this matrix in row-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.

This method will not increment the position of the given ByteBuffer.

Parameters:

index - the absolute position into the ByteBuffer

buffer - will receive the values of the upper 4x3 submatrix in row-major order

Returns:

the passed in buffer

transform

Vector4d transform(Vector4d v)

Transform/multiply the given vector by this matrix and store the result in that vector.

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• Vector4d.mul(Matrix4dc)

transform

Vector4d transform(Vector4dc v,
 Vector4d dest)

Transform/multiply the given vector by this matrix and store the result in dest.

Parameters:

v - the vector to transform

dest - will contain the result

Returns:

dest

See Also:

• Vector4d.mul(Matrix4dc, Vector4d)

transform

Vector4d transform(double x,
 double y,
 double z,
 double w,
 Vector4d dest)

Transform/multiply the vector (x, y, z, w) by this matrix and store the result in dest.

Parameters:

x - the x coordinate of the vector to transform

y - the y coordinate of the vector to transform

z - the z coordinate of the vector to transform

w - the w coordinate of the vector to transform

dest - will contain the result

Returns:

dest

transformTranspose

Vector4d transformTranspose(Vector4d v)

Transform/multiply the given vector by the transpose of this matrix and store the result in that vector.

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• Vector4d.mulTranspose(Matrix4dc)

transformTranspose

Vector4d transformTranspose(Vector4dc v,
 Vector4d dest)

Transform/multiply the given vector by the transpose of this matrix and store the result in dest.

Parameters:

v - the vector to transform and to hold the final result

dest - will contain the result

Returns:

dest

See Also:

• Vector4d.mulTranspose(Matrix4dc)

transformTranspose

Vector4d transformTranspose(double x,
 double y,
 double z,
 double w,
 Vector4d dest)

Transform/multiply the vector (x, y, z, w) by the transpose of this matrix and store the result in dest.

Parameters:

x - the x coordinate of the vector to transform

y - the y coordinate of the vector to transform

z - the z coordinate of the vector to transform

w - the w coordinate of the vector to transform

dest - will contain the result

Returns:

dest

transformProject

Vector4d transformProject(Vector4d v)

Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• Vector4d.mulProject(Matrix4dc)

transformProject

Vector4d transformProject(Vector4dc v,
 Vector4d dest)

Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.

Parameters:

v - the vector to transform

dest - will contain the result

Returns:

dest

See Also:

• Vector4d.mulProject(Matrix4dc, Vector4d)

transformProject

Vector3d transformProject(Vector4dc v,
 Vector3d dest)

Transform/multiply the given vector by this matrix, perform perspective divide and store the x, y and z components of the result in dest.

Parameters:

v - the vector to transform

dest - will contain the result

Returns:

dest

See Also:

• Vector3d.mulProject(Matrix4dc, Vector3d)

transformProject

Vector4d transformProject(double x,
 double y,
 double z,
 double w,
 Vector4d dest)

Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store the result in dest.

Parameters:

x - the x coordinate of the direction to transform

y - the y coordinate of the direction to transform

z - the z coordinate of the direction to transform

w - the w coordinate of the direction to transform

dest - will contain the result

Returns:

dest

transformProject

Vector3d transformProject(Vector3d v)

Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.

This method uses w=1.0 as the fourth vector component.

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• Vector3d.mulProject(Matrix4dc)

transformProject

Vector3d transformProject(Vector3dc v,
 Vector3d dest)

Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.

This method uses w=1.0 as the fourth vector component.

Parameters:

v - the vector to transform

dest - will contain the result

Returns:

dest

See Also:

• Vector3d.mulProject(Matrix4dc, Vector3d)

transformProject

Vector3d transformProject(double x,
 double y,
 double z,
 Vector3d dest)

Transform/multiply the vector (x, y, z) by this matrix, perform perspective divide and store the result in dest.

This method uses w=1.0 as the fourth vector component.

Parameters:

x - the x coordinate of the vector to transform

y - the y coordinate of the vector to transform

z - the z coordinate of the vector to transform

dest - will contain the result

Returns:

dest

transformProject

Vector3d transformProject(double x,
 double y,
 double z,
 double w,
 Vector3d dest)

Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store (x, y, z) of the result in dest.

Parameters:

x - the x coordinate of the vector to transform

y - the y coordinate of the vector to transform

z - the z coordinate of the vector to transform

w - the w coordinate of the vector to transform

dest - will contain the (x, y, z) components of the result

Returns:

dest

transformPosition

Vector3d transformPosition(Vector3d v)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by this matrix and store the result in that vector.

The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it will represent a position/location in 3D-space rather than a direction. This method is therefore not suited for perspective projection transformations as it will not save the w component of the transformed vector. For perspective projection use transform(Vector4d) or transformProject(Vector3d) when perspective divide should be applied, too.

In order to store the result in another vector, use transformPosition(Vector3dc, Vector3d).

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• transformPosition(Vector3dc, Vector3d)
• transform(Vector4d)
• transformProject(Vector3d)

transformPosition

Vector3d transformPosition(Vector3dc v,
 Vector3d dest)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it will represent a position/location in 3D-space rather than a direction. This method is therefore not suited for perspective projection transformations as it will not save the w component of the transformed vector. For perspective projection use transform(Vector4dc, Vector4d) or transformProject(Vector3dc, Vector3d) when perspective divide should be applied, too.

In order to store the result in the same vector, use transformPosition(Vector3d).

Parameters:

v - the vector to transform

dest - will hold the result

Returns:

dest

See Also:

• transformPosition(Vector3d)
• transform(Vector4dc, Vector4d)
• transformProject(Vector3dc, Vector3d)

transformPosition

Vector3d transformPosition(double x,
 double y,
 double z,
 Vector3d dest)

Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=1, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it will represent a position/location in 3D-space rather than a direction. This method is therefore not suited for perspective projection transformations as it will not save the w component of the transformed vector. For perspective projection use transform(double, double, double, double, Vector4d) or transformProject(double, double, double, Vector3d) when perspective divide should be applied, too.

Parameters:

x - the x coordinate of the position

y - the y coordinate of the position

z - the z coordinate of the position

dest - will hold the result

Returns:

dest

See Also:

• transform(double, double, double, double, Vector4d)
• transformProject(double, double, double, Vector3d)

transformDirection

Vector3d transformDirection(Vector3d v)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

In order to store the result in another vector, use transformDirection(Vector3dc, Vector3d).

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

transformDirection

Vector3d transformDirection(Vector3dc v,
 Vector3d dest)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

In order to store the result in the same vector, use transformDirection(Vector3d).

Parameters:

v - the vector to transform and to hold the final result

dest - will hold the result

Returns:

dest

transformDirection

Vector3f transformDirection(Vector3f v)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

In order to store the result in another vector, use transformDirection(Vector3fc, Vector3f).

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

transformDirection

Vector3f transformDirection(Vector3fc v,
 Vector3f dest)

Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

In order to store the result in the same vector, use transformDirection(Vector3f).

Parameters:

v - the vector to transform and to hold the final result

dest - will hold the result

Returns:

dest

transformDirection

Vector3d transformDirection(double x,
 double y,
 double z,
 Vector3d dest)

Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=0, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

Parameters:

x - the x coordinate of the direction to transform

y - the y coordinate of the direction to transform

z - the z coordinate of the direction to transform

dest - will hold the result

Returns:

dest

transformDirection

Vector3f transformDirection(double x,
 double y,
 double z,
 Vector3f dest)

Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=0, by this matrix and store the result in dest.

The given 3D-vector is treated as a 4D-vector with its w-component being 0.0, so it will represent a direction in 3D-space rather than a position. This method will therefore not take the translation part of the matrix into account.

Parameters:

x - the x coordinate of the direction to transform

y - the y coordinate of the direction to transform

z - the z coordinate of the direction to transform

dest - will hold the result

Returns:

dest

transformAffine

Vector4d transformAffine(Vector4d v)

Transform/multiply the given 4D-vector by assuming that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)).

In order to store the result in another vector, use transformAffine(Vector4dc, Vector4d).

Parameters:

v - the vector to transform and to hold the final result

Returns:

v

See Also:

• transformAffine(Vector4dc, Vector4d)

transformAffine

Vector4d transformAffine(Vector4dc v,
 Vector4d dest)

Transform/multiply the given 4D-vector by assuming that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and store the result in dest.

In order to store the result in the same vector, use transformAffine(Vector4d).

Parameters:

v - the vector to transform and to hold the final result

dest - will hold the result

Returns:

dest

See Also:

• transformAffine(Vector4d)

transformAffine

Vector4d transformAffine(double x,
 double y,
 double z,
 double w,
 Vector4d dest)

Transform/multiply the 4D-vector (x, y, z, w) by assuming that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and store the result in dest.

Parameters:

x - the x coordinate of the direction to transform

y - the y coordinate of the direction to transform

z - the z coordinate of the direction to transform

w - the w coordinate of the direction to transform

dest - will hold the result

Returns:

dest

scale

Matrix4d scale(Vector3dc xyz,
 Matrix4d dest)

Apply scaling to this matrix by scaling the base axes by the given xyz.x, xyz.y and xyz.z factors, respectively and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v , the scaling will be applied first!

Parameters:

xyz - the factors of the x, y and z component, respectively

dest - will hold the result

Returns:

dest

scale

Matrix4d scale(double x,
 double y,
 double z,
 Matrix4d dest)

Apply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v , the scaling will be applied first!

Parameters:

x - the factor of the x component

y - the factor of the y component

z - the factor of the z component

dest - will hold the result

Returns:

dest

scale

Matrix4d scale(double xyz,
 Matrix4d dest)

Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v , the scaling will be applied first!

Parameters:

xyz - the factor for all components

dest - will hold the result

Returns:

dest

See Also:

• scale(double, double, double, Matrix4d)

scaleXY

Matrix4d scaleXY(double x,
 double y,
 Matrix4d dest)

Apply scaling to this matrix by by scaling the X axis by x and the Y axis by y and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the scaling will be applied first!

Parameters:

x - the factor of the x component

y - the factor of the y component

dest - will hold the result

Returns:

dest

scaleAround

Matrix4d scaleAround(double sx,
 double sy,
 double sz,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Apply scaling to this matrix by scaling the base axes by the given sx, sy and sz factors while using (ox, oy, oz) as the scaling origin, and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v , the scaling will be applied first!

This method is equivalent to calling: translate(ox, oy, oz, dest).scale(sx, sy, sz).translate(-ox, -oy, -oz)

Parameters:

sx - the scaling factor of the x component

sy - the scaling factor of the y component

sz - the scaling factor of the z component

ox - the x coordinate of the scaling origin

oy - the y coordinate of the scaling origin

oz - the z coordinate of the scaling origin

dest - will hold the result

Returns:

dest

scaleAround

Matrix4d scaleAround(double factor,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Apply scaling to this matrix by scaling all three base axes by the given factor while using (ox, oy, oz) as the scaling origin, and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the scaling will be applied first!

This method is equivalent to calling: translate(ox, oy, oz, dest).scale(factor).translate(-ox, -oy, -oz)

Parameters:

factor - the scaling factor for all three axes

ox - the x coordinate of the scaling origin

oy - the y coordinate of the scaling origin

oz - the z coordinate of the scaling origin

dest - will hold the result

Returns:

this

scaleLocal

Matrix4d scaleLocal(double xyz,
 Matrix4d dest)

Pre-multiply scaling to this matrix by scaling all base axes by the given xyz factor, and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be S * M. So when transforming a vector v with the new matrix by using S * M * v , the scaling will be applied last!

Parameters:

xyz - the factor to scale all three base axes by

dest - will hold the result

Returns:

dest

scaleLocal

Matrix4d scaleLocal(double x,
 double y,
 double z,
 Matrix4d dest)

Pre-multiply scaling to this matrix by scaling the base axes by the given x, y and z factors and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be S * M. So when transforming a vector v with the new matrix by using S * M * v , the scaling will be applied last!

Parameters:

x - the factor of the x component

y - the factor of the y component

z - the factor of the z component

dest - will hold the result

Returns:

dest

scaleAroundLocal

Matrix4d scaleAroundLocal(double sx,
 double sy,
 double sz,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Pre-multiply scaling to this matrix by scaling the base axes by the given sx, sy and sz factors while using the given (ox, oy, oz) as the scaling origin, and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be S * M. So when transforming a vector v with the new matrix by using S * M * v , the scaling will be applied last!

This method is equivalent to calling: new Matrix4d().translate(ox, oy, oz).scale(sx, sy, sz).translate(-ox, -oy, -oz).mul(this, dest)

Parameters:

sx - the scaling factor of the x component

sy - the scaling factor of the y component

sz - the scaling factor of the z component

ox - the x coordinate of the scaling origin

oy - the y coordinate of the scaling origin

oz - the z coordinate of the scaling origin

dest - will hold the result

Returns:

dest

scaleAroundLocal

Matrix4d scaleAroundLocal(double factor,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Pre-multiply scaling to this matrix by scaling all three base axes by the given factor while using (ox, oy, oz) as the scaling origin, and store the result in dest.

If M is this matrix and S the scaling matrix, then the new matrix will be S * M. So when transforming a vector v with the new matrix by using S * M * v, the scaling will be applied last!

This method is equivalent to calling: new Matrix4d().translate(ox, oy, oz).scale(factor).translate(-ox, -oy, -oz).mul(this, dest)

Parameters:

factor - the scaling factor for all three axes

ox - the x coordinate of the scaling origin

oy - the y coordinate of the scaling origin

oz - the z coordinate of the scaling origin

dest - will hold the result

Returns:

this

rotate

Matrix4d rotate(double ang,
 double x,
 double y,
 double z,
 Matrix4d dest)

Apply rotation to this matrix by rotating the given amount of radians about the given axis specified as x, y and z components and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v , the rotation will be applied first!

Parameters:

ang - the angle is in radians

x - the x component of the axis

y - the y component of the axis

z - the z component of the axis

dest - will hold the result

Returns:

dest

rotateTranslation

Matrix4d rotateTranslation(double ang,
 double x,
 double y,
 double z,
 Matrix4d dest)

Apply rotation to this matrix, which is assumed to only contain a translation, by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.

This method assumes this to only contain a translation.

The axis described by the three components needs to be a unit vector.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

x - the x component of the axis

y - the y component of the axis

z - the z component of the axis

dest - will hold the result

Returns:

dest

rotateAffine

Matrix4d rotateAffine(double ang,
 double x,
 double y,
 double z,
 Matrix4d dest)

Apply rotation to this affine matrix by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.

This method assumes this to be affine.

The axis described by the three components needs to be a unit vector.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

x - the x component of the axis

y - the y component of the axis

z - the z component of the axis

dest - will hold the result

Returns:

dest

rotateAroundAffine

Matrix4d rotateAroundAffine(Quaterniondc quat,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this affine matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

This method is only applicable if this is an affine matrix.

This method is equivalent to calling: translate(ox, oy, oz, dest).rotate(quat).translate(-ox, -oy, -oz)

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

ox - the x coordinate of the rotation origin

oy - the y coordinate of the rotation origin

oz - the z coordinate of the rotation origin

dest - will hold the result

Returns:

dest

rotateAround

Matrix4d rotateAround(Quaterniondc quat,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

This method is equivalent to calling: translate(ox, oy, oz, dest).rotate(quat).translate(-ox, -oy, -oz)

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

ox - the x coordinate of the rotation origin

oy - the y coordinate of the rotation origin

oz - the z coordinate of the rotation origin

dest - will hold the result

Returns:

dest

rotateLocal

Matrix4d rotateLocal(double ang,
 double x,
 double y,
 double z,
 Matrix4d dest)

Pre-multiply a rotation to this matrix by rotating the given amount of radians about the specified (x, y, z) axis and store the result in dest.

The axis described by the three components needs to be a unit vector.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be R * M. So when transforming a vector v with the new matrix by using R * M * v, the rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

x - the x component of the axis

y - the y component of the axis

z - the z component of the axis

dest - will hold the result

Returns:

dest

rotateLocalX

Matrix4d rotateLocalX(double ang,
 Matrix4d dest)

Pre-multiply a rotation around the X axis to this matrix by rotating the given amount of radians about the X axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be R * M. So when transforming a vector v with the new matrix by using R * M * v, the rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians to rotate about the X axis

dest - will hold the result

Returns:

dest

rotateLocalY

Matrix4d rotateLocalY(double ang,
 Matrix4d dest)

Pre-multiply a rotation around the Y axis to this matrix by rotating the given amount of radians about the Y axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be R * M. So when transforming a vector v with the new matrix by using R * M * v, the rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians to rotate about the Y axis

dest - will hold the result

Returns:

dest

rotateLocalZ

Matrix4d rotateLocalZ(double ang,
 Matrix4d dest)

Pre-multiply a rotation around the Z axis to this matrix by rotating the given amount of radians about the Z axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be R * M. So when transforming a vector v with the new matrix by using R * M * v, the rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians to rotate about the Z axis

dest - will hold the result

Returns:

dest

rotateAroundLocal

Matrix4d rotateAroundLocal(Quaterniondc quat,
 double ox,
 double oy,
 double oz,
 Matrix4d dest)

Pre-multiply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix while using (ox, oy, oz) as the rotation origin, and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be Q * M. So when transforming a vector v with the new matrix by using Q * M * v, the quaternion rotation will be applied last!

This method is equivalent to calling: translateLocal(-ox, -oy, -oz, dest).rotateLocal(quat).translateLocal(ox, oy, oz)

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

ox - the x coordinate of the rotation origin

oy - the y coordinate of the rotation origin

oz - the z coordinate of the rotation origin

dest - will hold the result

Returns:

dest

translate

Matrix4d translate(Vector3dc offset,
 Matrix4d dest)

Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be M * T. So when transforming a vector v with the new matrix by using M * T * v, the translation will be applied first!

Parameters:

offset - the number of units in x, y and z by which to translate

dest - will hold the result

Returns:

dest

translate

Matrix4d translate(Vector3fc offset,
 Matrix4d dest)

Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be M * T. So when transforming a vector v with the new matrix by using M * T * v, the translation will be applied first!

Parameters:

offset - the number of units in x, y and z by which to translate

dest - will hold the result

Returns:

dest

translate

Matrix4d translate(double x,
 double y,
 double z,
 Matrix4d dest)

Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be M * T. So when transforming a vector v with the new matrix by using M * T * v, the translation will be applied first!

Parameters:

x - the offset to translate in x

y - the offset to translate in y

z - the offset to translate in z

dest - will hold the result

Returns:

dest

translateLocal

Matrix4d translateLocal(Vector3fc offset,
 Matrix4d dest)

Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be T * M. So when transforming a vector v with the new matrix by using T * M * v, the translation will be applied last!

Parameters:

offset - the number of units in x, y and z by which to translate

dest - will hold the result

Returns:

dest

translateLocal

Matrix4d translateLocal(Vector3dc offset,
 Matrix4d dest)

Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be T * M. So when transforming a vector v with the new matrix by using T * M * v, the translation will be applied last!

Parameters:

offset - the number of units in x, y and z by which to translate

dest - will hold the result

Returns:

dest

translateLocal

Matrix4d translateLocal(double x,
 double y,
 double z,
 Matrix4d dest)

Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in dest.

If M is this matrix and T the translation matrix, then the new matrix will be T * M. So when transforming a vector v with the new matrix by using T * M * v, the translation will be applied last!

Parameters:

x - the offset to translate in x

y - the offset to translate in y

z - the offset to translate in z

dest - will hold the result

Returns:

dest

rotateX

Matrix4d rotateX(double ang,
 Matrix4d dest)

Apply rotation about the X axis to this matrix by rotating the given amount of radians and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

dest - will hold the result

Returns:

dest

rotateY

Matrix4d rotateY(double ang,
 Matrix4d dest)

Apply rotation about the Y axis to this matrix by rotating the given amount of radians and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

dest - will hold the result

Returns:

dest

rotateZ

Matrix4d rotateZ(double ang,
 Matrix4d dest)

Apply rotation about the Z axis to this matrix by rotating the given amount of radians and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

ang - the angle in radians

dest - will hold the result

Returns:

dest

rotateTowardsXY

Matrix4d rotateTowardsXY(double dirX,
 double dirY,
 Matrix4d dest)

Apply rotation about the Z axis to align the local +X towards (dirX, dirY) and store the result in dest.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

The vector (dirX, dirY) must be a unit vector.

Parameters:

dirX - the x component of the normalized direction

dirY - the y component of the normalized direction

dest - will hold the result

Returns:

this

rotateXYZ

Matrix4d rotateXYZ(double angleX,
 double angleY,
 double angleZ,
 Matrix4d dest)

Apply rotation of angleX radians about the X axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

This method is equivalent to calling: rotateX(angleX, dest).rotateY(angleY).rotateZ(angleZ)

Parameters:

angleX - the angle to rotate about X

angleY - the angle to rotate about Y

angleZ - the angle to rotate about Z

dest - will hold the result

Returns:

dest

rotateAffineXYZ

Matrix4d rotateAffineXYZ(double angleX,
 double angleY,
 double angleZ,
 Matrix4d dest)

Apply rotation of angleX radians about the X axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

This method assumes that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrix only represents affine transformations, such as translation, rotation, scaling and shearing (in any combination).

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Parameters:

angleX - the angle to rotate about X

angleY - the angle to rotate about Y

angleZ - the angle to rotate about Z

dest - will hold the result

Returns:

dest

rotateZYX

Matrix4d rotateZYX(double angleZ,
 double angleY,
 double angleX,
 Matrix4d dest)

Apply rotation of angleZ radians about the Z axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleX radians about the X axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

This method is equivalent to calling: rotateZ(angleZ, dest).rotateY(angleY).rotateX(angleX)

Parameters:

angleZ - the angle to rotate about Z

angleY - the angle to rotate about Y

angleX - the angle to rotate about X

dest - will hold the result

Returns:

dest

rotateAffineZYX

Matrix4d rotateAffineZYX(double angleZ,
 double angleY,
 double angleX,
 Matrix4d dest)

Apply rotation of angleZ radians about the Z axis, followed by a rotation of angleY radians about the Y axis and followed by a rotation of angleX radians about the X axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

This method assumes that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrix only represents affine transformations, such as translation, rotation, scaling and shearing (in any combination).

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Parameters:

angleZ - the angle to rotate about Z

angleY - the angle to rotate about Y

angleX - the angle to rotate about X

dest - will hold the result

Returns:

dest

rotateYXZ

Matrix4d rotateYXZ(double angleY,
 double angleX,
 double angleZ,
 Matrix4d dest)

Apply rotation of angleY radians about the Y axis, followed by a rotation of angleX radians about the X axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

This method is equivalent to calling: rotateY(angleY, dest).rotateX(angleX).rotateZ(angleZ)

Parameters:

angleY - the angle to rotate about Y

angleX - the angle to rotate about X

angleZ - the angle to rotate about Z

dest - will hold the result

Returns:

dest

rotateAffineYXZ

Matrix4d rotateAffineYXZ(double angleY,
 double angleX,
 double angleZ,
 Matrix4d dest)

Apply rotation of angleY radians about the Y axis, followed by a rotation of angleX radians about the X axis and followed by a rotation of angleZ radians about the Z axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

This method assumes that this matrix represents an affine transformation (i.e. its last row is equal to (0, 0, 0, 1)) and can be used to speed up matrix multiplication if the matrix only represents affine transformations, such as translation, rotation, scaling and shearing (in any combination).

If M is this matrix and R the rotation matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the rotation will be applied first!

Parameters:

angleY - the angle to rotate about Y

angleX - the angle to rotate about X

angleZ - the angle to rotate about Z

dest - will hold the result

Returns:

dest

rotate

Matrix4d rotate(Quaterniondc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

dest - will hold the result

Returns:

dest

rotate

Matrix4d rotate(Quaternionfc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaternionfc

dest - will hold the result

Returns:

dest

rotateAffine

Matrix4d rotateAffine(Quaterniondc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this affine matrix and store the result in dest.

This method assumes this to be affine.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

dest - will hold the result

Returns:

dest

rotateTranslation

Matrix4d rotateTranslation(Quaterniondc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix, which is assumed to only contain a translation, and store the result in dest.

This method assumes this to only contain a translation.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

dest - will hold the result

Returns:

dest

rotateTranslation

Matrix4d rotateTranslation(Quaternionfc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix, which is assumed to only contain a translation, and store the result in dest.

This method assumes this to only contain a translation.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaternionfc

dest - will hold the result

Returns:

dest

rotateLocal

Matrix4d rotateLocal(Quaterniondc quat,
 Matrix4d dest)

Pre-multiply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be Q * M. So when transforming a vector v with the new matrix by using Q * M * v, the quaternion rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaterniondc

dest - will hold the result

Returns:

dest

rotateAffine

Matrix4d rotateAffine(Quaternionfc quat,
 Matrix4d dest)

Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this affine matrix and store the result in dest.

This method assumes this to be affine.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be M * Q. So when transforming a vector v with the new matrix by using M * Q * v, the quaternion rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaternionfc

dest - will hold the result

Returns:

dest

rotateLocal

Matrix4d rotateLocal(Quaternionfc quat,
 Matrix4d dest)

Pre-multiply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and Q the rotation matrix obtained from the given quaternion, then the new matrix will be Q * M. So when transforming a vector v with the new matrix by using Q * M * v, the quaternion rotation will be applied last!

Reference: http://en.wikipedia.org

Parameters:

quat - the Quaternionfc

dest - will hold the result

Returns:

dest

rotate

Matrix4d rotate(AxisAngle4f axisAngle,
 Matrix4d dest)

Apply a rotation transformation, rotating about the given AxisAngle4f and store the result in dest.

The axis described by the axis vector needs to be a unit vector.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and A the rotation matrix obtained from the given AxisAngle4f, then the new matrix will be M * A. So when transforming a vector v with the new matrix by using M * A * v, the AxisAngle4f rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

axisAngle - the AxisAngle4f (needs to be normalized)

dest - will hold the result

Returns:

dest

See Also:

• rotate(double, double, double, double, Matrix4d)

rotate

Matrix4d rotate(AxisAngle4d axisAngle,
 Matrix4d dest)

Apply a rotation transformation, rotating about the given AxisAngle4d and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and A the rotation matrix obtained from the given AxisAngle4d, then the new matrix will be M * A. So when transforming a vector v with the new matrix by using M * A * v, the AxisAngle4d rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

axisAngle - the AxisAngle4d (needs to be normalized)

dest - will hold the result

Returns:

dest

See Also:

• rotate(double, double, double, double, Matrix4d)

rotate

Matrix4d rotate(double angle,
 Vector3dc axis,
 Matrix4d dest)

Apply a rotation transformation, rotating the given radians about the specified axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and A the rotation matrix obtained from the given angle and axis, then the new matrix will be M * A. So when transforming a vector v with the new matrix by using M * A * v, the axis-angle rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

angle - the angle in radians

axis - the rotation axis (needs to be normalized)

dest - will hold the result

Returns:

dest

See Also:

• rotate(double, double, double, double, Matrix4d)

rotate

Matrix4d rotate(double angle,
 Vector3fc axis,
 Matrix4d dest)

Apply a rotation transformation, rotating the given radians about the specified axis and store the result in dest.

When used with a right-handed coordinate system, the produced rotation will rotate a vector counter-clockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a left-handed coordinate system, the rotation is clockwise.

If M is this matrix and A the rotation matrix obtained from the given angle and axis, then the new matrix will be M * A. So when transforming a vector v with the new matrix by using M * A * v, the axis-angle rotation will be applied first!

Reference: http://en.wikipedia.org

Parameters:

angle - the angle in radians

axis - the rotation axis (needs to be normalized)

dest - will hold the result

Returns:

dest

See Also:

• rotate(double, double, double, double, Matrix4d)

getRow

Vector4d getRow(int row,
 Vector4d dest)
         throws IndexOutOfBoundsException

Get the row at the given row index, starting with 0.

Parameters:

row - the row index in [0..3]

dest - will hold the row components

Returns:

the passed in destination

Throws:

IndexOutOfBoundsException - if row is not in [0..3]

getRow

Vector3d getRow(int row,
 Vector3d dest)
         throws IndexOutOfBoundsException

Get the first three components of the row at the given row index, starting with 0.

Parameters:

row - the row index in [0..3]

dest - will hold the first three row components

Returns:

the passed in destination

Throws:

IndexOutOfBoundsException - if row is not in [0..3]

getColumn

Vector4d getColumn(int column,
 Vector4d dest)
            throws IndexOutOfBoundsException

Get the column at the given column index, starting with 0.

Parameters:

column - the column index in [0..3]

dest - will hold the column components

Returns:

the passed in destination

Throws:

IndexOutOfBoundsException - if column is not in [0..3]

getColumn

Vector3d getColumn(int column,
 Vector3d dest)
            throws IndexOutOfBoundsException

Get the first three components of the column at the given column index, starting with 0.

Parameters:

column - the column index in [0..3]

dest - will hold the first three column components

Returns:

the passed in destination

Throws:

IndexOutOfBoundsException - if column is not in [0..3]

get

double get(int column,
 int row)

Get the matrix element value at the given column and row.

Parameters:

column - the colum index in [0..3]

row - the row index in [0..3]

Returns:

the element value

getRowColumn

double getRowColumn(int row,
 int column)

Get the matrix element value at the given row and column.

Parameters:

row - the row index in [0..3]

column - the colum index in [0..3]

Returns:

the element value

normal

Matrix4d normal(Matrix4d dest)

Compute a normal matrix from the upper left 3x3 submatrix of this and store it into the upper left 3x3 submatrix of dest. All other values of dest will be set to identity.

The normal matrix of m is the transpose of the inverse of m.

Parameters:

dest - will hold the result

Returns:

dest

normal

Matrix3d normal(Matrix3d dest)

Compute a normal matrix from the upper left 3x3 submatrix of this and store it into dest.

The normal matrix of m is the transpose of the inverse of m.

Parameters:

dest - will hold the result

Returns:

dest

See Also:

• get3x3(Matrix3d)

cofactor3x3

Matrix3d cofactor3x3(Matrix3d dest)

Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest.

The cofactor matrix can be used instead of normal(Matrix3d) to transform normals when the orientation of the normals with respect to the surface should be preserved.

Parameters:

dest - will hold the result

Returns:

dest

cofactor3x3

Matrix4d cofactor3x3(Matrix4d dest)

Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest. All other values of dest will be set to identity.

The cofactor matrix can be used instead of normal(Matrix4d) to transform normals when the orientation of the normals with respect to the surface should be preserved.

Parameters:

dest - will hold the result

Returns:

dest

normalize3x3

Matrix4d normalize3x3(Matrix4d dest)

Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.

The resulting matrix will map unit vectors to unit vectors, though a pair of orthogonal input unit vectors need not be mapped to a pair of orthogonal output vectors if the original matrix was not orthogonal itself (i.e. had skewing).

Parameters:

dest - will hold the result

Returns:

dest

normalize3x3

Matrix3d normalize3x3(Matrix3d dest)

Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.

The resulting matrix will map unit vectors to unit vectors, though a pair of orthogonal input unit vectors need not be mapped to a pair of orthogonal output vectors if the original matrix was not orthogonal itself (i.e. had skewing).

Parameters:

dest - will hold the result

Returns:

dest

unproject

Vector4d unproject(double winX,
 double winY,
 double winZ,
 int[] viewport,
 Vector4d dest)

Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInv() can be invoked on it.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

winZ - the z-coordinate, which is the depth value in [0..1]

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unprojectInv(double, double, double, int[], Vector4d)
• invert(Matrix4d)

unproject

Vector3d unproject(double winX,
 double winY,
 double winZ,
 int[] viewport,
 Vector3d dest)

Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInv() can be invoked on it.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

winZ - the z-coordinate, which is the depth value in [0..1]

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unprojectInv(double, double, double, int[], Vector3d)
• invert(Matrix4d)

unproject

Vector4d unproject(Vector3dc winCoords,
 int[] viewport,
 Vector4d dest)

Unproject the given window coordinates winCoords by this matrix using the specified viewport.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInv() can be invoked on it.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unprojectInv(double, double, double, int[], Vector4d)
• unproject(double, double, double, int[], Vector4d)
• invert(Matrix4d)

unproject

Vector3d unproject(Vector3dc winCoords,
 int[] viewport,
 Vector3d dest)

Unproject the given window coordinates winCoords by this matrix using the specified viewport.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInv() can be invoked on it.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unprojectInv(double, double, double, int[], Vector4d)
• unproject(double, double, double, int[], Vector4d)
• invert(Matrix4d)

unprojectRay

Matrix4d unprojectRay(double winX,
 double winY,
 int[] viewport,
 Vector3d originDest,
 Vector3d dirDest)

Unproject the given 2D window coordinates (winX, winY) by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInvRay() can be invoked on it.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

viewport - the viewport described by [x, y, width, height]

originDest - will hold the ray origin

dirDest - will hold the (unnormalized) ray direction

Returns:

this

See Also:

• unprojectInvRay(double, double, int[], Vector3d, Vector3d)
• invert(Matrix4d)

unprojectRay

Matrix4d unprojectRay(Vector2dc winCoords,
 int[] viewport,
 Vector3d originDest,
 Vector3d dirDest)

Unproject the given 2D window coordinates winCoords by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by the inverse of this matrix.

As a necessary computation step for unprojecting, this method computes the inverse of this matrix. In order to avoid computing the matrix inverse with every invocation, the inverse of this matrix can be built once outside using invert(Matrix4d) and then the method unprojectInvRay() can be invoked on it.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

originDest - will hold the ray origin

dirDest - will hold the (unnormalized) ray direction

Returns:

this

See Also:

• unprojectInvRay(double, double, int[], Vector3d, Vector3d)
• unprojectRay(double, double, int[], Vector3d, Vector3d)
• invert(Matrix4d)

unprojectInv

Vector4d unprojectInv(Vector3dc winCoords,
 int[] viewport,
 Vector4d dest)

Unproject the given window coordinates winCoords by this matrix using the specified viewport.

This method differs from unproject() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by this matrix.

The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unproject(Vector3dc, int[], Vector4d)

unprojectInv

Vector4d unprojectInv(double winX,
 double winY,
 double winZ,
 int[] viewport,
 Vector4d dest)

Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.

This method differs from unproject() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by this matrix.

The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

winZ - the z-coordinate, which is the depth value in [0..1]

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unproject(double, double, double, int[], Vector4d)

unprojectInv

Vector3d unprojectInv(Vector3dc winCoords,
 int[] viewport,
 Vector3d dest)

Unproject the given window coordinates winCoords by this matrix using the specified viewport.

This method differs from unproject() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by this matrix.

The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unproject(Vector3dc, int[], Vector3d)

unprojectInv

Vector3d unprojectInv(double winX,
 double winY,
 double winZ,
 int[] viewport,
 Vector3d dest)

Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.

This method differs from unproject() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

This method first converts the given window coordinates to normalized device coordinates in the range [-1..1] and then transforms those NDC coordinates by this matrix.

The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

winZ - the z-coordinate, which is the depth value in [0..1]

viewport - the viewport described by [x, y, width, height]

dest - will hold the unprojected position

Returns:

dest

See Also:

• unproject(double, double, double, int[], Vector3d)

unprojectInvRay

Matrix4d unprojectInvRay(Vector2dc winCoords,
 int[] viewport,
 Vector3d originDest,
 Vector3d dirDest)

Unproject the given window coordinates winCoords by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.

This method differs from unprojectRay() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

Parameters:

winCoords - the window coordinates to unproject

viewport - the viewport described by [x, y, width, height]

originDest - will hold the ray origin

dirDest - will hold the (unnormalized) ray direction

Returns:

this

See Also:

• unprojectRay(Vector2dc, int[], Vector3d, Vector3d)

unprojectInvRay

Matrix4d unprojectInvRay(double winX,
 double winY,
 int[] viewport,
 Vector3d originDest,
 Vector3d dirDest)

Unproject the given 2D window coordinates (winX, winY) by this matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC z = -1.0 and goes through NDC z = +1.0.

This method differs from unprojectRay() in that it assumes that this is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation.

Parameters:

winX - the x-coordinate in window coordinates (pixels)

winY - the y-coordinate in window coordinates (pixels)

viewport - the viewport described by [x, y, width, height]

originDest - will hold the ray origin

dirDest - will hold the (unnormalized) ray direction

Returns:

this

See Also:

• unprojectRay(double, double, int[], Vector3d, Vector3d)

project

Vector4d project(double x,
 double y,
 double z,
 int[] viewport,
 Vector4d winCoordsDest)

Project the given (x, y, z) position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.

This method transforms the given coordinates by this matrix including perspective division to obtain normalized device coordinates, and then translates these into window coordinates by using the given viewport settings [x, y, width, height].

The depth range of the returned winCoordsDest.z will be [0..1], which is also the OpenGL default.

Parameters:

x - the x-coordinate of the position to project

y - the y-coordinate of the position to project

z - the z-coordinate of the position to project

viewport - the viewport described by [x, y, width, height]

winCoordsDest - will hold the projected window coordinates

Returns:

winCoordsDest

project

Vector3d project(double x,
 double y,
 double z,
 int[] viewport,
 Vector3d winCoordsDest)

Project the given (x, y, z) position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.

This method transforms the given coordinates by this matrix including perspective division to obtain normalized device coordinates, and then translates these into window coordinates by using the given viewport settings [x, y, width, height].

The depth range of the returned winCoordsDest.z will be [0..1], which is also the OpenGL default.

Parameters:

x - the x-coordinate of the position to project

y - the y-coordinate of the position to project

z - the z-coordinate of the position to project

viewport - the viewport described by [x, y, width, height]

winCoordsDest - will hold the projected window coordinates

Returns:

winCoordsDest

project

Vector4d project(Vector3dc position,
 int[] viewport,
 Vector4d winCoordsDest)

Project the given position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.

This method transforms the given coordinates by this matrix including perspective division to obtain normalized device coordinates, and then translates these into window coordinates by using the given viewport settings [x, y, width, height].

The depth range of the returned winCoordsDest.z will be [0..1], which is also the OpenGL default.

Parameters:

position - the position to project into window coordinates

viewport - the viewport described by [x, y, width, height]

winCoordsDest - will hold the projected window coordinates

Returns:

winCoordsDest

See Also:

• project(double, double, double, int[], Vector4d)

project

Vector3d project(Vector3dc position,
 int[] viewport,
 Vector3d winCoordsDest)

Project the given position via this matrix using the specified viewport and store the resulting window coordinates in winCoordsDest.

This method transforms the given coordinates by this matrix including perspective division to obtain normalized device coordinates, and then translates these into window coordinates by using the given viewport settings [x, y, width, height].

The depth range of the returned winCoordsDest.z will be [0..1], which is also the OpenGL default.

Parameters:

position - the position to project into window coordinates

viewport - the viewport described by [x, y, width, height]

winCoordsDest - will hold the projected window coordinates

Returns:

winCoordsDest

See Also:

• project(double, double, double, int[], Vector4d)

reflect

Matrix4d reflect(double a,
 double b,
 double c,
 double d,
 Matrix4d dest)

Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the equation x*a + y*b + z*c + d = 0 and store the result in dest.

The vector (a, b, c) must be a unit vector.

If M is this matrix and R the reflection matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the reflection will be applied first!

Reference: msdn.microsoft.com

Parameters:

a - the x factor in the plane equation

b - the y factor in the plane equation

c - the z factor in the plane equation

d - the constant in the plane equation

dest - will hold the result

Returns:

dest

reflect

Matrix4d reflect(double nx,
 double ny,
 double nz,
 double px,
 double py,
 double pz,
 Matrix4d dest)

Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in dest.

If M is this matrix and R the reflection matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the reflection will be applied first!

Parameters:

nx - the x-coordinate of the plane normal

ny - the y-coordinate of the plane normal

nz - the z-coordinate of the plane normal

px - the x-coordinate of a point on the plane

py - the y-coordinate of a point on the plane

pz - the z-coordinate of a point on the plane

dest - will hold the result

Returns:

dest

reflect

Matrix4d reflect(Quaterniondc orientation,
 Vector3dc point,
 Matrix4d dest)

Apply a mirror/reflection transformation to this matrix that reflects about a plane specified via the plane orientation and a point on the plane, and store the result in dest.

This method can be used to build a reflection transformation based on the orientation of a mirror object in the scene. It is assumed that the default mirror plane's normal is (0, 0, 1). So, if the given Quaterniondc is the identity (does not apply any additional rotation), the reflection plane will be z=0, offset by the given point.

If M is this matrix and R the reflection matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the reflection will be applied first!

Parameters:

orientation - the plane orientation

point - a point on the plane

dest - will hold the result

Returns:

dest

reflect

Matrix4d reflect(Vector3dc normal,
 Vector3dc point,
 Matrix4d dest)

Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in dest.

If M is this matrix and R the reflection matrix, then the new matrix will be M * R. So when transforming a vector v with the new matrix by using M * R * v, the reflection will be applied first!

Parameters:

normal - the plane normal

point - a point on the plane

dest - will hold the result

Returns:

dest

ortho

Matrix4d ortho(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

zNear - near clipping plane distance

zFar - far clipping plane distance

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

ortho

Matrix4d ortho(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

Returns:

dest

orthoLH

Matrix4d orthoLH(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an orthographic projection transformation for a left-handed coordiante system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

zNear - near clipping plane distance

zFar - far clipping plane distance

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

orthoLH

Matrix4d orthoLH(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an orthographic projection transformation for a left-handed coordiante system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

Returns:

dest

orthoSymmetric

Matrix4d orthoSymmetric(double width,
 double height,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply a symmetric orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

This method is equivalent to calling ortho() with left=-width/2, right=+width/2, bottom=-height/2 and top=+height/2.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

width - the distance between the right and left frustum edges

height - the distance between the top and bottom frustum edges

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

Returns:

dest

orthoSymmetric

Matrix4d orthoSymmetric(double width,
 double height,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply a symmetric orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

This method is equivalent to calling ortho() with left=-width/2, right=+width/2, bottom=-height/2 and top=+height/2.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

width - the distance between the right and left frustum edges

height - the distance between the top and bottom frustum edges

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

Returns:

dest

orthoSymmetricLH

Matrix4d orthoSymmetricLH(double width,
 double height,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply a symmetric orthographic projection transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

This method is equivalent to calling orthoLH() with left=-width/2, right=+width/2, bottom=-height/2 and top=+height/2.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

width - the distance between the right and left frustum edges

height - the distance between the top and bottom frustum edges

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

Returns:

dest

orthoSymmetricLH

Matrix4d orthoSymmetricLH(double width,
 double height,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply a symmetric orthographic projection transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

This method is equivalent to calling orthoLH() with left=-width/2, right=+width/2, bottom=-height/2 and top=+height/2.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

width - the distance between the right and left frustum edges

height - the distance between the top and bottom frustum edges

zNear - near clipping plane distance

zFar - far clipping plane distance

dest - will hold the result

Returns:

dest

ortho2D

Matrix4d ortho2D(double left,
 double right,
 double bottom,
 double top,
 Matrix4d dest)

Apply an orthographic projection transformation for a right-handed coordinate system to this matrix and store the result in dest.

This method is equivalent to calling ortho() with zNear=-1 and zFar=+1.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

dest - will hold the result

Returns:

dest

See Also:

• ortho(double, double, double, double, double, double, Matrix4d)

ortho2DLH

Matrix4d ortho2DLH(double left,
 double right,
 double bottom,
 double top,
 Matrix4d dest)

Apply an orthographic projection transformation for a left-handed coordinate system to this matrix and store the result in dest.

This method is equivalent to calling orthoLH() with zNear=-1 and zFar=+1.

If M is this matrix and O the orthographic projection matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the orthographic projection transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance from the center to the left frustum edge

right - the distance from the center to the right frustum edge

bottom - the distance from the center to the bottom frustum edge

top - the distance from the center to the top frustum edge

dest - will hold the result

Returns:

dest

See Also:

• orthoLH(double, double, double, double, double, double, Matrix4d)

lookAlong

Matrix4d lookAlong(Vector3dc dir,
 Vector3dc up,
 Matrix4d dest)

Apply a rotation transformation to this matrix to make -z point along dir and store the result in dest.

If M is this matrix and L the lookalong rotation matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookalong rotation transformation will be applied first!

This is equivalent to calling lookAt with eye = (0, 0, 0) and center = dir.

Parameters:

dir - the direction in space to look along

up - the direction of 'up'

dest - will hold the result

Returns:

dest

See Also:

• lookAlong(double, double, double, double, double, double, Matrix4d)
• lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)

lookAlong

Matrix4d lookAlong(double dirX,
 double dirY,
 double dirZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a rotation transformation to this matrix to make -z point along dir and store the result in dest.

If M is this matrix and L the lookalong rotation matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookalong rotation transformation will be applied first!

This is equivalent to calling lookAt() with eye = (0, 0, 0) and center = dir.

Parameters:

dirX - the x-coordinate of the direction to look along

dirY - the y-coordinate of the direction to look along

dirZ - the z-coordinate of the direction to look along

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

See Also:

• lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)

lookAt

Matrix4d lookAt(Vector3dc eye,
 Vector3dc center,
 Vector3dc up,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eye - the position of the camera

center - the point in space to look at

up - the direction of 'up'

dest - will hold the result

Returns:

dest

See Also:

• lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)

lookAt

Matrix4d lookAt(double eyeX,
 double eyeY,
 double eyeZ,
 double centerX,
 double centerY,
 double centerZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eyeX - the x-coordinate of the eye/camera location

eyeY - the y-coordinate of the eye/camera location

eyeZ - the z-coordinate of the eye/camera location

centerX - the x-coordinate of the point to look at

centerY - the y-coordinate of the point to look at

centerZ - the z-coordinate of the point to look at

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

See Also:

• lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)

lookAtPerspective

Matrix4d lookAtPerspective(double eyeX,
 double eyeY,
 double eyeZ,
 double centerX,
 double centerY,
 double centerZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns -z with center - eye and store the result in dest.

This method assumes this to be a perspective transformation, obtained via frustum() or perspective() or one of their overloads.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eyeX - the x-coordinate of the eye/camera location

eyeY - the y-coordinate of the eye/camera location

eyeZ - the z-coordinate of the eye/camera location

centerX - the x-coordinate of the point to look at

centerY - the y-coordinate of the point to look at

centerZ - the z-coordinate of the point to look at

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

lookAtLH

Matrix4d lookAtLH(Vector3dc eye,
 Vector3dc center,
 Vector3dc up,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eye - the position of the camera

center - the point in space to look at

up - the direction of 'up'

dest - will hold the result

Returns:

dest

lookAtLH

Matrix4d lookAtLH(double eyeX,
 double eyeY,
 double eyeZ,
 double centerX,
 double centerY,
 double centerZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eyeX - the x-coordinate of the eye/camera location

eyeY - the y-coordinate of the eye/camera location

eyeZ - the z-coordinate of the eye/camera location

centerX - the x-coordinate of the point to look at

centerY - the y-coordinate of the point to look at

centerZ - the z-coordinate of the point to look at

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

See Also:

• lookAtLH(Vector3dc, Vector3dc, Vector3dc, Matrix4d)

lookAtPerspectiveLH

Matrix4d lookAtPerspectiveLH(double eyeX,
 double eyeY,
 double eyeZ,
 double centerX,
 double centerY,
 double centerZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns +z with center - eye and store the result in dest.

This method assumes this to be a perspective transformation, obtained via frustumLH() or perspectiveLH() or one of their overloads.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

Parameters:

eyeX - the x-coordinate of the eye/camera location

eyeY - the y-coordinate of the eye/camera location

eyeZ - the z-coordinate of the eye/camera location

centerX - the x-coordinate of the point to look at

centerY - the y-coordinate of the point to look at

centerZ - the z-coordinate of the point to look at

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

tile

Matrix4d tile(int x,
 int y,
 int w,
 int h,
 Matrix4d dest)

This method is equivalent to calling: translate(w-1-2*x, h-1-2*y, 0, dest).scale(w, h, 1)

If M is this matrix and T the created transformation matrix, then the new matrix will be M * T. So when transforming a vector v with the new matrix by using M * T * v, the created transformation will be applied first!

Parameters:

x - the tile's x coordinate/index (should be in [0..w))

y - the tile's y coordinate/index (should be in [0..h))

w - the number of tiles along the x axis

h - the number of tiles along the y axis

dest - will hold the result

Returns:

dest

perspective

Matrix4d perspective(double fovy,
 double aspect,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

Returns:

dest

perspective

Matrix4d perspective(double fovy,
 double aspect,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

perspectiveRect

Matrix4d perspectiveRect(double width,
 double height,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

width - the width of the near frustum plane

height - the height of the near frustum plane

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

Returns:

dest

perspectiveRect

Matrix4d perspectiveRect(double width,
 double height,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

width - the width of the near frustum plane

height - the height of the near frustum plane

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

perspectiveOffCenter

Matrix4d perspectiveOffCenter(double fovy,
 double offAngleX,
 double offAngleY,
 double aspect,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

The given angles offAngleX and offAngleY are the horizontal and vertical angles between the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZ-plane.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

offAngleX - the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes

offAngleY - the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

Returns:

dest

perspectiveOffCenter

Matrix4d perspectiveOffCenter(double fovy,
 double offAngleX,
 double offAngleY,
 double aspect,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

The given angles offAngleX and offAngleY are the horizontal and vertical angles between the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZ-plane.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

offAngleX - the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes

offAngleY - the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

perspectiveOffCenterFov

Matrix4d perspectiveOffCenterFov(double angleLeft,
 double angleRight,
 double angleDown,
 double angleUp,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

The given angles angleLeft and angleRight are the horizontal angles between the left and right frustum planes, respectively, and a line perpendicular to the near and far frustum planes. The angles angleDown and angleUp are the vertical angles between the bottom and top frustum planes, respectively, and a line perpendicular to the near and far frustum planes.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

angleLeft - the horizontal angle between left frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleRight - the horizontal angle between right frustum plane and a line perpendicular to the near/far frustum planes

angleDown - the vertical angle between bottom frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleUp - the vertical angle between top frustum plane and a line perpendicular to the near/far frustum planes

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

perspectiveOffCenterFov

Matrix4d perspectiveOffCenterFov(double angleLeft,
 double angleRight,
 double angleDown,
 double angleUp,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

The given angles angleLeft and angleRight are the horizontal angles between the left and right frustum planes, respectively, and a line perpendicular to the near and far frustum planes. The angles angleDown and angleUp are the vertical angles between the bottom and top frustum planes, respectively, and a line perpendicular to the near and far frustum planes.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

angleLeft - the horizontal angle between left frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleRight - the horizontal angle between right frustum plane and a line perpendicular to the near/far frustum planes

angleDown - the vertical angle between bottom frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleUp - the vertical angle between top frustum plane and a line perpendicular to the near/far frustum planes

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

perspectiveOffCenterFovLH

Matrix4d perspectiveOffCenterFovLH(double angleLeft,
 double angleRight,
 double angleDown,
 double angleUp,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

The given angles angleLeft and angleRight are the horizontal angles between the left and right frustum planes, respectively, and a line perpendicular to the near and far frustum planes. The angles angleDown and angleUp are the vertical angles between the bottom and top frustum planes, respectively, and a line perpendicular to the near and far frustum planes.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

angleLeft - the horizontal angle between left frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleRight - the horizontal angle between right frustum plane and a line perpendicular to the near/far frustum planes

angleDown - the vertical angle between bottom frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleUp - the vertical angle between top frustum plane and a line perpendicular to the near/far frustum planes

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

perspectiveOffCenterFovLH

Matrix4d perspectiveOffCenterFovLH(double angleLeft,
 double angleRight,
 double angleDown,
 double angleUp,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an asymmetric off-center perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

The given angles angleLeft and angleRight are the horizontal angles between the left and right frustum planes, respectively, and a line perpendicular to the near and far frustum planes. The angles angleDown and angleUp are the vertical angles between the bottom and top frustum planes, respectively, and a line perpendicular to the near and far frustum planes.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

angleLeft - the horizontal angle between left frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleRight - the horizontal angle between right frustum plane and a line perpendicular to the near/far frustum planes

angleDown - the vertical angle between bottom frustum plane and a line perpendicular to the near/far frustum planes. For a symmetric frustum, this value is negative.

angleUp - the vertical angle between top frustum plane and a line perpendicular to the near/far frustum planes

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

perspectiveLH

Matrix4d perspectiveLH(double fovy,
 double aspect,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

perspectiveLH

Matrix4d perspectiveLH(double fovy,
 double aspect,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and P the perspective projection matrix, then the new matrix will be M * P. So when transforming a vector v with the new matrix by using M * P * v, the perspective projection will be applied first!

Parameters:

fovy - the vertical field of view in radians (must be greater than zero and less than PI)

aspect - the aspect ratio (i.e. width / height; must be greater than zero)

zNear - near clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

frustum

Matrix4d frustum(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and F the frustum matrix, then the new matrix will be M * F. So when transforming a vector v with the new matrix by using M * F * v, the frustum transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance along the x-axis to the left frustum edge

right - the distance along the x-axis to the right frustum edge

bottom - the distance along the y-axis to the bottom frustum edge

top - the distance along the y-axis to the top frustum edge

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

frustum

Matrix4d frustum(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and F the frustum matrix, then the new matrix will be M * F. So when transforming a vector v with the new matrix by using M * F * v, the frustum transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance along the x-axis to the left frustum edge

right - the distance along the x-axis to the right frustum edge

bottom - the distance along the y-axis to the bottom frustum edge

top - the distance along the y-axis to the top frustum edge

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

frustumLH

Matrix4d frustumLH(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 boolean zZeroToOne,
 Matrix4d dest)

Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in dest.

If M is this matrix and F the frustum matrix, then the new matrix will be M * F. So when transforming a vector v with the new matrix by using M * F * v, the frustum transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance along the x-axis to the left frustum edge

right - the distance along the x-axis to the right frustum edge

bottom - the distance along the y-axis to the bottom frustum edge

top - the distance along the y-axis to the top frustum edge

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

zZeroToOne - whether to use Vulkan's and Direct3D's NDC z range of [0..+1] when true or whether to use OpenGL's NDC z range of [-1..+1] when false

dest - will hold the result

Returns:

dest

frustumLH

Matrix4d frustumLH(double left,
 double right,
 double bottom,
 double top,
 double zNear,
 double zFar,
 Matrix4d dest)

Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.

If M is this matrix and F the frustum matrix, then the new matrix will be M * F. So when transforming a vector v with the new matrix by using M * F * v, the frustum transformation will be applied first!

Reference: http://www.songho.ca

Parameters:

left - the distance along the x-axis to the left frustum edge

right - the distance along the x-axis to the right frustum edge

bottom - the distance along the y-axis to the bottom frustum edge

top - the distance along the y-axis to the top frustum edge

zNear - near clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the near clipping plane will be at positive infinity. In that case, zFar may not also be Double.POSITIVE_INFINITY.

zFar - far clipping plane distance. This value must be greater than zero. If the special value Double.POSITIVE_INFINITY is used, the far clipping plane will be at positive infinity. In that case, zNear may not also be Double.POSITIVE_INFINITY.

dest - will hold the result

Returns:

dest

frustumPlane

Vector4d frustumPlane(int plane,
 Vector4d dest)

Calculate a frustum plane of this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given dest.

Generally, this method computes the frustum plane in the local frame of any coordinate system that existed before this transformation was applied to it in order to yield homogeneous clipping space.

The frustum plane will be given in the form of a general plane equation: a*x + b*y + c*z + d = 0, where the given Vector4d components will hold the (a, b, c, d) values of the equation.

The plane normal, which is (a, b, c), is directed "inwards" of the frustum. Any plane/point test using a*x + b*y + c*z + d therefore will yield a result greater than zero if the point is within the frustum (i.e. at the positive side of the frustum plane).

For performing frustum culling, the class FrustumIntersection should be used instead of manually obtaining the frustum planes and testing them against points, spheres or axis-aligned boxes.

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

plane - one of the six possible planes, given as numeric constants PLANE_NX, PLANE_PX, PLANE_NY, PLANE_PY, PLANE_NZ and PLANE_PZ

dest - will hold the computed plane equation. The plane equation will be normalized, meaning that (a, b, c) will be a unit vector

Returns:

dest

frustumCorner

Vector3d frustumCorner(int corner,
 Vector3d point)

Compute the corner coordinates of the frustum defined by this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given point.

Generally, this method computes the frustum corners in the local frame of any coordinate system that existed before this transformation was applied to it in order to yield homogeneous clipping space.

Reference: http://geomalgorithms.com

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

corner - one of the eight possible corners, given as numeric constants CORNER_NXNYNZ, CORNER_PXNYNZ, CORNER_PXPYNZ, CORNER_NXPYNZ, CORNER_PXNYPZ, CORNER_NXNYPZ, CORNER_NXPYPZ, CORNER_PXPYPZ

point - will hold the resulting corner point coordinates

Returns:

point

perspectiveOrigin

Vector3d perspectiveOrigin(Vector3d origin)

Compute the eye/origin of the perspective frustum transformation defined by this matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given origin.

Note that this method will only work using perspective projections obtained via one of the perspective methods, such as perspective() or frustum().

Generally, this method computes the origin in the local frame of any coordinate system that existed before this transformation was applied to it in order to yield homogeneous clipping space.

This method is equivalent to calling: invert(new Matrix4d()).transformProject(0, 0, -1, 0, origin) and in the case of an already available inverse of this matrix, the method perspectiveInvOrigin(Vector3d) on the inverse of the matrix should be used instead.

Reference: http://geomalgorithms.com

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

origin - will hold the origin of the coordinate system before applying this perspective projection transformation

Returns:

origin

perspectiveInvOrigin

Vector3d perspectiveInvOrigin(Vector3d dest)

Compute the eye/origin of the inverse of the perspective frustum transformation defined by this matrix, which can be the inverse of a projection matrix or the inverse of a combined modelview-projection matrix, and store the result in the given dest.

Note that this method will only work using perspective projections obtained via one of the perspective methods, such as perspective() or frustum().

If the inverse of the modelview-projection matrix is not available, then calling perspectiveOrigin(Vector3d) on the original modelview-projection matrix is preferred.

Parameters:

dest - will hold the result

Returns:

dest

See Also:

• perspectiveOrigin(Vector3d)

perspectiveFov

double perspectiveFov()

Return the vertical field-of-view angle in radians of this perspective transformation matrix.

Note that this method will only work using perspective projections obtained via one of the perspective methods, such as perspective() or frustum().

For orthogonal transformations this method will return 0.0.

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Returns:

the vertical field-of-view angle in radians

perspectiveNear

double perspectiveNear()

Extract the near clip plane distance from this perspective projection matrix.

This method only works if this is a perspective projection matrix, for example obtained via perspective(double, double, double, double, Matrix4d).

Returns:

the near clip plane distance

perspectiveFar

double perspectiveFar()

Extract the far clip plane distance from this perspective projection matrix.

This method only works if this is a perspective projection matrix, for example obtained via perspective(double, double, double, double, Matrix4d).

Returns:

the far clip plane distance

frustumRayDir

Vector3d frustumRayDir(double x,
 double y,
 Vector3d dir)

Obtain the direction of a ray starting at the center of the coordinate system and going through the near frustum plane.

This method computes the dir vector in the local frame of any coordinate system that existed before this transformation was applied to it in order to yield homogeneous clipping space.

The parameters x and y are used to interpolate the generated ray direction from the bottom-left to the top-right frustum corners.

For optimal efficiency when building many ray directions over the whole frustum, it is recommended to use this method only in order to compute the four corner rays at (0, 0), (1, 0), (0, 1) and (1, 1) and then bilinearly interpolating between them; or to use the FrustumRayBuilder.

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

x - the interpolation factor along the left-to-right frustum planes, within [0..1]

y - the interpolation factor along the bottom-to-top frustum planes, within [0..1]

dir - will hold the normalized ray direction in the local frame of the coordinate system before transforming to homogeneous clipping space using this matrix

Returns:

dir

positiveZ

Vector3d positiveZ(Vector3d dir)

Obtain the direction of +Z before the transformation represented by this matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +Z by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).invert();
 inv.transformDirection(dir.set(0, 0, 1)).normalize();
 

If this is already an orthogonal matrix, then consider using normalizedPositiveZ(Vector3d) instead.

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +Z

Returns:

dir

normalizedPositiveZ

Vector3d normalizedPositiveZ(Vector3d dir)

Obtain the direction of +Z before the transformation represented by this orthogonal matrix is applied. This method only produces correct results if this is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +Z by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).transpose();
 inv.transformDirection(dir.set(0, 0, 1));
 

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +Z

Returns:

dir

positiveX

Vector3d positiveX(Vector3d dir)

Obtain the direction of +X before the transformation represented by this matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +X by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).invert();
 inv.transformDirection(dir.set(1, 0, 0)).normalize();
 

If this is already an orthogonal matrix, then consider using normalizedPositiveX(Vector3d) instead.

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +X

Returns:

dir

normalizedPositiveX

Vector3d normalizedPositiveX(Vector3d dir)

Obtain the direction of +X before the transformation represented by this orthogonal matrix is applied. This method only produces correct results if this is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +X by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).transpose();
 inv.transformDirection(dir.set(1, 0, 0));
 

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +X

Returns:

dir

positiveY

Vector3d positiveY(Vector3d dir)

Obtain the direction of +Y before the transformation represented by this matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +Y by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).invert();
 inv.transformDirection(dir.set(0, 1, 0)).normalize();
 

If this is already an orthogonal matrix, then consider using normalizedPositiveY(Vector3d) instead.

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +Y

Returns:

dir

normalizedPositiveY

Vector3d normalizedPositiveY(Vector3d dir)

Obtain the direction of +Y before the transformation represented by this orthogonal matrix is applied. This method only produces correct results if this is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to +Y by this matrix.

This method is equivalent to the following code:

 Matrix4d inv = new Matrix4d(this).transpose();
 inv.transformDirection(dir.set(0, 1, 0));
 

Reference: http://www.euclideanspace.com

Parameters:

dir - will hold the direction of +Y

Returns:

dir

originAffine

Vector3d originAffine(Vector3d origin)

Obtain the position that gets transformed to the origin by this affine matrix. This can be used to get the position of the "camera" from a given view transformation matrix.

This method only works with affine matrices.

This method is equivalent to the following code:

 Matrix4f inv = new Matrix4f(this).invertAffine();
 inv.transformPosition(origin.set(0, 0, 0));
 

Parameters:

origin - will hold the position transformed to the origin

Returns:

origin

origin

Vector3d origin(Vector3d origin)

Obtain the position that gets transformed to the origin by this matrix. This can be used to get the position of the "camera" from a given view/projection transformation matrix.

This method is equivalent to the following code:

 Matrix4f inv = new Matrix4f(this).invert();
 inv.transformPosition(origin.set(0, 0, 0));
 

Parameters:

origin - will hold the position transformed to the origin

Returns:

origin

shadow

Matrix4d shadow(Vector4dc light,
 double a,
 double b,
 double c,
 double d,
 Matrix4d dest)

Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation x*a + y*b + z*c + d = 0 as if casting a shadow from a given light position/direction light and store the result in dest.

If light.w is 0.0 the light is being treated as a directional light; if it is 1.0 it is a point light.

If M is this matrix and S the shadow matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the shadow projection will be applied first!

Reference: ftp.sgi.com

Parameters:

light - the light's vector

a - the x factor in the plane equation

b - the y factor in the plane equation

c - the z factor in the plane equation

d - the constant in the plane equation

dest - will hold the result

Returns:

dest

shadow

Matrix4d shadow(double lightX,
 double lightY,
 double lightZ,
 double lightW,
 double a,
 double b,
 double c,
 double d,
 Matrix4d dest)

Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation x*a + y*b + z*c + d = 0 as if casting a shadow from a given light position/direction (lightX, lightY, lightZ, lightW) and store the result in dest.

If lightW is 0.0 the light is being treated as a directional light; if it is 1.0 it is a point light.

If M is this matrix and S the shadow matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the shadow projection will be applied first!

Reference: ftp.sgi.com

Parameters:

lightX - the x-component of the light's vector

lightY - the y-component of the light's vector

lightZ - the z-component of the light's vector

lightW - the w-component of the light's vector

a - the x factor in the plane equation

b - the y factor in the plane equation

c - the z factor in the plane equation

d - the constant in the plane equation

dest - will hold the result

Returns:

dest

shadow

Matrix4d shadow(Vector4dc light,
 Matrix4dc planeTransform,
 Matrix4d dest)

Apply a projection transformation to this matrix that projects onto the plane with the general plane equation y = 0 as if casting a shadow from a given light position/direction light and store the result in dest.

Before the shadow projection is applied, the plane is transformed via the specified planeTransformation.

If light.w is 0.0 the light is being treated as a directional light; if it is 1.0 it is a point light.

If M is this matrix and S the shadow matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the shadow projection will be applied first!

Parameters:

light - the light's vector

planeTransform - the transformation to transform the implied plane y = 0 before applying the projection

dest - will hold the result

Returns:

dest

shadow

Matrix4d shadow(double lightX,
 double lightY,
 double lightZ,
 double lightW,
 Matrix4dc planeTransform,
 Matrix4d dest)

Apply a projection transformation to this matrix that projects onto the plane with the general plane equation y = 0 as if casting a shadow from a given light position/direction (lightX, lightY, lightZ, lightW) and store the result in dest.

Before the shadow projection is applied, the plane is transformed via the specified planeTransformation.

If lightW is 0.0 the light is being treated as a directional light; if it is 1.0 it is a point light.

If M is this matrix and S the shadow matrix, then the new matrix will be M * S. So when transforming a vector v with the new matrix by using M * S * v, the shadow projection will be applied first!

Parameters:

lightX - the x-component of the light vector

lightY - the y-component of the light vector

lightZ - the z-component of the light vector

lightW - the w-component of the light vector

planeTransform - the transformation to transform the implied plane y = 0 before applying the projection

dest - will hold the result

Returns:

dest

pick

Matrix4d pick(double x,
 double y,
 double width,
 double height,
 int[] viewport,
 Matrix4d dest)

Apply a picking transformation to this matrix using the given window coordinates (x, y) as the pick center and the given (width, height) as the size of the picking region in window coordinates, and store the result in dest.

Parameters:

x - the x coordinate of the picking region center in window coordinates

y - the y coordinate of the picking region center in window coordinates

width - the width of the picking region in window coordinates

height - the height of the picking region in window coordinates

viewport - the viewport described by [x, y, width, height]

dest - the destination matrix, which will hold the result

Returns:

dest

isAffine

boolean isAffine()

Determine whether this matrix describes an affine transformation. This is the case iff its last row is equal to (0, 0, 0, 1).

Returns:

true iff this matrix is affine; false otherwise

arcball

Matrix4d arcball(double radius,
 double centerX,
 double centerY,
 double centerZ,
 double angleX,
 double angleY,
 Matrix4d dest)

Apply an arcball view transformation to this matrix with the given radius and center (centerX, centerY, centerZ) position of the arcball and the specified X and Y rotation angles, and store the result in dest.

This method is equivalent to calling: translate(0, 0, -radius, dest).rotateX(angleX).rotateY(angleY).translate(-centerX, -centerY, -centerZ)

Parameters:

radius - the arcball radius

centerX - the x coordinate of the center position of the arcball

centerY - the y coordinate of the center position of the arcball

centerZ - the z coordinate of the center position of the arcball

angleX - the rotation angle around the X axis in radians

angleY - the rotation angle around the Y axis in radians

dest - will hold the result

Returns:

dest

arcball

Matrix4d arcball(double radius,
 Vector3dc center,
 double angleX,
 double angleY,
 Matrix4d dest)

Apply an arcball view transformation to this matrix with the given radius and center position of the arcball and the specified X and Y rotation angles, and store the result in dest.

This method is equivalent to calling: translate(0, 0, -radius).rotateX(angleX).rotateY(angleY).translate(-center.x, -center.y, -center.z)

Parameters:

radius - the arcball radius

center - the center position of the arcball

angleX - the rotation angle around the X axis in radians

angleY - the rotation angle around the Y axis in radians

dest - will hold the result

Returns:

dest

projectedGridRange

Matrix4d projectedGridRange(Matrix4dc projector,
 double sLower,
 double sUpper,
 Matrix4d dest)

Compute the range matrix for the Projected Grid transformation as described in chapter "2.4.2 Creating the range conversion matrix" of the paper Real-time water rendering - Introducing the projected grid concept based on the inverse of the view-projection matrix which is assumed to be this, and store that range matrix into dest.

If the projected grid will not be visible then this method returns null.

This method uses the y = 0 plane for the projection.

Parameters:

projector - the projector view-projection transformation

sLower - the lower (smallest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid

sUpper - the upper (highest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid

dest - will hold the resulting range matrix

Returns:

the computed range matrix; or null if the projected grid will not be visible

perspectiveFrustumSlice

Matrix4d perspectiveFrustumSlice(double near,
 double far,
 Matrix4d dest)

Change the near and far clip plane distances of this perspective frustum transformation matrix and store the result in dest.

This method only works if this is a perspective projection frustum transformation, for example obtained via perspective() or frustum().

Parameters:

near - the new near clip plane distance

far - the new far clip plane distance

dest - will hold the resulting matrix

Returns:

dest

See Also:

• perspective(double, double, double, double, Matrix4d)
• frustum(double, double, double, double, double, double, Matrix4d)

orthoCrop

Matrix4d orthoCrop(Matrix4dc view,
 Matrix4d dest)

Build an ortographic projection transformation that fits the view-projection transformation represented by this into the given affine view transformation.

The transformation represented by this must be given as the inverse of a typical combined camera view-projection transformation, whose projection can be either orthographic or perspective.

The view must be an affine transformation which in the application of Cascaded Shadow Maps is usually the light view transformation. It be obtained via any affine transformation or for example via lookAt().

Reference: OpenGL SDK - Cascaded Shadow Maps

Parameters:

view - the view transformation to build a corresponding orthographic projection to fit the frustum of this

dest - will hold the crop projection transformation

Returns:

dest

transformAab

Matrix4d transformAab(double minX,
 double minY,
 double minZ,
 double maxX,
 double maxY,
 double maxZ,
 Vector3d outMin,
 Vector3d outMax)

Transform the axis-aligned box given as the minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ) by this affine matrix and compute the axis-aligned box of the result whose minimum corner is stored in outMin and maximum corner stored in outMax.

Reference: http://dev.theomader.com

Parameters:

minX - the x coordinate of the minimum corner of the axis-aligned box

minY - the y coordinate of the minimum corner of the axis-aligned box

minZ - the z coordinate of the minimum corner of the axis-aligned box

maxX - the x coordinate of the maximum corner of the axis-aligned box

maxY - the y coordinate of the maximum corner of the axis-aligned box

maxZ - the y coordinate of the maximum corner of the axis-aligned box

outMin - will hold the minimum corner of the resulting axis-aligned box

outMax - will hold the maximum corner of the resulting axis-aligned box

Returns:

this

transformAab

Matrix4d transformAab(Vector3dc min,
 Vector3dc max,
 Vector3d outMin,
 Vector3d outMax)

Transform the axis-aligned box given as the minimum corner min and maximum corner max by this affine matrix and compute the axis-aligned box of the result whose minimum corner is stored in outMin and maximum corner stored in outMax.

Parameters:

min - the minimum corner of the axis-aligned box

max - the maximum corner of the axis-aligned box

outMin - will hold the minimum corner of the resulting axis-aligned box

outMax - will hold the maximum corner of the resulting axis-aligned box

Returns:

this

lerp

Matrix4d lerp(Matrix4dc other,
 double t,
 Matrix4d dest)

Linearly interpolate this and other using the given interpolation factor t and store the result in dest.

If t is 0.0 then the result is this. If the interpolation factor is 1.0 then the result is other.

Parameters:

other - the other matrix

t - the interpolation factor between 0.0 and 1.0

dest - will hold the result

Returns:

dest

rotateTowards

Matrix4d rotateTowards(Vector3dc direction,
 Vector3dc up,
 Matrix4d dest)

Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local +Z axis with direction and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

This method is equivalent to calling: mulAffine(new Matrix4d().lookAt(new Vector3d(), new Vector3d(dir).negate(), up).invertAffine(), dest)

Parameters:

direction - the direction to rotate towards

up - the up vector

dest - will hold the result

Returns:

dest

See Also:

• rotateTowards(double, double, double, double, double, double, Matrix4d)

rotateTowards

Matrix4d rotateTowards(double dirX,
 double dirY,
 double dirZ,
 double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local +Z axis with dir and store the result in dest.

If M is this matrix and L the lookat matrix, then the new matrix will be M * L. So when transforming a vector v with the new matrix by using M * L * v, the lookat transformation will be applied first!

This method is equivalent to calling: mulAffine(new Matrix4d().lookAt(0, 0, 0, -dirX, -dirY, -dirZ, upX, upY, upZ).invertAffine(), dest)

Parameters:

dirX - the x-coordinate of the direction to rotate towards

dirY - the y-coordinate of the direction to rotate towards

dirZ - the z-coordinate of the direction to rotate towards

upX - the x-coordinate of the up vector

upY - the y-coordinate of the up vector

upZ - the z-coordinate of the up vector

dest - will hold the result

Returns:

dest

See Also:

• rotateTowards(Vector3dc, Vector3dc, Matrix4d)

getEulerAnglesXYZ

Vector3d getEulerAnglesXYZ(Vector3d dest)

Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of this and store the extracted Euler angles in dest.

This method assumes that the upper left of this only represents a rotation without scaling.

The Euler angles are always returned as the angle around X in the Vector3d.x field, the angle around Y in the Vector3d.y field and the angle around Z in the Vector3d.z field of the supplied Vector3d instance.

Note that the returned Euler angles must be applied in the order X * Y * Z to obtain the identical matrix. This means that calling rotateXYZ(double, double, double, Matrix4d) using the obtained Euler angles will yield the same rotation as the original matrix from which the Euler angles were obtained, so in the below code the matrix m2 should be identical to m (disregarding possible floating-point inaccuracies).

 Matrix4d m = ...; // <- matrix only representing rotation
 Matrix4d n = new Matrix4d();
 n.rotateXYZ(m.getEulerAnglesXYZ(new Vector3d()));
 

Reference: http://en.wikipedia.org/

Parameters:

dest - will hold the extracted Euler angles

Returns:

dest

getEulerAnglesZYX

Vector3d getEulerAnglesZYX(Vector3d dest)

Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of this and store the extracted Euler angles in dest.

This method assumes that the upper left of this only represents a rotation without scaling.

Note that the returned Euler angles must be applied in the order Z * Y * X to obtain the identical matrix. This means that calling rotateZYX(double, double, double, Matrix4d) using the obtained Euler angles will yield the same rotation as the original matrix from which the Euler angles were obtained, so in the below code the matrix m2 should be identical to m (disregarding possible floating-point inaccuracies).

 Matrix4d m = ...; // <- matrix only representing rotation
 Matrix4d n = new Matrix4d();
 n.rotateZYX(m.getEulerAnglesZYX(new Vector3d()));
 

Reference: http://nghiaho.com/

Parameters:

dest - will hold the extracted Euler angles

Returns:

dest

testPoint

boolean testPoint(double x,
 double y,
 double z)

Test whether the given point (x, y, z) is within the frustum defined by this matrix.

This method assumes this matrix to be a transformation from any arbitrary coordinate system/space M into standard OpenGL clip space and tests whether the given point with the coordinates (x, y, z) given in space M is within the clip space.

When testing multiple points using the same transformation matrix, FrustumIntersection should be used instead.

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

x - the x-coordinate of the point

y - the y-coordinate of the point

z - the z-coordinate of the point

Returns:

true if the given point is inside the frustum; false otherwise

testSphere

boolean testSphere(double x,
 double y,
 double z,
 double r)

Test whether the given sphere is partly or completely within or outside of the frustum defined by this matrix.

This method assumes this matrix to be a transformation from any arbitrary coordinate system/space M into standard OpenGL clip space and tests whether the given sphere with the coordinates (x, y, z) given in space M is within the clip space.

When testing multiple spheres using the same transformation matrix, or more sophisticated/optimized intersection algorithms are required, FrustumIntersection should be used instead.

The algorithm implemented by this method is conservative. This means that in certain circumstances a false positive can occur, when the method returns true for spheres that are actually not visible. See iquilezles.org for an examination of this problem.

Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

x - the x-coordinate of the sphere's center

y - the y-coordinate of the sphere's center

z - the z-coordinate of the sphere's center

r - the sphere's radius

Returns:

true if the given sphere is partly or completely inside the frustum; false otherwise

testAab

boolean testAab(double minX,
 double minY,
 double minZ,
 double maxX,
 double maxY,
 double maxZ)

Test whether the given axis-aligned box is partly or completely within or outside of the frustum defined by this matrix. The box is specified via its min and max corner coordinates.

This method assumes this matrix to be a transformation from any arbitrary coordinate system/space M into standard OpenGL clip space and tests whether the given axis-aligned box with its minimum corner coordinates (minX, minY, minZ) and maximum corner coordinates (maxX, maxY, maxZ) given in space M is within the clip space.

When testing multiple axis-aligned boxes using the same transformation matrix, or more sophisticated/optimized intersection algorithms are required, FrustumIntersection should be used instead.

The algorithm implemented by this method is conservative. This means that in certain circumstances a false positive can occur, when the method returns -1 for boxes that are actually not visible/do not intersect the frustum. See iquilezles.org for an examination of this problem.

Reference: Efficient View Frustum Culling
Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

Parameters:

minX - the x-coordinate of the minimum corner

minY - the y-coordinate of the minimum corner

minZ - the z-coordinate of the minimum corner

maxX - the x-coordinate of the maximum corner

maxY - the y-coordinate of the maximum corner

maxZ - the z-coordinate of the maximum corner

Returns:

true if the axis-aligned box is completely or partly inside of the frustum; false otherwise

obliqueZ

Matrix4d obliqueZ(double a,
 double b,
 Matrix4d dest)

Apply an oblique projection transformation to this matrix with the given values for a and b and store the result in dest.

If M is this matrix and O the oblique transformation matrix, then the new matrix will be M * O. So when transforming a vector v with the new matrix by using M * O * v, the oblique transformation will be applied first!

The oblique transformation is defined as:

 x' = x + a*z
 y' = y + a*z
 z' = z
 

or in matrix form:

 1 0 a 0
 0 1 b 0
 0 0 1 0
 0 0 0 1
 

Parameters:

a - the value for the z factor that applies to x

b - the value for the z factor that applies to y

dest - will hold the result

Returns:

dest

withLookAtUp

Matrix4d withLookAtUp(Vector3dc up,
 Matrix4d dest)

Apply a transformation to this matrix to ensure that the local Y axis (as obtained by positiveY(Vector3d)) will be coplanar to the plane spanned by the local Z axis (as obtained by positiveZ(Vector3d)) and the given vector up, and store the result in dest.

This effectively ensures that the resulting matrix will be equal to the one obtained from calling Matrix4d.setLookAt(Vector3dc, Vector3dc, Vector3dc) with the current local origin of this matrix (as obtained by originAffine(Vector3d)), the sum of this position and the negated local Z axis as well as the given vector up.

This method must only be called on isAffine() matrices.

Parameters:

up - the up vector

dest - will hold the result

Returns:

this

withLookAtUp

Matrix4d withLookAtUp(double upX,
 double upY,
 double upZ,
 Matrix4d dest)

Apply a transformation to this matrix to ensure that the local Y axis (as obtained by positiveY(Vector3d)) will be coplanar to the plane spanned by the local Z axis (as obtained by positiveZ(Vector3d)) and the given vector (upX, upY, upZ), and store the result in dest.

This effectively ensures that the resulting matrix will be equal to the one obtained from calling Matrix4d.setLookAt(double, double, double, double, double, double, double, double, double) called with the current local origin of this matrix (as obtained by originAffine(Vector3d)), the sum of this position and the negated local Z axis as well as the given vector (upX, upY, upZ).

This method must only be called on isAffine() matrices.

Parameters:

upX - the x coordinate of the up vector

upY - the y coordinate of the up vector

upZ - the z coordinate of the up vector

dest - will hold the result

Returns:

this

mapXZY

Matrix4d mapXZY(Matrix4d dest)

Multiply this by the matrix

 1 0 0 0
 0 0 1 0
 0 1 0 0
 0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapXZnY

Matrix4d mapXZnY(Matrix4d dest)

Multiply this by the matrix

 1 0  0 0
 0 0 -1 0
 0 1  0 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapXnYnZ

Matrix4d mapXnYnZ(Matrix4d dest)

Multiply this by the matrix

 1  0  0 0
 0 -1  0 0
 0  0 -1 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapXnZY

Matrix4d mapXnZY(Matrix4d dest)

Multiply this by the matrix

 1  0 0 0
 0  0 1 0
 0 -1 0 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapXnZnY

Matrix4d mapXnZnY(Matrix4d dest)

Multiply this by the matrix

 1  0  0 0
 0  0 -1 0
 0 -1  0 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYXZ

Matrix4d mapYXZ(Matrix4d dest)

Multiply this by the matrix

 0 1 0 0
 1 0 0 0
 0 0 1 0
 0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYXnZ

Matrix4d mapYXnZ(Matrix4d dest)

Multiply this by the matrix

 0 1  0 0
 1 0  0 0
 0 0 -1 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYZX

Matrix4d mapYZX(Matrix4d dest)

Multiply this by the matrix

 0 0 1 0
 1 0 0 0
 0 1 0 0
 0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYZnX

Matrix4d mapYZnX(Matrix4d dest)

Multiply this by the matrix

 0 0 -1 0
 1 0  0 0
 0 1  0 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYnXZ

Matrix4d mapYnXZ(Matrix4d dest)

Multiply this by the matrix

 0 -1 0 0
 1  0 0 0
 0  0 1 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYnXnZ

Matrix4d mapYnXnZ(Matrix4d dest)

Multiply this by the matrix

 0 -1  0 0
 1  0  0 0
 0  0 -1 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYnZX

Matrix4d mapYnZX(Matrix4d dest)

Multiply this by the matrix

 0  0 1 0
 1  0 0 0
 0 -1 0 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapYnZnX

Matrix4d mapYnZnX(Matrix4d dest)

Multiply this by the matrix

 0  0 -1 0
 1  0  0 0
 0 -1  0 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZXY

Matrix4d mapZXY(Matrix4d dest)

Multiply this by the matrix

 0 1 0 0
 0 0 1 0
 1 0 0 0
 0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZXnY

Matrix4d mapZXnY(Matrix4d dest)

Multiply this by the matrix

 0 1  0 0
 0 0 -1 0
 1 0  0 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZYX

Matrix4d mapZYX(Matrix4d dest)

Multiply this by the matrix

 0 0 1 0
 0 1 0 0
 1 0 0 0
 0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZYnX

Matrix4d mapZYnX(Matrix4d dest)

Multiply this by the matrix

 0 0 -1 0
 0 1  0 0
 1 0  0 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZnXY

Matrix4d mapZnXY(Matrix4d dest)

Multiply this by the matrix

 0 -1 0 0
 0  0 1 0
 1  0 0 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZnXnY

Matrix4d mapZnXnY(Matrix4d dest)

Multiply this by the matrix

 0 -1  0 0
 0  0 -1 0
 1  0  0 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZnYX

Matrix4d mapZnYX(Matrix4d dest)

Multiply this by the matrix

 0  0 1 0
 0 -1 0 0
 1  0 0 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapZnYnX

Matrix4d mapZnYnX(Matrix4d dest)

Multiply this by the matrix

 0  0 -1 0
 0 -1  0 0
 1  0  0 0
 0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXYnZ

Matrix4d mapnXYnZ(Matrix4d dest)

Multiply this by the matrix

 -1 0  0 0
  0 1  0 0
  0 0 -1 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXZY

Matrix4d mapnXZY(Matrix4d dest)

Multiply this by the matrix

 -1 0 0 0
  0 0 1 0
  0 1 0 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXZnY

Matrix4d mapnXZnY(Matrix4d dest)

Multiply this by the matrix

 -1 0  0 0
  0 0 -1 0
  0 1  0 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXnYZ

Matrix4d mapnXnYZ(Matrix4d dest)

Multiply this by the matrix

 -1  0 0 0
  0 -1 0 0
  0  0 1 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXnYnZ

Matrix4d mapnXnYnZ(Matrix4d dest)

Multiply this by the matrix

 -1  0  0 0
  0 -1  0 0
  0  0 -1 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXnZY

Matrix4d mapnXnZY(Matrix4d dest)

Multiply this by the matrix

 -1  0 0 0
  0  0 1 0
  0 -1 0 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnXnZnY

Matrix4d mapnXnZnY(Matrix4d dest)

Multiply this by the matrix

 -1  0  0 0
  0  0 -1 0
  0 -1  0 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYXZ

Matrix4d mapnYXZ(Matrix4d dest)

Multiply this by the matrix

  0 1 0 0
 -1 0 0 0
  0 0 1 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYXnZ

Matrix4d mapnYXnZ(Matrix4d dest)

Multiply this by the matrix

  0 1  0 0
 -1 0  0 0
  0 0 -1 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYZX

Matrix4d mapnYZX(Matrix4d dest)

Multiply this by the matrix

  0 0 1 0
 -1 0 0 0
  0 1 0 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYZnX

Matrix4d mapnYZnX(Matrix4d dest)

Multiply this by the matrix

  0 0 -1 0
 -1 0  0 0
  0 1  0 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYnXZ

Matrix4d mapnYnXZ(Matrix4d dest)

Multiply this by the matrix

  0 -1 0 0
 -1  0 0 0
  0  0 1 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYnXnZ

Matrix4d mapnYnXnZ(Matrix4d dest)

Multiply this by the matrix

  0 -1  0 0
 -1  0  0 0
  0  0 -1 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYnZX

Matrix4d mapnYnZX(Matrix4d dest)

Multiply this by the matrix

  0  0 1 0
 -1  0 0 0
  0 -1 0 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnYnZnX

Matrix4d mapnYnZnX(Matrix4d dest)

Multiply this by the matrix

  0  0 -1 0
 -1  0  0 0
  0 -1  0 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZXY

Matrix4d mapnZXY(Matrix4d dest)

Multiply this by the matrix

  0 1 0 0
  0 0 1 0
 -1 0 0 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZXnY

Matrix4d mapnZXnY(Matrix4d dest)

Multiply this by the matrix

  0 1  0 0
  0 0 -1 0
 -1 0  0 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZYX

Matrix4d mapnZYX(Matrix4d dest)

Multiply this by the matrix

  0 0 1 0
  0 1 0 0
 -1 0 0 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZYnX

Matrix4d mapnZYnX(Matrix4d dest)

Multiply this by the matrix

  0 0 -1 0
  0 1  0 0
 -1 0  0 0
  0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZnXY

Matrix4d mapnZnXY(Matrix4d dest)

Multiply this by the matrix

  0 -1 0 0
  0  0 1 0
 -1  0 0 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZnXnY

Matrix4d mapnZnXnY(Matrix4d dest)

Multiply this by the matrix

  0 -1  0 0
  0  0 -1 0
 -1  0  0 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZnYX

Matrix4d mapnZnYX(Matrix4d dest)

Multiply this by the matrix

  0  0 1 0
  0 -1 0 0
 -1  0 0 0
  0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

mapnZnYnX

Matrix4d mapnZnYnX(Matrix4d dest)

Multiply this by the matrix

  0  0 -1 0
  0 -1  0 0
 -1  0  0 0
  0  0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

negateX

Matrix4d negateX(Matrix4d dest)

Multiply this by the matrix

 -1 0 0 0
  0 1 0 0
  0 0 1 0
  0 0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

negateY

Matrix4d negateY(Matrix4d dest)

Multiply this by the matrix

 1  0 0 0
 0 -1 0 0
 0  0 1 0
 0  0 0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

negateZ

Matrix4d negateZ(Matrix4d dest)

Multiply this by the matrix

 1 0  0 0
 0 1  0 0
 0 0 -1 0
 0 0  0 1
 

and store the result in dest.

Parameters:

dest - will hold the result

Returns:

dest

equals

boolean equals(Matrix4dc m,
 double delta)

Compare the matrix elements of this matrix with the given matrix using the given delta and return whether all of them are equal within a maximum difference of delta.

Please note that this method is not used by any data structure such as ArrayList HashSet or HashMap and their operations, such as ArrayList.contains(Object) or HashSet.remove(Object), since those data structures only use the Object.equals(Object) and Object.hashCode() methods.

Parameters:

m - the other matrix

delta - the allowed maximum difference

Returns:

true whether all of the matrix elements are equal; false otherwise

isFinite

boolean isFinite()

Determine whether all matrix elements are finite floating-point values, that is, they are not NaN and not infinity.

Returns:

true if all components are finite floating-point values; false otherwise