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 int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, -1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, -1, 1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, -1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (-1, 1, 1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, -1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, -1, 1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, -1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumCorner(int, Vector3d) identifying the corner (1, 1, 1) when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=-1 when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=-1 when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=-1 when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation x=1 when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation y=1 when using the identity matrix.
    static int
    Argument to the first parameter of frustumPlane(int, Vector4d) identifying the plane with equation z=1 when using the identity matrix.
    static byte
    Bit returned by properties() to indicate that the matrix represents an affine transformation.
    static byte
    Bit returned by properties() to indicate that the matrix represents the identity transformation.
    static byte
    Bit returned by properties() to indicate that the upper-left 3x3 submatrix represents an orthogonal matrix (i.e. orthonormal basis).
    static byte
    Bit returned by properties() to indicate that the matrix represents a perspective transformation.
    static byte
    Bit returned by properties() to indicate that the matrix represents a pure translation transformation.
  • Method Summary

    Modifier and Type
    Method
    Description
    add​(Matrix4dc other, Matrix4d dest)
    Component-wise add this and other and store the result in dest.
    add4x3​(Matrix4dc other, Matrix4d dest)
    Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.
    add4x3​(Matrix4fc other, Matrix4d dest)
    Component-wise add the upper 4x3 submatrices of this and other and store the result in dest.
    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.
    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.
    Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest.
    Compute the cofactor matrix of the upper left 3x3 submatrix of this and store it into dest.
    double
    Return the determinant of this matrix.
    double
    Return the determinant of the upper left 3x3 submatrix of this matrix.
    double
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    get​(int index, ByteBuffer buffer)
    Store this matrix in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
    get​(int index, DoubleBuffer buffer)
    Store this matrix in column-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.
    get​(int index, FloatBuffer buffer)
    Store this matrix in column-major order into the supplied FloatBuffer starting at the specified absolute buffer position/index.
    get​(ByteBuffer buffer)
    Store this matrix in column-major order into the supplied ByteBuffer at the current buffer position.
    get​(DoubleBuffer buffer)
    Store this matrix in column-major order into the supplied DoubleBuffer at the current buffer position.
    get​(FloatBuffer buffer)
    Store this matrix in column-major order into the supplied FloatBuffer at the current buffer position.
    get​(Matrix4d dest)
    Get the current values of this matrix and store them into dest.
    get3x3​(Matrix3d dest)
    Get the current values of the upper left 3x3 submatrix of this matrix and store them into dest.
    get4x3​(Matrix4x3d dest)
    Get the current values of the upper 4x3 submatrix of this matrix and store them into dest.
    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.
    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.
    Store the upper 4x3 submatrix of this matrix in row-major order into the supplied ByteBuffer at the current buffer position.
    Store the upper 4x3 submatrix of this matrix in row-major order into the supplied DoubleBuffer at the current buffer position.
    getColumn​(int column, Vector3d dest)
    Get the first three components of the column at the given column index, starting with 0.
    getColumn​(int column, Vector4d dest)
    Get the column at the given column index, starting with 0.
    Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of this and store the extracted Euler angles in dest.
    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.
    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.
    Get the current values of this matrix and store the represented rotation into the given Quaterniond.
    Get the current values of this matrix and store the represented rotation into the given Quaternionf.
    getRow​(int row, Vector3d dest)
    Get the first three components of the row at the given row index, starting with 0.
    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.
    getScale​(Vector3d dest)
    Get the scaling factors of this matrix for the three base axes.
    getToAddress​(long address)
    Store this matrix in column-major order at the given off-heap address.
    Get only the translation components (m30, m31, m32) of this matrix and store them in the given vector xyz.
    getTransposed​(int index, ByteBuffer buffer)
    Store the transpose of this matrix in column-major order into the supplied ByteBuffer starting at the specified absolute buffer position/index.
    getTransposed​(int index, DoubleBuffer buffer)
    Store the transpose of this matrix in column-major order into the supplied DoubleBuffer starting at the specified absolute buffer position/index.
    Store the transpose of this matrix in column-major order into the supplied ByteBuffer at the current buffer position.
    Store the transpose of this matrix in column-major order into the supplied DoubleBuffer at the current buffer position.
    Get the current values of this matrix and store the represented rotation into the given Quaterniond.
    Get the current values of this matrix and store the represented rotation into the given Quaternionf.
    invert​(Matrix4d dest)
    Invert this matrix and store the result in 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.
    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.
    Invert this orthographic projection matrix and store the result into the given 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.
    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.
    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
    Determine whether this matrix describes an affine transformation.
    boolean
    Determine whether all matrix elements are finite floating-point values, that is, they are not NaN and not infinity.
    lerp​(Matrix4dc other, double t, Matrix4d dest)
    Linearly interpolate this and other using the given interpolation factor t and store the result in dest.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    mul​(Matrix3x2dc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    mul​(Matrix3x2fc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    mul​(Matrix4dc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    mul​(Matrix4fc right, Matrix4d dest)
    Multiply this matrix by the supplied parameter matrix and store the result in dest.
    mul​(Matrix4x3dc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    mul​(Matrix4x3fc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    mul0​(Matrix4dc right, Matrix4d dest)
    Multiply this matrix by the supplied right matrix and store the result in dest.
    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.
    Component-wise multiply the upper 4x3 submatrices of this by other and store the result in dest.
    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.
    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.
    Component-wise multiply this by other and store the result in dest.
    mulLocal​(Matrix4dc left, Matrix4d dest)
    Pre-multiply this matrix by the supplied left matrix and store the result in dest.
    Pre-multiply this matrix by the supplied left matrix, both of which are assumed to be affine, and store the result in dest.
    Multiply this orthographic projection matrix by the supplied affine view matrix and store the result in dest.
    Multiply this symmetric perspective projection matrix by the supplied affine view matrix and store the result in dest.
    Multiply this symmetric perspective projection matrix by the supplied view matrix and store the result in 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.
    normal​(Matrix3d dest)
    Compute a normal matrix from the upper left 3x3 submatrix of this and store it into dest.
    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.
    Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.
    Normalize the upper left 3x3 submatrix of this matrix and store the result in dest.
    Obtain the direction of +X before the transformation represented by this orthogonal matrix is applied.
    Obtain the direction of +Y before the transformation represented by this orthogonal matrix is applied.
    Obtain the direction of +Z before the transformation represented by this orthogonal matrix is applied.
    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.
    origin​(Vector3d origin)
    Obtain the position that gets transformed to the origin by this matrix.
    Obtain the position that gets transformed to the origin by this affine matrix.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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
    Extract the far clip plane distance from this perspective projection matrix.
    double
    Return the vertical field-of-view angle in radians of this perspective transformation matrix.
    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.
    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.
    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.
    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
    Extract the near clip plane distance from this perspective projection matrix.
    perspectiveOffCenter​(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar)
    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.
    perspectiveOffCenter​(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, boolean zZeroToOne)
    Apply an asymmetric off-center perspective projection frustum transformation using for a right-handed coordinate system the given NDC z range to this matrix.
    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.
    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.
    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.
    perspectiveRect​(double width, double height, double zNear, double zFar)
    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.
    perspectiveRect​(double width, double height, double zNear, double zFar, boolean zZeroToOne)
    Apply a symmetric perspective projection frustum transformation using for a right-handed coordinate system the given NDC z range to this matrix.
    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.
    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.
    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.
    Obtain the direction of +X before the transformation represented by this matrix is applied.
    Obtain the direction of +Y before the transformation represented by this matrix is applied.
    Obtain the direction of +Z before the transformation represented by this matrix is applied.
    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.
    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.
    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.
    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.
    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
    Return the assumed properties of this matrix.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    rotate​(AxisAngle4d axisAngle, Matrix4d dest)
    Apply a rotation transformation, rotating about the given AxisAngle4d and store the result in dest.
    rotate​(AxisAngle4f axisAngle, Matrix4d dest)
    Apply a rotation transformation, rotating about the given AxisAngle4f and store the result in dest.
    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.
    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.
    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.
    Apply the rotation - and possibly scaling - transformation of the given Quaterniondc to this affine matrix and store the result in dest.
    Apply the rotation - and possibly scaling - transformation of the given Quaternionfc to this affine matrix and store the result in dest.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    Pre-multiply the rotation - and possibly scaling - transformation of the given Quaterniondc to this matrix and store the result in dest.
    Pre-multiply the rotation - and possibly scaling - transformation of the given Quaternionfc to this matrix and store the result in dest.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    sub​(Matrix4dc subtrahend, Matrix4d dest)
    Component-wise subtract subtrahend from this and store the result in dest.
    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.
    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.
    Transform/multiply the given vector by this matrix and store the result in that vector.
    Transform/multiply the given vector by this matrix and store the result in dest.
    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.
    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.
    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.
    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)).
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    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.
    Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
    Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.
    Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
    Transform/multiply the given vector by this matrix, perform perspective divide and store the x, y and z components of the result in dest.
    Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.
    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.
    Transform/multiply the given vector by the transpose of this matrix and store the result in that vector.
    Transform/multiply the given vector by the transpose of this matrix and store the result in dest.
    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.
    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.
    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.
    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.
    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.
    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.
    Transpose this matrix and store the result into dest.
    Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
    Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
    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.
    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.
    unproject​(Vector3dc winCoords, int[] viewport, Vector3d dest)
    Unproject the given window coordinates winCoords by this matrix using the specified viewport.
    unproject​(Vector3dc winCoords, int[] viewport, Vector4d dest)
    Unproject the given window coordinates winCoords by this matrix using the specified viewport.
    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.
    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.
    unprojectInv​(Vector3dc winCoords, int[] viewport, Vector3d dest)
    Unproject the given window coordinates winCoords by this matrix using the specified viewport.
    unprojectInv​(Vector3dc winCoords, int[] viewport, Vector4d dest)
    Unproject the given window coordinates winCoords by this matrix using the specified viewport.
    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.
    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.
    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.
    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.
    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.
    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

  • 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 the transpose of 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 getTransposed(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:
      getTransposed(int, DoubleBuffer)
    • getTransposed

      DoubleBuffer getTransposed(int index, DoubleBuffer buffer)
      Store the transpose of 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
    • getTransposed

      ByteBuffer getTransposed(ByteBuffer buffer)
      Store the transpose of 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 getTransposed(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:
      getTransposed(int, ByteBuffer)
    • getTransposed

      ByteBuffer getTransposed(int index, ByteBuffer buffer)
      Store the transpose of 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
    • 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
    • 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
    • perspectiveRect

      Matrix4d perspectiveRect(double width, double height, double zNear, double zFar, boolean zZeroToOne)
      Apply a symmetric perspective projection frustum transformation using for a right-handed coordinate system the given NDC z range to this matrix.

      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.
      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:
      this
    • perspectiveRect

      Matrix4d perspectiveRect(double width, double height, double zNear, double zFar)
      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.

      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.
      Returns:
      this
    • 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
    • perspectiveOffCenter

      Matrix4d perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, boolean zZeroToOne)
      Apply an asymmetric off-center perspective projection frustum transformation using for a right-handed coordinate system the given NDC z range to this matrix.

      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.
      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:
      this
    • perspectiveOffCenter

      Matrix4d perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar)
      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.

      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.
      Returns:
      this
    • 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. 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
    • 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. 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
    • 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. 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
    • 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. 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
    • 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 reflection 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 reflection 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 reflection 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 reflection 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)
    • 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
    • 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