Interface Matrix4dc
 All Known Implementing Classes:
Matrix4d
,Matrix4dStack
 Author:
 Kai Burjack

Field Summary
Modifier and TypeFieldDescriptionstatic int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationx=1
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationy=1
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationz=1
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationx=1
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationy=1
when using the identity matrix.static int
Argument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationz=1
when using the identity matrix.static byte
Bit returned byproperties()
to indicate that the matrix represents an affine transformation.static byte
Bit returned byproperties()
to indicate that the matrix represents the identity transformation.static byte
Bit returned byproperties()
to indicate that the upperleft 3x3 submatrix represents an orthogonal matrix (i.e. orthonormal basis).static byte
Bit returned byproperties()
to indicate that the matrix represents a perspective transformation.static byte
Bit returned byproperties()
to indicate that the matrix represents a pure translation transformation. 
Method Summary
Modifier and TypeMethodDescriptionComponentwise addthis
andother
and store the result indest
.Componentwise add the upper 4x3 submatrices ofthis
andother
and store the result indest
.Componentwise add the upper 4x3 submatrices ofthis
andother
and store the result indest
.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 givenradius
and center(centerX, centerY, centerZ)
position of the arcball and the specified X and Y rotation angles, and store the result indest
.Apply an arcball view transformation to this matrix with the givenradius
andcenter
position of the arcball and the specified X and Y rotation angles, and store the result indest
.cofactor3x3(Matrix3d dest)
Compute the cofactor matrix of the upper left 3x3 submatrix ofthis
and store it intodest
.cofactor3x3(Matrix4d dest)
Compute the cofactor matrix of the upper left 3x3 submatrix ofthis
and store it intodest
.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 anaffine
transformation and thus its last row is equal to(0, 0, 0, 1)
.boolean
Compare the matrix elements ofthis
matrix with the given matrix using the givendelta
and return whether all of them are equal within a maximum difference ofdelta
.Componentwise add the upper 4x3 submatrices ofthis
andother
by first multiplying each component ofother
's 4x3 submatrix byotherFactor
, adding that tothis
and storing the final result indest
.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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.frustum(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)
Apply an arbitrary perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.frustumCorner(int corner, Vector3d point)
Compute the corner coordinates of the frustum defined bythis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givenpoint
.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 lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.frustumLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)
Apply an arbitrary perspective projection frustum transformation for a lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.frustumPlane(int plane, Vector4d dest)
Calculate a frustum plane ofthis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givendest
.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 columnmajor order.double[]
get(double[] arr, int offset)
Store this matrix into the supplied double array in columnmajor order at the given offset.float[]
get(float[] arr)
Store the elements of this matrix as float values in columnmajor order into the supplied float array.float[]
get(float[] arr, int offset)
Store the elements of this matrix as float values in columnmajor 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 columnmajor order into the suppliedByteBuffer
starting at the specified absolute buffer position/index.get(int index, DoubleBuffer buffer)
Store this matrix in columnmajor order into the suppliedDoubleBuffer
starting at the specified absolute buffer position/index.get(int index, FloatBuffer buffer)
Store this matrix in columnmajor order into the suppliedFloatBuffer
starting at the specified absolute buffer position/index.get(ByteBuffer buffer)
Store this matrix in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.get(DoubleBuffer buffer)
Store this matrix in columnmajor order into the suppliedDoubleBuffer
at the current bufferposition
.get(FloatBuffer buffer)
Store this matrix in columnmajor order into the suppliedFloatBuffer
at the current bufferposition
.Get the current values ofthis
matrix and store them intodest
.Get the current values of the upper left 3x3 submatrix ofthis
matrix and store them intodest
.get4x3(Matrix4x3d dest)
Get the current values of the upper 4x3 submatrix ofthis
matrix and store them intodest
.get4x3Transposed(int index, ByteBuffer buffer)
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedByteBuffer
starting at the specified absolute buffer position/index.get4x3Transposed(int index, DoubleBuffer buffer)
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedDoubleBuffer
starting at the specified absolute buffer position/index.get4x3Transposed(ByteBuffer buffer)
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedByteBuffer
at the current bufferposition
.get4x3Transposed(DoubleBuffer buffer)
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedDoubleBuffer
at the current bufferposition
.Get the first three components of the column at the givencolumn
index, starting with0
.Get the column at the givencolumn
index, starting with0
.getEulerAnglesZYX(Vector3d dest)
Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix ofthis
and store the extracted Euler angles indest
.getFloats(int index, ByteBuffer buffer)
Store the elements of this matrix as float values in columnmajor order into the suppliedByteBuffer
starting at the specified absolute buffer position/index.getFloats(ByteBuffer buffer)
Store the elements of this matrix as float values in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.getNormalizedRotation(Quaterniond dest)
Get the current values ofthis
matrix and store the represented rotation into the givenQuaterniond
.getNormalizedRotation(Quaternionf dest)
Get the current values ofthis
matrix and store the represented rotation into the givenQuaternionf
.Get the first three components of the row at the givenrow
index, starting with0
.Get the row at the givenrow
index, starting with0
.double
getRowColumn(int row, int column)
Get the matrix element value at the given row and column.Get the scaling factors ofthis
matrix for the three base axes.getToAddress(long address)
Store this matrix in columnmajor order at the given offheap address.getTranslation(Vector3d dest)
Get only the translation components(m30, m31, m32)
of this matrix and store them in the given vectorxyz
.getTransposed(int index, ByteBuffer buffer)
Store the transpose of this matrix in columnmajor order into the suppliedByteBuffer
starting at the specified absolute buffer position/index.getTransposed(int index, DoubleBuffer buffer)
Store the transpose of this matrix in columnmajor order into the suppliedDoubleBuffer
starting at the specified absolute buffer position/index.getTransposed(ByteBuffer buffer)
Store the transpose of this matrix in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.getTransposed(DoubleBuffer buffer)
Store the transpose of this matrix in columnmajor order into the suppliedDoubleBuffer
at the current bufferposition
.Get the current values ofthis
matrix and store the represented rotation into the givenQuaterniond
.Get the current values ofthis
matrix and store the represented rotation into the givenQuaternionf
.Invertthis
matrix and store the result indest
.invertAffine(Matrix4d dest)
Invert this matrix by assuming that it is anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and write the result intodest
.invertFrustum(Matrix4d dest)
Ifthis
is an arbitrary perspective projection matrix obtained via one of thefrustum()
methods, then this method builds the inverse ofthis
and stores it into the givendest
.invertOrtho(Matrix4d dest)
Invertthis
orthographic projection matrix and store the result into the givendest
.invertPerspective(Matrix4d dest)
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation, then this method builds the inverse ofthis
and stores it into the givendest
.invertPerspectiveView(Matrix4dc view, Matrix4d dest)
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation and the givenview
matrix isaffine
and has unit scaling (for example by being obtained vialookAt()
), then this method builds the inverse ofthis * view
and stores it into the givendest
.invertPerspectiveView(Matrix4x3dc view, Matrix4d dest)
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation and the givenview
matrix has unit scaling, then this method builds the inverse ofthis * view
and stores it into the givendest
.boolean
isAffine()
Determine whether this matrix describes an affine transformation.boolean
isFinite()
Linearly interpolatethis
andother
using the given interpolation factort
and store the result indest
.lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest)
Apply a rotation transformation to this matrix to makez
point alongdir
and store the result indest
.Apply a rotation transformation to this matrix to makez
point alongdir
and store the result indest
.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 righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.Apply a "lookat" transformation to this matrix for a righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.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 lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.Apply a "lookat" transformation to this matrix for a lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.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 righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.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 lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.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 indest
.mul(Matrix3x2dc right, Matrix4d dest)
Multiply this matrix by the suppliedright
matrix and store the result indest
.mul(Matrix3x2fc right, Matrix4d dest)
Multiply this matrix by the suppliedright
matrix and store the result indest
.Multiply this matrix by the suppliedright
matrix and store the result indest
.Multiply this matrix by the supplied parameter matrix and store the result indest
.mul(Matrix4x3dc right, Matrix4d dest)
Multiply this matrix by the suppliedright
matrix and store the result indest
.mul(Matrix4x3fc right, Matrix4d dest)
Multiply this matrix by the suppliedright
matrix and store the result indest
.Multiply this matrix by the suppliedright
matrix and store the result indest
.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 indest
.mul4x3ComponentWise(Matrix4dc other, Matrix4d dest)
Componentwise multiply the upper 4x3 submatrices ofthis
byother
and store the result indest
.Multiply this matrix by the suppliedright
matrix, both of which are assumed to beaffine
, and store the result indest
.mulAffineR(Matrix4dc right, Matrix4d dest)
Multiply this matrix by the suppliedright
matrix, which is assumed to beaffine
, and store the result indest
.mulComponentWise(Matrix4dc other, Matrix4d dest)
Componentwise multiplythis
byother
and store the result indest
.Premultiply this matrix by the suppliedleft
matrix and store the result indest
.mulLocalAffine(Matrix4dc left, Matrix4d dest)
Premultiply this matrix by the suppliedleft
matrix, both of which are assumed to beaffine
, and store the result indest
.mulOrthoAffine(Matrix4dc view, Matrix4d dest)
Multiplythis
orthographic projection matrix by the suppliedaffine
view
matrix and store the result indest
.mulPerspectiveAffine(Matrix4dc view, Matrix4d dest)
Multiplythis
symmetric perspective projection matrix by the suppliedaffine
view
matrix and store the result indest
.mulPerspectiveAffine(Matrix4x3dc view, Matrix4d dest)
Multiplythis
symmetric perspective projection matrix by the suppliedview
matrix and store the result indest
.mulTranslationAffine(Matrix4dc right, Matrix4d dest)
Multiply this matrix, which is assumed to only contain a translation, by the suppliedright
matrix, which is assumed to beaffine
, and store the result indest
.Compute a normal matrix from the upper left 3x3 submatrix ofthis
and store it intodest
.Compute a normal matrix from the upper left 3x3 submatrix ofthis
and store it into the upper left 3x3 submatrix ofdest
.normalize3x3(Matrix3d dest)
Normalize the upper left 3x3 submatrix of this matrix and store the result indest
.normalize3x3(Matrix4d dest)
Normalize the upper left 3x3 submatrix of this matrix and store the result indest
.normalizedPositiveX(Vector3d dir)
Obtain the direction of+X
before the transformation represented bythis
orthogonal matrix is applied.normalizedPositiveY(Vector3d dir)
Obtain the direction of+Y
before the transformation represented bythis
orthogonal matrix is applied.normalizedPositiveZ(Vector3d dir)
Obtain the direction of+Z
before the transformation represented bythis
orthogonal matrix is applied.Apply an oblique projection transformation to this matrix with the given values fora
andb
and store the result indest
.Obtain the position that gets transformed to the origin bythis
matrix.originAffine(Vector3d origin)
Obtain the position that gets transformed to the origin bythis
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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.ortho(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)
Apply an orthographic projection transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.Apply an orthographic projection transformation for a righthanded coordinate system to this matrix and store the result indest
.Apply an orthographic projection transformation for a lefthanded coordinate system to this matrix and store the result indest
.Build an ortographic projection transformation that fits the viewprojection transformation represented bythis
into the given affineview
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 lefthanded coordiante system using the given NDC z range to this matrix and store the result indest
.orthoLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest)
Apply an orthographic projection transformation for a lefthanded coordiante system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.orthoSymmetric(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)
Apply a symmetric orthographic projection transformation for a righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.orthoSymmetric(double width, double height, double zNear, double zFar, Matrix4d dest)
Apply a symmetric orthographic projection transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.orthoSymmetricLH(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)
Apply a symmetric orthographic projection transformation for a lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.orthoSymmetricLH(double width, double height, double zNear, double zFar, Matrix4d dest)
Apply a symmetric orthographic projection transformation for a lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.perspective(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.perspective(double fovy, double aspect, double zNear, double zFar, Matrix4d dest)
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.double
Extract the far clip plane distance fromthis
perspective projection matrix.double
Return the vertical fieldofview angle in radians of this perspective transformation matrix.perspectiveFrustumSlice(double near, double far, Matrix4d dest)
Change the near and far clip plane distances ofthis
perspective frustum transformation matrix and store the result indest
.perspectiveInvOrigin(Vector3d dest)
Compute the eye/origin of the inverse of the perspective frustum transformation defined bythis
matrix, which can be the inverse of a projection matrix or the inverse of a combined modelviewprojection matrix, and store the result in the givendest
.perspectiveLH(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest)
Apply a symmetric perspective projection frustum transformation for a lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.perspectiveLH(double fovy, double aspect, double zNear, double zFar, Matrix4d dest)
Apply a symmetric perspective projection frustum transformation for a lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.double
Extract the near clip plane distance fromthis
perspective projection matrix.perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar)
Apply an asymmetric offcenter perspective projection frustum transformation for a righthanded 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 offcenter perspective projection frustum transformation using for a righthanded 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 offcenter perspective projection frustum transformation for a righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, Matrix4d dest)
Apply an asymmetric offcenter perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.perspectiveOrigin(Vector3d origin)
Compute the eye/origin of the perspective frustum transformation defined bythis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givenorigin
.perspectiveRect(double width, double height, double zNear, double zFar)
Apply a symmetric perspective projection frustum transformation for a righthanded 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 righthanded 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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.perspectiveRect(double width, double height, double zNear, double zFar, Matrix4d dest)
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.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 indest
.Obtain the direction of+X
before the transformation represented bythis
matrix is applied.Obtain the direction of+Y
before the transformation represented bythis
matrix is applied.Obtain the direction of+Z
before the transformation represented bythis
matrix is applied.Project the given(x, y, z)
position viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.Project the given(x, y, z)
position viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.Project the givenposition
viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.Project the givenposition
viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.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 Realtime water rendering  Introducing the projected grid concept based on the inverse of the viewprojection matrix which is assumed to bethis
, and store that range matrix intodest
.int
Return the assumed properties of this matrix.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 indest
.Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the equationx*a + y*b + z*c + d = 0
and store the result indest
.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 indest
.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 indest
.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 indest
.Apply a rotation transformation, rotating the given radians about the specified axis and store the result indest
.Apply a rotation transformation, rotating the given radians about the specified axis and store the result indest
.rotate(AxisAngle4d axisAngle, Matrix4d dest)
Apply a rotation transformation, rotating about the givenAxisAngle4d
and store the result indest
.rotate(AxisAngle4f axisAngle, Matrix4d dest)
Apply a rotation transformation, rotating about the givenAxisAngle4f
and store the result indest
.rotate(Quaterniondc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix and store the result indest
.rotate(Quaternionfc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix and store the result indest
.rotateAffine(double ang, double x, double y, double z, Matrix4d dest)
Apply rotation to thisaffine
matrix by rotating the given amount of radians about the specified(x, y, z)
axis and store the result indest
.rotateAffine(Quaterniondc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to thisaffine
matrix and store the result indest
.rotateAffine(Quaternionfc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to thisaffine
matrix and store the result indest
.rotateAffineXYZ(double angleX, double angleY, double angleZ, Matrix4d dest)
Apply rotation ofangleX
radians about the X axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.rotateAffineYXZ(double angleY, double angleX, double angleZ, Matrix4d dest)
Apply rotation ofangleY
radians about the Y axis, followed by a rotation ofangleX
radians about the X axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.rotateAffineZYX(double angleZ, double angleY, double angleX, Matrix4d dest)
Apply rotation ofangleZ
radians about the Z axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleX
radians about the X axis and store the result indest
.rotateAround(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.rotateAroundAffine(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to thisaffine
matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.rotateAroundLocal(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest)
Premultiply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.rotateLocal(double ang, double x, double y, double z, Matrix4d dest)
Premultiply a rotation to this matrix by rotating the given amount of radians about the specified(x, y, z)
axis and store the result indest
.rotateLocal(Quaterniondc quat, Matrix4d dest)
Premultiply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix and store the result indest
.rotateLocal(Quaternionfc quat, Matrix4d dest)
Premultiply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix and store the result indest
.rotateLocalX(double ang, Matrix4d dest)
Premultiply a rotation around the X axis to this matrix by rotating the given amount of radians about the X axis and store the result indest
.rotateLocalY(double ang, Matrix4d dest)
Premultiply a rotation around the Y axis to this matrix by rotating the given amount of radians about the Y axis and store the result indest
.rotateLocalZ(double ang, Matrix4d dest)
Premultiply a rotation around the Z axis to this matrix by rotating the given amount of radians about the Z axis and store the result indest
.rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest)
Apply a model transformation to this matrix for a righthanded coordinate system, that aligns the local+Z
axis withdir
and store the result indest
.rotateTowards(Vector3dc direction, Vector3dc up, Matrix4d dest)
Apply a model transformation to this matrix for a righthanded coordinate system, that aligns the local+Z
axis withdirection
and store the result indest
.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 indest
.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 indest
.rotateTranslation(Quaterniondc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix, which is assumed to only contain a translation, and store the result indest
.rotateTranslation(Quaternionfc quat, Matrix4d dest)
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix, which is assumed to only contain a translation, and store the result indest
.Apply rotation about the X axis to this matrix by rotating the given amount of radians and store the result indest
.Apply rotation ofangleX
radians about the X axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.Apply rotation about the Y axis to this matrix by rotating the given amount of radians and store the result indest
.Apply rotation ofangleY
radians about the Y axis, followed by a rotation ofangleX
radians about the X axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.Apply rotation about the Z axis to this matrix by rotating the given amount of radians and store the result indest
.Apply rotation ofangleZ
radians about the Z axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleX
radians about the X axis and store the result indest
.Apply scaling tothis
matrix by scaling the base axes by the given x, y and z factors and store the result indest
.Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor and store the result indest
.Apply scaling tothis
matrix by scaling the base axes by the givenxyz.x
,xyz.y
andxyz.z
factors, respectively and store the result indest
.scaleAround(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest)
Apply scaling tothis
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 indest
.scaleAround(double factor, double ox, double oy, double oz, Matrix4d dest)
Apply scaling to this matrix by scaling all three base axes by the givenfactor
while using(ox, oy, oz)
as the scaling origin, and store the result indest
.scaleAroundLocal(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest)
Premultiply scaling tothis
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 indest
.scaleAroundLocal(double factor, double ox, double oy, double oz, Matrix4d dest)
Premultiply scaling to this matrix by scaling all three base axes by the givenfactor
while using(ox, oy, oz)
as the scaling origin, and store the result indest
.scaleLocal(double x, double y, double z, Matrix4d dest)
Premultiply scaling tothis
matrix by scaling the base axes by the given x, y and z factors and store the result indest
.scaleLocal(double xyz, Matrix4d dest)
Premultiply scaling tothis
matrix by scaling all base axes by the givenxyz
factor, and store the result indest
.Apply scaling to this matrix by by scaling the X axis byx
and the Y axis byy
and store the result indest
.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 equationx*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 indest
.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 equationy = 0
as if casting a shadow from a given light position/direction(lightX, lightY, lightZ, lightW)
and store the result indest
.Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equationx*a + y*b + z*c + d = 0
as if casting a shadow from a given light position/directionlight
and store the result indest
.Apply a projection transformation to this matrix that projects onto the plane with the general plane equationy = 0
as if casting a shadow from a given light position/directionlight
and store the result indest
.Componentwise subtractsubtrahend
fromthis
and store the result indest
.Componentwise subtract the upper 4x3 submatrices ofsubtrahend
fromthis
and store the result indest
.boolean
testAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ)
Test whether the given axisaligned box is partly or completely within or outside of the frustum defined bythis
matrix.boolean
testPoint(double x, double y, double z)
Test whether the given point(x, y, z)
is within the frustum defined bythis
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 bythis
matrix.Transform/multiply the vector(x, y, z, w)
by this matrix and store the result indest
.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 indest
.transformAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ, Vector3d outMin, Vector3d outMax)
Transform the axisaligned box given as the minimum corner(minX, minY, minZ)
and maximum corner(maxX, maxY, maxZ)
bythis
affine
matrix and compute the axisaligned box of the result whose minimum corner is stored inoutMin
and maximum corner stored inoutMax
.transformAab(Vector3dc min, Vector3dc max, Vector3d outMin, Vector3d outMax)
Transform the axisaligned box given as the minimum cornermin
and maximum cornermax
bythis
affine
matrix and compute the axisaligned box of the result whose minimum corner is stored inoutMin
and maximum corner stored inoutMax
.transformAffine(double x, double y, double z, double w, Vector4d dest)
Transform/multiply the 4Dvector(x, y, z, w)
by assuming thatthis
matrix represents anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and store the result indest
.Transform/multiply the given 4Dvector by assuming thatthis
matrix represents anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
).transformAffine(Vector4dc v, Vector4d dest)
Transform/multiply the given 4Dvector by assuming thatthis
matrix represents anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and store the result indest
.transformDirection(double x, double y, double z, Vector3d dest)
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.transformDirection(double x, double y, double z, Vector3f dest)
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result in that vector.transformDirection(Vector3dc v, Vector3d dest)
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result in that vector.transformDirection(Vector3fc v, Vector3f dest)
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.transformPosition(double x, double y, double z, Vector3d dest)
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=1, by this matrix and store the result indest
.Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=1, by this matrix and store the result in that vector.transformPosition(Vector3dc v, Vector3d dest)
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=1, by this matrix and store the result indest
.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 indest
.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 indest
.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 indest
.Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.transformProject(Vector3dc v, Vector3d dest)
Transform/multiply the given vector by this matrix, perform perspective divide and store the result indest
.Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.transformProject(Vector4dc v, Vector3d dest)
Transform/multiply the given vector by this matrix, perform perspective divide and store thex
,y
andz
components of the result indest
.transformProject(Vector4dc v, Vector4d dest)
Transform/multiply the given vector by this matrix, perform perspective divide and store the result indest
.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 indest
.Transform/multiply the given vector by the transpose of this matrix and store the result in that vector.transformTranspose(Vector4dc v, Vector4d dest)
Transform/multiply the given vector by the transpose of this matrix and store the result indest
.Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.translateLocal(double x, double y, double z, Matrix4d dest)
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.translateLocal(Vector3dc offset, Matrix4d dest)
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.translateLocal(Vector3fc offset, Matrix4d dest)
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.Transposethis
matrix and store the result intodest
.transpose3x3(Matrix3d dest)
Transpose only the upper left 3x3 submatrix of this matrix and store the result indest
.transpose3x3(Matrix4d dest)
Transpose only the upper left 3x3 submatrix of this matrix and store the result indest
.Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector3d dest)
Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector4d dest)
Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.unprojectInv(Vector3dc winCoords, int[] viewport, Vector3d dest)
Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.unprojectInv(Vector3dc winCoords, int[] viewport, Vector4d dest)
Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.unprojectInvRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest)
Unproject the given 2D window coordinates(winX, winY)
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +1.0
.unprojectInvRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest)
Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +1.0
.unprojectRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest)
Unproject the given 2D window coordinates(winX, winY)
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +1.0
.unprojectRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest)
Unproject the given 2D window coordinateswinCoords
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +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 bypositiveY(Vector3d)
) will be coplanar to the plane spanned by the local Z axis (as obtained bypositiveZ(Vector3d)
) and the given vector(upX, upY, upZ)
, and store the result indest
.withLookAtUp(Vector3dc up, Matrix4d dest)
Apply a transformation to this matrix to ensure that the local Y axis (as obtained bypositiveY(Vector3d)
) will be coplanar to the plane spanned by the local Z axis (as obtained bypositiveZ(Vector3d)
) and the given vectorup
, and store the result indest
.

Field Details

PLANE_NX
static final int PLANE_NXArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationx=1
when using the identity matrix. See Also:
 Constant Field Values

PLANE_PX
static final int PLANE_PXArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationx=1
when using the identity matrix. See Also:
 Constant Field Values

PLANE_NY
static final int PLANE_NYArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationy=1
when using the identity matrix. See Also:
 Constant Field Values

PLANE_PY
static final int PLANE_PYArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationy=1
when using the identity matrix. See Also:
 Constant Field Values

PLANE_NZ
static final int PLANE_NZArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationz=1
when using the identity matrix. See Also:
 Constant Field Values

PLANE_PZ
static final int PLANE_PZArgument to the first parameter offrustumPlane(int, Vector4d)
identifying the plane with equationz=1
when using the identity matrix. See Also:
 Constant Field Values

CORNER_NXNYNZ
static final int CORNER_NXNYNZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_PXNYNZ
static final int CORNER_PXNYNZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_PXPYNZ
static final int CORNER_PXPYNZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_NXPYNZ
static final int CORNER_NXPYNZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_PXNYPZ
static final int CORNER_PXNYPZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_NXNYPZ
static final int CORNER_NXNYPZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_NXPYPZ
static final int CORNER_NXPYPZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

CORNER_PXPYPZ
static final int CORNER_PXPYPZArgument to the first parameter offrustumCorner(int, Vector3d)
identifying the corner(1, 1, 1)
when using the identity matrix. See Also:
 Constant Field Values

PROPERTY_PERSPECTIVE
static final byte PROPERTY_PERSPECTIVEBit returned byproperties()
to indicate that the matrix represents a perspective transformation. See Also:
 Constant Field Values

PROPERTY_AFFINE
static final byte PROPERTY_AFFINEBit returned byproperties()
to indicate that the matrix represents an affine transformation. See Also:
 Constant Field Values

PROPERTY_IDENTITY
static final byte PROPERTY_IDENTITYBit returned byproperties()
to indicate that the matrix represents the identity transformation. See Also:
 Constant Field Values

PROPERTY_TRANSLATION
static final byte PROPERTY_TRANSLATIONBit returned byproperties()
to indicate that the matrix represents a pure translation transformation. See Also:
 Constant Field Values

PROPERTY_ORTHONORMAL
static final byte PROPERTY_ORTHONORMALBit returned byproperties()
to indicate that the upperleft 3x3 submatrix represents an orthogonal matrix (i.e. orthonormal basis). For practical reasons, this property also always impliesPROPERTY_AFFINE
in this implementation. See Also:
 Constant Field Values


Method Details

properties
int properties()Return the assumed properties of this matrix. This is a bitcombination ofPROPERTY_IDENTITY
,PROPERTY_AFFINE
,PROPERTY_TRANSLATION
andPROPERTY_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
Multiply this matrix by the suppliedright
matrix and store the result indest
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the multiplicationdest
 will hold the result Returns:
 dest

mul0
Multiply this matrix by the suppliedright
matrix and store the result indest
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first!This method neither assumes nor checks for any matrix properties of
this
orright
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 multiplicationdest
 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 indest
.If
M
isthis
matrix andR
theright
matrix whose elements are supplied via the parameters, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
r00
 the m00 element of the right matrixr01
 the m01 element of the right matrixr02
 the m02 element of the right matrixr03
 the m03 element of the right matrixr10
 the m10 element of the right matrixr11
 the m11 element of the right matrixr12
 the m12 element of the right matrixr13
 the m13 element of the right matrixr20
 the m20 element of the right matrixr21
 the m21 element of the right matrixr22
 the m22 element of the right matrixr23
 the m23 element of the right matrixr30
 the m30 element of the right matrixr31
 the m31 element of the right matrixr32
 the m32 element of the right matrixr33
 the m33 element of the right matrixdest
 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 indest
.If
M
isthis
matrix andR
theright
matrix whose elements are supplied via the parameters, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
r00
 the m00 element of the right matrixr01
 the m01 element of the right matrixr02
 the m02 element of the right matrixr10
 the m10 element of the right matrixr11
 the m11 element of the right matrixr12
 the m12 element of the right matrixr20
 the m20 element of the right matrixr21
 the m21 element of the right matrixr22
 the m22 element of the right matrixdest
 the destination matrix, which will hold the result Returns:
 this

mulLocal
Premultiply this matrix by the suppliedleft
matrix and store the result indest
.If
M
isthis
matrix andL
theleft
matrix, then the new matrix will beL * M
. So when transforming a vectorv
with the new matrix by usingL * M * v
, the transformation ofthis
matrix will be applied first! Parameters:
left
 the left operand of the matrix multiplicationdest
 the destination matrix, which will hold the result Returns:
 dest

mulLocalAffine
Premultiply this matrix by the suppliedleft
matrix, both of which are assumed to beaffine
, and store the result indest
.This method assumes that
this
matrix and the givenleft
matrix both represent anaffine
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 ofleft
.If
M
isthis
matrix andL
theleft
matrix, then the new matrix will beL * M
. So when transforming a vectorv
with the new matrix by usingL * M * v
, the transformation ofthis
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
Multiply this matrix by the suppliedright
matrix and store the result indest
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the matrix multiplicationdest
 the destination matrix, which will hold the result Returns:
 dest

mul
Multiply this matrix by the suppliedright
matrix and store the result indest
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the matrix multiplicationdest
 the destination matrix, which will hold the result Returns:
 dest

mul
Multiply this matrix by the suppliedright
matrix and store the result indest
.The last row of the
right
matrix is assumed to be(0, 0, 0, 1)
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the matrix multiplicationdest
 the destination matrix, which will hold the result Returns:
 dest

mul
Multiply this matrix by the suppliedright
matrix and store the result indest
.The last row of the
right
matrix is assumed to be(0, 0, 0, 1)
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the matrix multiplicationdest
 the destination matrix, which will hold the result Returns:
 dest

mul
Multiply this matrix by the supplied parameter matrix and store the result indest
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the transformation of the right matrix will be applied first! Parameters:
right
 the right operand of the multiplicationdest
 will hold the result Returns:
 dest

mulPerspectiveAffine
Multiplythis
symmetric perspective projection matrix by the suppliedaffine
view
matrix and store the result indest
.If
P
isthis
matrix andV
theview
matrix, then the new matrix will beP * V
. So when transforming a vectorv
with the new matrix by usingP * V * v
, the transformation of theview
matrix will be applied first! Parameters:
view
 theaffine
matrix to multiplythis
symmetric perspective projection matrix bydest
 the destination matrix, which will hold the result Returns:
 dest

mulPerspectiveAffine
Multiplythis
symmetric perspective projection matrix by the suppliedview
matrix and store the result indest
.If
P
isthis
matrix andV
theview
matrix, then the new matrix will beP * V
. So when transforming a vectorv
with the new matrix by usingP * V * v
, the transformation of theview
matrix will be applied first! Parameters:
view
 the matrix to multiplythis
symmetric perspective projection matrix bydest
 the destination matrix, which will hold the result Returns:
 dest

mulAffineR
Multiply this matrix by the suppliedright
matrix, which is assumed to beaffine
, and store the result indest
.This method assumes that the given
right
matrix represents anaffine
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
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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
Multiply this matrix by the suppliedright
matrix, both of which are assumed to beaffine
, and store the result indest
.This method assumes that
this
matrix and the givenright
matrix both represent anaffine
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 ofright
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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
Multiply this matrix, which is assumed to only contain a translation, by the suppliedright
matrix, which is assumed to beaffine
, and store the result indest
.This method assumes that
this
matrix only contains a translation, and that the givenright
matrix represents anaffine
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 ofright
.If
M
isthis
matrix andR
theright
matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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
Multiplythis
orthographic projection matrix by the suppliedaffine
view
matrix and store the result indest
.If
M
isthis
matrix andV
theview
matrix, then the new matrix will beM * V
. So when transforming a vectorv
with the new matrix by usingM * V * v
, the transformation of theview
matrix will be applied first! Parameters:
view
 the affine matrix which to multiplythis
withdest
 the destination matrix, which will hold the result Returns:
 dest

fma4x3
Componentwise add the upper 4x3 submatrices ofthis
andother
by first multiplying each component ofother
's 4x3 submatrix byotherFactor
, adding that tothis
and storing the final result indest
.The other components of
dest
will be set to the ones ofthis
.The matrices
this
andother
will not be changed. Parameters:
other
 the other matrixotherFactor
 the factor to multiply each of the other matrix's 4x3 componentsdest
 will hold the result Returns:
 dest

add
Componentwise addthis
andother
and store the result indest
. Parameters:
other
 the other addenddest
 will hold the result Returns:
 dest

sub
Componentwise subtractsubtrahend
fromthis
and store the result indest
. Parameters:
subtrahend
 the subtrahenddest
 will hold the result Returns:
 dest

mulComponentWise
Componentwise multiplythis
byother
and store the result indest
. Parameters:
other
 the other matrixdest
 will hold the result Returns:
 dest

add4x3
Componentwise add the upper 4x3 submatrices ofthis
andother
and store the result indest
.The other components of
dest
will be set to the ones ofthis
. Parameters:
other
 the other addenddest
 will hold the result Returns:
 dest

add4x3
Componentwise add the upper 4x3 submatrices ofthis
andother
and store the result indest
.The other components of
dest
will be set to the ones ofthis
. Parameters:
other
 the other addenddest
 will hold the result Returns:
 dest

sub4x3
Componentwise subtract the upper 4x3 submatrices ofsubtrahend
fromthis
and store the result indest
.The other components of
dest
will be set to the ones ofthis
. Parameters:
subtrahend
 the subtrahenddest
 will hold the result Returns:
 dest

mul4x3ComponentWise
Componentwise multiply the upper 4x3 submatrices ofthis
byother
and store the result indest
.The other components of
dest
will be set to the ones ofthis
. Parameters:
other
 the other matrixdest
 will hold the result Returns:
 dest

determinant
double determinant()Return the determinant of this matrix.If
this
matrix represents anaffine
transformation, such as translation, rotation, scaling and shearing, and thus its last row is equal to(0, 0, 0, 1)
, thendeterminantAffine()
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 anaffine
transformation and thus its last row is equal to(0, 0, 0, 1)
. Returns:
 the determinant

invert
Invertthis
matrix and store the result indest
.If
this
matrix represents anaffine
transformation, such as translation, rotation, scaling and shearing, and thus its last row is equal to(0, 0, 0, 1)
, theninvertAffine(Matrix4d)
can be used instead of this method. Parameters:
dest
 will hold the result Returns:
 dest
 See Also:
invertAffine(Matrix4d)

invertPerspective
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation, then this method builds the inverse ofthis
and stores it into the givendest
.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 ofthis
 Returns:
 dest
 See Also:
perspective(double, double, double, double, Matrix4d)

invertFrustum
Ifthis
is an arbitrary perspective projection matrix obtained via one of thefrustum()
methods, then this method builds the inverse ofthis
and stores it into the givendest
.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()
, theninvertPerspective(Matrix4d)
should be used instead. Parameters:
dest
 will hold the inverse ofthis
 Returns:
 dest
 See Also:
frustum(double, double, double, double, double, double, Matrix4d)
,invertPerspective(Matrix4d)

invertOrtho
Invertthis
orthographic projection matrix and store the result into the givendest
.This method can be used to quickly obtain the inverse of an orthographic projection matrix.
 Parameters:
dest
 will hold the inverse ofthis
 Returns:
 dest

invertPerspectiveView
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation and the givenview
matrix isaffine
and has unit scaling (for example by being obtained vialookAt()
), then this method builds the inverse ofthis * view
and stores it into the givendest
.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()
andlookAt()
or other methods, that build affine matrices, such astranslate
androtate(double, double, double, double, Matrix4d)
, except forscale()
.For the special cases of the matrices
this
andview
mentioned above, this method is equivalent to the following code:dest.set(this).mul(view).invert();
 Parameters:
view
 the view transformation (must beaffine
and have unit scaling)dest
 will hold the inverse ofthis * view
 Returns:
 dest

invertPerspectiveView
Ifthis
is a perspective projection matrix obtained via one of theperspective()
methods, that is, ifthis
is a symmetrical perspective frustum transformation and the givenview
matrix has unit scaling, then this method builds the inverse ofthis * view
and stores it into the givendest
.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()
andlookAt()
or other methods, that build affine matrices, such astranslate
androtate(double, double, double, double, Matrix4d)
, except forscale()
.For the special cases of the matrices
this
andview
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 ofthis * view
 Returns:
 dest

invertAffine
Invert this matrix by assuming that it is anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and write the result intodest
. Parameters:
dest
 will hold the result Returns:
 dest

transpose
Transposethis
matrix and store the result intodest
. Parameters:
dest
 will hold the result Returns:
 dest

transpose3x3
Transpose only the upper left 3x3 submatrix of this matrix and store the result indest
.All other matrix elements are left unchanged.
 Parameters:
dest
 will hold the result Returns:
 dest

transpose3x3
Transpose only the upper left 3x3 submatrix of this matrix and store the result indest
. Parameters:
dest
 will hold the result Returns:
 dest

getTranslation
Get only the translation components(m30, m31, m32)
of this matrix and store them in the given vectorxyz
. Parameters:
dest
 will hold the translation components of this matrix Returns:
 dest

getScale
Get the scaling factors ofthis
matrix for the three base axes. Parameters:
dest
 will hold the scaling factors forx
,y
andz
 Returns:
 dest

get
Get the current values ofthis
matrix and store them intodest
. Parameters:
dest
 the destination matrix Returns:
 the passed in destination

get4x3
Get the current values of the upper 4x3 submatrix ofthis
matrix and store them intodest
. Parameters:
dest
 the destination matrix Returns:
 the passed in destination

get3x3
Get the current values of the upper left 3x3 submatrix ofthis
matrix and store them intodest
. Parameters:
dest
 the destination matrix Returns:
 the passed in destination

getUnnormalizedRotation
Get the current values ofthis
matrix and store the represented rotation into the givenQuaternionf
.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 destinationQuaternionf
 Returns:
 the passed in destination
 See Also:
Quaternionf.setFromUnnormalized(Matrix4dc)

getNormalizedRotation
Get the current values ofthis
matrix and store the represented rotation into the givenQuaternionf
.This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
 Parameters:
dest
 the destinationQuaternionf
 Returns:
 the passed in destination
 See Also:
Quaternionf.setFromNormalized(Matrix4dc)

getUnnormalizedRotation
Get the current values ofthis
matrix and store the represented rotation into the givenQuaterniond
.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 destinationQuaterniond
 Returns:
 the passed in destination
 See Also:
Quaterniond.setFromUnnormalized(Matrix4dc)

getNormalizedRotation
Get the current values ofthis
matrix and store the represented rotation into the givenQuaterniond
.This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
 Parameters:
dest
 the destinationQuaterniond
 Returns:
 the passed in destination
 See Also:
Quaterniond.setFromNormalized(Matrix4dc)

get
Store this matrix in columnmajor order into the suppliedDoubleBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
get(int, DoubleBuffer)

get
Store this matrix in columnmajor order into the suppliedDoubleBuffer
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 theDoubleBuffer
buffer
 will receive the values of this matrix in columnmajor order Returns:
 the passed in buffer

get
Store this matrix in columnmajor order into the suppliedFloatBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
get(int, FloatBuffer)

get
Store this matrix in columnmajor order into the suppliedFloatBuffer
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 FloatBufferbuffer
 will receive the values of this matrix in columnmajor order Returns:
 the passed in buffer

get
Store this matrix in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
get(int, ByteBuffer)

get
Store this matrix in columnmajor order into the suppliedByteBuffer
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 ByteBufferbuffer
 will receive the values of this matrix in columnmajor order Returns:
 the passed in buffer

getToAddress
Store this matrix in columnmajor order at the given offheap 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 offheap address where to store this matrix Returns:
 this

getFloats
Store the elements of this matrix as float values in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
getFloats(int, ByteBuffer)

getFloats
Store the elements of this matrix as float values in columnmajor order into the suppliedByteBuffer
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 ByteBufferbuffer
 will receive the elements of this matrix as float values in columnmajor order Returns:
 the passed in buffer

get
double[] get(double[] arr, int offset)Store this matrix into the supplied double array in columnmajor order at the given offset. Parameters:
arr
 the array to write the matrix values intooffset
 the offset into the array Returns:
 the passed in array

get
double[] get(double[] arr)Store this matrix into the supplied double array in columnmajor 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 columnmajor 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 intooffset
 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 columnmajor 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
Store the transpose of this matrix in columnmajor order into the suppliedDoubleBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
getTransposed(int, DoubleBuffer)

getTransposed
Store the transpose of this matrix in columnmajor order into the suppliedDoubleBuffer
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 DoubleBufferbuffer
 will receive the values of this matrix in columnmajor order Returns:
 the passed in buffer

getTransposed
Store the transpose of this matrix in columnmajor order into the suppliedByteBuffer
at the current bufferposition
.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 columnmajor order at its current position Returns:
 the passed in buffer
 See Also:
getTransposed(int, ByteBuffer)

getTransposed
Store the transpose of this matrix in columnmajor order into the suppliedByteBuffer
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 ByteBufferbuffer
 will receive the values of this matrix in columnmajor order Returns:
 the passed in buffer

get4x3Transposed
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedDoubleBuffer
at the current bufferposition
.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 rowmajor order at its current position Returns:
 the passed in buffer
 See Also:
get4x3Transposed(int, DoubleBuffer)

get4x3Transposed
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedDoubleBuffer
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 DoubleBufferbuffer
 will receive the values of the upper 4x3 submatrix in rowmajor order Returns:
 the passed in buffer

get4x3Transposed
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedByteBuffer
at the current bufferposition
.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 rowmajor order at its current position Returns:
 the passed in buffer
 See Also:
get4x3Transposed(int, ByteBuffer)

get4x3Transposed
Store the upper 4x3 submatrix ofthis
matrix in rowmajor order into the suppliedByteBuffer
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 ByteBufferbuffer
 will receive the values of the upper 4x3 submatrix in rowmajor order Returns:
 the passed in buffer

transform
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
Transform/multiply the given vector by this matrix and store the result indest
. Parameters:
v
 the vector to transformdest
 will contain the result Returns:
 dest
 See Also:
Vector4d.mul(Matrix4dc, Vector4d)

transform
Transform/multiply the vector(x, y, z, w)
by this matrix and store the result indest
. Parameters:
x
 the x coordinate of the vector to transformy
 the y coordinate of the vector to transformz
 the z coordinate of the vector to transformw
 the w coordinate of the vector to transformdest
 will contain the result Returns:
 dest

transformTranspose
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
Transform/multiply the given vector by the transpose of this matrix and store the result indest
. Parameters:
v
 the vector to transform and to hold the final resultdest
 will contain the result Returns:
 dest
 See Also:
Vector4d.mulTranspose(Matrix4dc)

transformTranspose
Transform/multiply the vector(x, y, z, w)
by the transpose of this matrix and store the result indest
. Parameters:
x
 the x coordinate of the vector to transformy
 the y coordinate of the vector to transformz
 the z coordinate of the vector to transformw
 the w coordinate of the vector to transformdest
 will contain the result Returns:
 dest

transformProject
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
Transform/multiply the given vector by this matrix, perform perspective divide and store the result indest
. Parameters:
v
 the vector to transformdest
 will contain the result Returns:
 dest
 See Also:
Vector4d.mulProject(Matrix4dc, Vector4d)

transformProject
Transform/multiply the given vector by this matrix, perform perspective divide and store thex
,y
andz
components of the result indest
. Parameters:
v
 the vector to transformdest
 will contain the result Returns:
 dest
 See Also:
Vector3d.mulProject(Matrix4dc, Vector3d)

transformProject
Transform/multiply the vector(x, y, z, w)
by this matrix, perform perspective divide and store the result indest
. Parameters:
x
 the x coordinate of the direction to transformy
 the y coordinate of the direction to transformz
 the z coordinate of the direction to transformw
 the w coordinate of the direction to transformdest
 will contain the result Returns:
 dest

transformProject
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
Transform/multiply the given vector by this matrix, perform perspective divide and store the result indest
.This method uses
w=1.0
as the fourth vector component. Parameters:
v
 the vector to transformdest
 will contain the result Returns:
 dest
 See Also:
Vector3d.mulProject(Matrix4dc, Vector3d)

transformProject
Transform/multiply the vector(x, y, z)
by this matrix, perform perspective divide and store the result indest
.This method uses
w=1.0
as the fourth vector component. Parameters:
x
 the x coordinate of the vector to transformy
 the y coordinate of the vector to transformz
 the z coordinate of the vector to transformdest
 will contain the result Returns:
 dest

transformProject
Transform/multiply the vector(x, y, z, w)
by this matrix, perform perspective divide and store(x, y, z)
of the result indest
. Parameters:
x
 the x coordinate of the vector to transformy
 the y coordinate of the vector to transformz
 the z coordinate of the vector to transformw
 the w coordinate of the vector to transformdest
 will contain the(x, y, z)
components of the result Returns:
 dest

transformPosition
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=1, by this matrix and store the result in that vector.The given 3Dvector is treated as a 4Dvector with its wcomponent being 1.0, so it will represent a position/location in 3Dspace 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 usetransform(Vector4d)
ortransformProject(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
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=1, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being 1.0, so it will represent a position/location in 3Dspace 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 usetransform(Vector4dc, Vector4d)
ortransformProject(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 transformdest
 will hold the result Returns:
 dest
 See Also:
transformPosition(Vector3d)
,transform(Vector4dc, Vector4d)
,transformProject(Vector3dc, Vector3d)

transformPosition
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=1, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being 1.0, so it will represent a position/location in 3Dspace 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 usetransform(double, double, double, double, Vector4d)
ortransformProject(double, double, double, Vector3d)
when perspective divide should be applied, too. Parameters:
x
 the x coordinate of the positiony
 the y coordinate of the positionz
 the z coordinate of the positiondest
 will hold the result Returns:
 dest
 See Also:
transform(double, double, double, double, Vector4d)
,transformProject(double, double, double, Vector3d)

transformDirection
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result in that vector.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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 resultdest
 will hold the result Returns:
 dest

transformDirection
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result in that vector.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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
Transform/multiply the given 3Dvector, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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 resultdest
 will hold the result Returns:
 dest

transformDirection
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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 transformy
 the y coordinate of the direction to transformz
 the z coordinate of the direction to transformdest
 will hold the result Returns:
 dest

transformDirection
Transform/multiply the 3Dvector(x, y, z)
, as if it was a 4Dvector with w=0, by this matrix and store the result indest
.The given 3Dvector is treated as a 4Dvector with its wcomponent being
0.0
, so it will represent a direction in 3Dspace 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 transformy
 the y coordinate of the direction to transformz
 the z coordinate of the direction to transformdest
 will hold the result Returns:
 dest

transformAffine
Transform/multiply the given 4Dvector by assuming thatthis
matrix represents anaffine
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
Transform/multiply the given 4Dvector by assuming thatthis
matrix represents anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and store the result indest
.In order to store the result in the same vector, use
transformAffine(Vector4d)
. Parameters:
v
 the vector to transform and to hold the final resultdest
 will hold the result Returns:
 dest
 See Also:
transformAffine(Vector4d)

transformAffine
Transform/multiply the 4Dvector(x, y, z, w)
by assuming thatthis
matrix represents anaffine
transformation (i.e. its last row is equal to(0, 0, 0, 1)
) and store the result indest
. Parameters:
x
 the x coordinate of the direction to transformy
 the y coordinate of the direction to transformz
 the z coordinate of the direction to transformw
 the w coordinate of the direction to transformdest
 will hold the result Returns:
 dest

scale
Apply scaling tothis
matrix by scaling the base axes by the givenxyz.x
,xyz.y
andxyz.z
factors, respectively and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the scaling will be applied first! Parameters:
xyz
 the factors of the x, y and z component, respectivelydest
 will hold the result Returns:
 dest

scale
Apply scaling tothis
matrix by scaling the base axes by the given x, y and z factors and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the scaling will be applied first! Parameters:
x
 the factor of the x componenty
 the factor of the y componentz
 the factor of the z componentdest
 will hold the result Returns:
 dest

scale
Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the scaling will be applied first! Parameters:
xyz
 the factor for all componentsdest
 will hold the result Returns:
 dest
 See Also:
scale(double, double, double, Matrix4d)

scaleXY
Apply scaling to this matrix by by scaling the X axis byx
and the Y axis byy
and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the scaling will be applied first! Parameters:
x
 the factor of the x componenty
 the factor of the y componentdest
 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 tothis
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 indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * 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 componentsy
 the scaling factor of the y componentsz
 the scaling factor of the z componentox
 the x coordinate of the scaling originoy
 the y coordinate of the scaling originoz
 the z coordinate of the scaling origindest
 will hold the result Returns:
 dest

scaleAround
Apply scaling to this matrix by scaling all three base axes by the givenfactor
while using(ox, oy, oz)
as the scaling origin, and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * 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 axesox
 the x coordinate of the scaling originoy
 the y coordinate of the scaling originoz
 the z coordinate of the scaling origindest
 will hold the result Returns:
 this

scaleLocal
Premultiply scaling tothis
matrix by scaling all base axes by the givenxyz
factor, and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beS * M
. So when transforming a vectorv
with the new matrix by usingS * M * v
, the scaling will be applied last! Parameters:
xyz
 the factor to scale all three base axes bydest
 will hold the result Returns:
 dest

scaleLocal
Premultiply scaling tothis
matrix by scaling the base axes by the given x, y and z factors and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beS * M
. So when transforming a vectorv
with the new matrix by usingS * M * v
, the scaling will be applied last! Parameters:
x
 the factor of the x componenty
 the factor of the y componentz
 the factor of the z componentdest
 will hold the result Returns:
 dest

scaleAroundLocal
Matrix4d scaleAroundLocal(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest)Premultiply scaling tothis
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 indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beS * M
. So when transforming a vectorv
with the new matrix by usingS * 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 componentsy
 the scaling factor of the y componentsz
 the scaling factor of the z componentox
 the x coordinate of the scaling originoy
 the y coordinate of the scaling originoz
 the z coordinate of the scaling origindest
 will hold the result Returns:
 dest

scaleAroundLocal
Premultiply scaling to this matrix by scaling all three base axes by the givenfactor
while using(ox, oy, oz)
as the scaling origin, and store the result indest
.If
M
isthis
matrix andS
the scaling matrix, then the new matrix will beS * M
. So when transforming a vectorv
with the new matrix by usingS * 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 axesox
 the x coordinate of the scaling originoy
 the y coordinate of the scaling originoz
 the z coordinate of the scaling origindest
 will hold the result Returns:
 this

rotate
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 indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first! Parameters:
ang
 the angle is in radiansx
 the x component of the axisy
 the y component of the axisz
 the z component of the axisdest
 will hold the result Returns:
 dest

rotateTranslation
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 indest
.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 righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansx
 the x component of the axisy
 the y component of the axisz
 the z component of the axisdest
 will hold the result Returns:
 dest

rotateAffine
Apply rotation to thisaffine
matrix by rotating the given amount of radians about the specified(x, y, z)
axis and store the result indest
.This method assumes
this
to beaffine
.The axis described by the three components needs to be a unit vector.
When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansx
 the x component of the axisy
 the y component of the axisz
 the z component of the axisdest
 will hold the result Returns:
 dest

rotateAroundAffine
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to thisaffine
matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!This method is only applicable if
this
is anaffine
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
 theQuaterniondc
ox
 the x coordinate of the rotation originoy
 the y coordinate of the rotation originoz
 the z coordinate of the rotation origindest
 will hold the result Returns:
 dest

rotateAround
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * 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
 theQuaterniondc
ox
 the x coordinate of the rotation originoy
 the y coordinate of the rotation originoz
 the z coordinate of the rotation origindest
 will hold the result Returns:
 dest

rotateLocal
Premultiply a rotation to this matrix by rotating the given amount of radians about the specified(x, y, z)
axis and store the result indest
.The axis described by the three components needs to be a unit vector.
When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beR * M
. So when transforming a vectorv
with the new matrix by usingR * M * v
, the rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansx
 the x component of the axisy
 the y component of the axisz
 the z component of the axisdest
 will hold the result Returns:
 dest

rotateLocalX
Premultiply a rotation around the X axis to this matrix by rotating the given amount of radians about the X axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beR * M
. So when transforming a vectorv
with the new matrix by usingR * M * v
, the rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radians to rotate about the X axisdest
 will hold the result Returns:
 dest

rotateLocalY
Premultiply a rotation around the Y axis to this matrix by rotating the given amount of radians about the Y axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beR * M
. So when transforming a vectorv
with the new matrix by usingR * M * v
, the rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radians to rotate about the Y axisdest
 will hold the result Returns:
 dest

rotateLocalZ
Premultiply a rotation around the Z axis to this matrix by rotating the given amount of radians about the Z axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beR * M
. So when transforming a vectorv
with the new matrix by usingR * M * v
, the rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radians to rotate about the Z axisdest
 will hold the result Returns:
 dest

rotateAroundLocal
Premultiply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix while using(ox, oy, oz)
as the rotation origin, and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beQ * M
. So when transforming a vectorv
with the new matrix by usingQ * 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
 theQuaterniondc
ox
 the x coordinate of the rotation originoy
 the y coordinate of the rotation originoz
 the z coordinate of the rotation origindest
 will hold the result Returns:
 dest

translate
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beM * T
. So when transforming a vectorv
with the new matrix by usingM * T * v
, the translation will be applied first! Parameters:
offset
 the number of units in x, y and z by which to translatedest
 will hold the result Returns:
 dest

translate
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beM * T
. So when transforming a vectorv
with the new matrix by usingM * T * v
, the translation will be applied first! Parameters:
offset
 the number of units in x, y and z by which to translatedest
 will hold the result Returns:
 dest

translate
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beM * T
. So when transforming a vectorv
with the new matrix by usingM * T * v
, the translation will be applied first! Parameters:
x
 the offset to translate in xy
 the offset to translate in yz
 the offset to translate in zdest
 will hold the result Returns:
 dest

translateLocal
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beT * M
. So when transforming a vectorv
with the new matrix by usingT * M * v
, the translation will be applied last! Parameters:
offset
 the number of units in x, y and z by which to translatedest
 will hold the result Returns:
 dest

translateLocal
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beT * M
. So when transforming a vectorv
with the new matrix by usingT * M * v
, the translation will be applied last! Parameters:
offset
 the number of units in x, y and z by which to translatedest
 will hold the result Returns:
 dest

translateLocal
Premultiply a translation to this matrix by translating by the given number of units in x, y and z and store the result indest
.If
M
isthis
matrix andT
the translation matrix, then the new matrix will beT * M
. So when transforming a vectorv
with the new matrix by usingT * M * v
, the translation will be applied last! Parameters:
x
 the offset to translate in xy
 the offset to translate in yz
 the offset to translate in zdest
 will hold the result Returns:
 dest

rotateX
Apply rotation about the X axis to this matrix by rotating the given amount of radians and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansdest
 will hold the result Returns:
 dest

rotateY
Apply rotation about the Y axis to this matrix by rotating the given amount of radians and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansdest
 will hold the result Returns:
 dest

rotateZ
Apply rotation about the Z axis to this matrix by rotating the given amount of radians and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
ang
 the angle in radiansdest
 will hold the result Returns:
 dest

rotateTowardsXY
Apply rotation about the Z axis to align the local+X
towards(dirX, dirY)
and store the result indest
.If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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 directiondirY
 the y component of the normalized directiondest
 will hold the result Returns:
 this

rotateXYZ
Apply rotation ofangleX
radians about the X axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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 XangleY
 the angle to rotate about YangleZ
 the angle to rotate about Zdest
 will hold the result Returns:
 dest

rotateAffineXYZ
Apply rotation ofangleX
radians about the X axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
This method assumes that
this
matrix represents anaffine
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
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first! Parameters:
angleX
 the angle to rotate about XangleY
 the angle to rotate about YangleZ
 the angle to rotate about Zdest
 will hold the result Returns:
 dest

rotateZYX
Apply rotation ofangleZ
radians about the Z axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleX
radians about the X axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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 ZangleY
 the angle to rotate about YangleX
 the angle to rotate about Xdest
 will hold the result Returns:
 dest

rotateAffineZYX
Apply rotation ofangleZ
radians about the Z axis, followed by a rotation ofangleY
radians about the Y axis and followed by a rotation ofangleX
radians about the X axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
This method assumes that
this
matrix represents anaffine
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
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first! Parameters:
angleZ
 the angle to rotate about ZangleY
 the angle to rotate about YangleX
 the angle to rotate about Xdest
 will hold the result Returns:
 dest

rotateYXZ
Apply rotation ofangleY
radians about the Y axis, followed by a rotation ofangleX
radians about the X axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * 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 YangleX
 the angle to rotate about XangleZ
 the angle to rotate about Zdest
 will hold the result Returns:
 dest

rotateAffineYXZ
Apply rotation ofangleY
radians about the Y axis, followed by a rotation ofangleX
radians about the X axis and followed by a rotation ofangleZ
radians about the Z axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
This method assumes that
this
matrix represents anaffine
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
isthis
matrix andR
the rotation matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the rotation will be applied first! Parameters:
angleY
 the angle to rotate about YangleX
 the angle to rotate about XangleZ
 the angle to rotate about Zdest
 will hold the result Returns:
 dest

rotate
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaterniondc
dest
 will hold the result Returns:
 dest

rotate
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaternionfc
dest
 will hold the result Returns:
 dest

rotateAffine
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to thisaffine
matrix and store the result indest
.This method assumes
this
to beaffine
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaterniondc
dest
 will hold the result Returns:
 dest

rotateTranslation
Apply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix, which is assumed to only contain a translation, and store the result indest
.This method assumes
this
to only contain a translation.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaterniondc
dest
 will hold the result Returns:
 dest

rotateTranslation
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix, which is assumed to only contain a translation, and store the result indest
.This method assumes
this
to only contain a translation.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaternionfc
dest
 will hold the result Returns:
 dest

rotateLocal
Premultiply the rotation  and possibly scaling  transformation of the givenQuaterniondc
to this matrix and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beQ * M
. So when transforming a vectorv
with the new matrix by usingQ * M * v
, the quaternion rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaterniondc
dest
 will hold the result Returns:
 dest

rotateAffine
Apply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to thisaffine
matrix and store the result indest
.This method assumes
this
to beaffine
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beM * Q
. So when transforming a vectorv
with the new matrix by usingM * Q * v
, the quaternion rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaternionfc
dest
 will hold the result Returns:
 dest

rotateLocal
Premultiply the rotation  and possibly scaling  transformation of the givenQuaternionfc
to this matrix and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andQ
the rotation matrix obtained from the given quaternion, then the new matrix will beQ * M
. So when transforming a vectorv
with the new matrix by usingQ * M * v
, the quaternion rotation will be applied last!Reference: http://en.wikipedia.org
 Parameters:
quat
 theQuaternionfc
dest
 will hold the result Returns:
 dest

rotate
Apply a rotation transformation, rotating about the givenAxisAngle4f
and store the result indest
.The axis described by the
axis
vector needs to be a unit vector.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andA
the rotation matrix obtained from the givenAxisAngle4f
, then the new matrix will beM * A
. So when transforming a vectorv
with the new matrix by usingM * A * v
, theAxisAngle4f
rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
axisAngle
 theAxisAngle4f
(needs to benormalized
)dest
 will hold the result Returns:
 dest
 See Also:
rotate(double, double, double, double, Matrix4d)

rotate
Apply a rotation transformation, rotating about the givenAxisAngle4d
and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andA
the rotation matrix obtained from the givenAxisAngle4d
, then the new matrix will beM * A
. So when transforming a vectorv
with the new matrix by usingM * A * v
, theAxisAngle4d
rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
axisAngle
 theAxisAngle4d
(needs to benormalized
)dest
 will hold the result Returns:
 dest
 See Also:
rotate(double, double, double, double, Matrix4d)

rotate
Apply a rotation transformation, rotating the given radians about the specified axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andA
the rotation matrix obtained from the given angle and axis, then the new matrix will beM * A
. So when transforming a vectorv
with the new matrix by usingM * A * v
, the axisangle rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
angle
 the angle in radiansaxis
 the rotation axis (needs to benormalized
)dest
 will hold the result Returns:
 dest
 See Also:
rotate(double, double, double, double, Matrix4d)

rotate
Apply a rotation transformation, rotating the given radians about the specified axis and store the result indest
.When used with a righthanded coordinate system, the produced rotation will rotate a vector counterclockwise around the rotation axis, when viewing along the negative axis direction towards the origin. When used with a lefthanded coordinate system, the rotation is clockwise.
If
M
isthis
matrix andA
the rotation matrix obtained from the given angle and axis, then the new matrix will beM * A
. So when transforming a vectorv
with the new matrix by usingM * A * v
, the axisangle rotation will be applied first!Reference: http://en.wikipedia.org
 Parameters:
angle
 the angle in radiansaxis
 the rotation axis (needs to benormalized
)dest
 will hold the result Returns:
 dest
 See Also:
rotate(double, double, double, double, Matrix4d)

getRow
Get the row at the givenrow
index, starting with0
. Parameters:
row
 the row index in[0..3]
dest
 will hold the row components Returns:
 the passed in destination
 Throws:
IndexOutOfBoundsException
 ifrow
is not in[0..3]

getRow
Get the first three components of the row at the givenrow
index, starting with0
. Parameters:
row
 the row index in[0..3]
dest
 will hold the first three row components Returns:
 the passed in destination
 Throws:
IndexOutOfBoundsException
 ifrow
is not in[0..3]

getColumn
Get the column at the givencolumn
index, starting with0
. Parameters:
column
 the column index in[0..3]
dest
 will hold the column components Returns:
 the passed in destination
 Throws:
IndexOutOfBoundsException
 ifcolumn
is not in[0..3]

getColumn
Get the first three components of the column at the givencolumn
index, starting with0
. Parameters:
column
 the column index in[0..3]
dest
 will hold the first three column components Returns:
 the passed in destination
 Throws:
IndexOutOfBoundsException
 ifcolumn
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
Compute a normal matrix from the upper left 3x3 submatrix ofthis
and store it into the upper left 3x3 submatrix ofdest
. All other values ofdest
will be set to identity.The normal matrix of
m
is the transpose of the inverse ofm
. Parameters:
dest
 will hold the result Returns:
 dest

normal
Compute a normal matrix from the upper left 3x3 submatrix ofthis
and store it intodest
.The normal matrix of
m
is the transpose of the inverse ofm
. Parameters:
dest
 will hold the result Returns:
 dest
 See Also:
get3x3(Matrix3d)

cofactor3x3
Compute the cofactor matrix of the upper left 3x3 submatrix ofthis
and store it intodest
.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
Compute the cofactor matrix of the upper left 3x3 submatrix ofthis
and store it intodest
. All other values ofdest
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
Normalize the upper left 3x3 submatrix of this matrix and store the result indest
.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
Normalize the upper left 3x3 submatrix of this matrix and store the result indest
.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
Unproject the given window coordinates(winX, winY, winZ)
bythis
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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInv()
can be invoked on it. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)winZ
 the zcoordinate, 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
Unproject the given window coordinates(winX, winY, winZ)
bythis
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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInv()
can be invoked on it. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)winZ
 the zcoordinate, 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
Unproject the given window coordinateswinCoords
bythis
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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInv()
can be invoked on it. Parameters:
winCoords
 the window coordinates to unprojectviewport
 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
Unproject the given window coordinateswinCoords
bythis
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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInv()
can be invoked on it. Parameters:
winCoords
 the window coordinates to unprojectviewport
 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)
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInvRay()
can be invoked on it. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)viewport
 the viewport described by[x, y, width, height]
originDest
 will hold the ray origindirDest
 will hold the (unnormalized) ray direction Returns:
 this
 See Also:
unprojectInvRay(double, double, int[], Vector3d, Vector3d)
,invert(Matrix4d)

unprojectRay
Unproject the given 2D window coordinateswinCoords
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +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 ofthis
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 ofthis
matrix can be built once outside usinginvert(Matrix4d)
and then the methodunprojectInvRay()
can be invoked on it. Parameters:
winCoords
 the window coordinates to unprojectviewport
 the viewport described by[x, y, width, height]
originDest
 will hold the ray origindirDest
 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
Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.This method differs from
unproject()
in that it assumes thatthis
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 bythis
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 unprojectviewport
 the viewport described by[x, y, width, height]
dest
 will hold the unprojected position Returns:
 dest
 See Also:
unproject(Vector3dc, int[], Vector4d)

unprojectInv
Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.This method differs from
unproject()
in that it assumes thatthis
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 bythis
matrix.The depth range of
winZ
is assumed to be[0..1]
, which is also the OpenGL default. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)winZ
 the zcoordinate, 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
Unproject the given window coordinateswinCoords
bythis
matrix using the specified viewport.This method differs from
unproject()
in that it assumes thatthis
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 bythis
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 unprojectviewport
 the viewport described by[x, y, width, height]
dest
 will hold the unprojected position Returns:
 dest
 See Also:
unproject(Vector3dc, int[], Vector3d)

unprojectInv
Unproject the given window coordinates(winX, winY, winZ)
bythis
matrix using the specified viewport.This method differs from
unproject()
in that it assumes thatthis
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 bythis
matrix.The depth range of
winZ
is assumed to be[0..1]
, which is also the OpenGL default. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)winZ
 the zcoordinate, 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 coordinateswinCoords
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +1.0
.This method differs from
unprojectRay()
in that it assumes thatthis
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 unprojectviewport
 the viewport described by[x, y, width, height]
originDest
 will hold the ray origindirDest
 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)
bythis
matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDCz = 1.0
and goes through NDCz = +1.0
.This method differs from
unprojectRay()
in that it assumes thatthis
is already the inverse matrix of the original projection matrix. It exists to avoid recomputing the matrix inverse with every invocation. Parameters:
winX
 the xcoordinate in window coordinates (pixels)winY
 the ycoordinate in window coordinates (pixels)viewport
 the viewport described by[x, y, width, height]
originDest
 will hold the ray origindirDest
 will hold the (unnormalized) ray direction Returns:
 this
 See Also:
unprojectRay(double, double, int[], Vector3d, Vector3d)

project
Project the given(x, y, z)
position viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.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 givenviewport
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 xcoordinate of the position to projecty
 the ycoordinate of the position to projectz
 the zcoordinate of the position to projectviewport
 the viewport described by[x, y, width, height]
winCoordsDest
 will hold the projected window coordinates Returns:
 winCoordsDest

project
Project the given(x, y, z)
position viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.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 givenviewport
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 xcoordinate of the position to projecty
 the ycoordinate of the position to projectz
 the zcoordinate of the position to projectviewport
 the viewport described by[x, y, width, height]
winCoordsDest
 will hold the projected window coordinates Returns:
 winCoordsDest

project
Project the givenposition
viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.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 givenviewport
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 coordinatesviewport
 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
Project the givenposition
viathis
matrix using the specified viewport and store the resulting window coordinates inwinCoordsDest
.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 givenviewport
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 coordinatesviewport
 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
Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the equationx*a + y*b + z*c + d = 0
and store the result indest
.The vector
(a, b, c)
must be a unit vector.If
M
isthis
matrix andR
the reflection matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the reflection will be applied first!Reference: msdn.microsoft.com
 Parameters:
a
 the x factor in the plane equationb
 the y factor in the plane equationc
 the z factor in the plane equationd
 the constant in the plane equationdest
 will hold the result Returns:
 dest

reflect
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 indest
.If
M
isthis
matrix andR
the reflection matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the reflection will be applied first! Parameters:
nx
 the xcoordinate of the plane normalny
 the ycoordinate of the plane normalnz
 the zcoordinate of the plane normalpx
 the xcoordinate of a point on the planepy
 the ycoordinate of a point on the planepz
 the zcoordinate of a point on the planedest
 will hold the result Returns:
 dest

reflect
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 indest
.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 givenQuaterniondc
is the identity (does not apply any additional rotation), the reflection plane will bez=0
, offset by the givenpoint
.If
M
isthis
matrix andR
the reflection matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the reflection will be applied first! Parameters:
orientation
 the plane orientationpoint
 a point on the planedest
 will hold the result Returns:
 dest

reflect
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 indest
.If
M
isthis
matrix andR
the reflection matrix, then the new matrix will beM * R
. So when transforming a vectorv
with the new matrix by usingM * R * v
, the reflection will be applied first! Parameters:
normal
 the plane normalpoint
 a point on the planedest
 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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgezNear
 near clipping plane distancezFar
 far clipping plane distancezZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
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 righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgezNear
 near clipping plane distancezFar
 far clipping plane distancedest
 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 lefthanded coordiante system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgezNear
 near clipping plane distancezFar
 far clipping plane distancezZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
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 lefthanded coordiante system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgezNear
 near clipping plane distancezFar
 far clipping plane distancedest
 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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.This method is equivalent to calling
ortho()
withleft=width/2
,right=+width/2
,bottom=height/2
andtop=+height/2
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgesheight
 the distance between the top and bottom frustum edgeszNear
 near clipping plane distancezFar
 far clipping plane distancedest
 will hold the resultzZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 dest

orthoSymmetric
Apply a symmetric orthographic projection transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.This method is equivalent to calling
ortho()
withleft=width/2
,right=+width/2
,bottom=height/2
andtop=+height/2
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgesheight
 the distance between the top and bottom frustum edgeszNear
 near clipping plane distancezFar
 far clipping plane distancedest
 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 lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.This method is equivalent to calling
orthoLH()
withleft=width/2
,right=+width/2
,bottom=height/2
andtop=+height/2
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgesheight
 the distance between the top and bottom frustum edgeszNear
 near clipping plane distancezFar
 far clipping plane distancedest
 will hold the resultzZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 dest

orthoSymmetricLH
Apply a symmetric orthographic projection transformation for a lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.This method is equivalent to calling
orthoLH()
withleft=width/2
,right=+width/2
,bottom=height/2
andtop=+height/2
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgesheight
 the distance between the top and bottom frustum edgeszNear
 near clipping plane distancezFar
 far clipping plane distancedest
 will hold the result Returns:
 dest

ortho2D
Apply an orthographic projection transformation for a righthanded coordinate system to this matrix and store the result indest
.This method is equivalent to calling
ortho()
withzNear=1
andzFar=+1
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgedest
 will hold the result Returns:
 dest
 See Also:
ortho(double, double, double, double, double, double, Matrix4d)

ortho2DLH
Apply an orthographic projection transformation for a lefthanded coordinate system to this matrix and store the result indest
.This method is equivalent to calling
orthoLH()
withzNear=1
andzFar=+1
.If
M
isthis
matrix andO
the orthographic projection matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 edgeright
 the distance from the center to the right frustum edgebottom
 the distance from the center to the bottom frustum edgetop
 the distance from the center to the top frustum edgedest
 will hold the result Returns:
 dest
 See Also:
orthoLH(double, double, double, double, double, double, Matrix4d)

lookAlong
Apply a rotation transformation to this matrix to makez
point alongdir
and store the result indest
.If
M
isthis
matrix andL
the lookalong rotation matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookalong rotation transformation will be applied first!This is equivalent to calling
lookAt
witheye = (0, 0, 0)
andcenter = dir
. Parameters:
dir
 the direction in space to look alongup
 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 makez
point alongdir
and store the result indest
.If
M
isthis
matrix andL
the lookalong rotation matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookalong rotation transformation will be applied first!This is equivalent to calling
lookAt()
witheye = (0, 0, 0)
andcenter = dir
. Parameters:
dirX
 the xcoordinate of the direction to look alongdirY
 the ycoordinate of the direction to look alongdirZ
 the zcoordinate of the direction to look alongupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 will hold the result Returns:
 dest
 See Also:
lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)

lookAt
Apply a "lookat" transformation to this matrix for a righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eye
 the position of the cameracenter
 the point in space to look atup
 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 righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eyeX
 the xcoordinate of the eye/camera locationeyeY
 the ycoordinate of the eye/camera locationeyeZ
 the zcoordinate of the eye/camera locationcenterX
 the xcoordinate of the point to look atcenterY
 the ycoordinate of the point to look atcenterZ
 the zcoordinate of the point to look atupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 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 righthanded coordinate system, that alignsz
withcenter  eye
and store the result indest
.This method assumes
this
to be a perspective transformation, obtained viafrustum()
orperspective()
or one of their overloads.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eyeX
 the xcoordinate of the eye/camera locationeyeY
 the ycoordinate of the eye/camera locationeyeZ
 the zcoordinate of the eye/camera locationcenterX
 the xcoordinate of the point to look atcenterY
 the ycoordinate of the point to look atcenterZ
 the zcoordinate of the point to look atupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 will hold the result Returns:
 dest

lookAtLH
Apply a "lookat" transformation to this matrix for a lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eye
 the position of the cameracenter
 the point in space to look atup
 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 lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eyeX
 the xcoordinate of the eye/camera locationeyeY
 the ycoordinate of the eye/camera locationeyeZ
 the zcoordinate of the eye/camera locationcenterX
 the xcoordinate of the point to look atcenterY
 the ycoordinate of the point to look atcenterZ
 the zcoordinate of the point to look atupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 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 lefthanded coordinate system, that aligns+z
withcenter  eye
and store the result indest
.This method assumes
this
to be a perspective transformation, obtained viafrustumLH()
orperspectiveLH()
or one of their overloads.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * L * v
, the lookat transformation will be applied first! Parameters:
eyeX
 the xcoordinate of the eye/camera locationeyeY
 the ycoordinate of the eye/camera locationeyeZ
 the zcoordinate of the eye/camera locationcenterX
 the xcoordinate of the point to look atcenterY
 the ycoordinate of the point to look atcenterZ
 the zcoordinate of the point to look atupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)aspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.dest
 will hold the resultzZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 dest

perspective
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)aspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * P * v
, the perspective projection will be applied first! Parameters:
width
 the width of the near frustum planeheight
 the height of the near frustum planezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.dest
 will hold the resultzZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 dest

perspectiveRect
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * P * v
, the perspective projection will be applied first! Parameters:
width
 the width of the near frustum planeheight
 the height of the near frustum planezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 righthanded coordinate system the given NDC z range to this matrix.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * P * v
, the perspective projection will be applied first! Parameters:
width
 the width of the near frustum planeheight
 the height of the near frustum planezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.zZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 this

perspectiveRect
Apply a symmetric perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * P * v
, the perspective projection will be applied first! Parameters:
width
 the width of the near frustum planeheight
 the height of the near frustum planezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 offcenter perspective projection frustum transformation for a righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.The given angles
offAngleX
andoffAngleY
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, whenoffAngleY
is justfovy/2
then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZplane.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)offAngleX
 the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planesoffAngleY
 the vertical angle between the line of sight and the line crossing the center of the near and far frustum planesaspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.dest
 will hold the resultzZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 dest

perspectiveOffCenter
Matrix4d perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar, Matrix4d dest)Apply an asymmetric offcenter perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.The given angles
offAngleX
andoffAngleY
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, whenoffAngleY
is justfovy/2
then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZplane.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)offAngleX
 the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planesoffAngleY
 the vertical angle between the line of sight and the line crossing the center of the near and far frustum planesaspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 offcenter perspective projection frustum transformation using for a righthanded coordinate system the given NDC z range to this matrix.The given angles
offAngleX
andoffAngleY
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, whenoffAngleY
is justfovy/2
then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZplane.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)offAngleX
 the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planesoffAngleY
 the vertical angle between the line of sight and the line crossing the center of the near and far frustum planesaspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.zZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
 Returns:
 this

perspectiveOffCenter
Matrix4d perspectiveOffCenter(double fovy, double offAngleX, double offAngleY, double aspect, double zNear, double zFar)Apply an asymmetric offcenter perspective projection frustum transformation for a righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix.The given angles
offAngleX
andoffAngleY
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, whenoffAngleY
is justfovy/2
then the projection frustum is rotated towards +Y and the bottom frustum plane is parallel to the XZplane.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)offAngleX
 the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planesoffAngleY
 the vertical angle between the line of sight and the line crossing the center of the near and far frustum planesaspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)aspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.zZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
dest
 will hold the result Returns:
 dest

perspectiveLH
Apply a symmetric perspective projection frustum transformation for a lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andP
the perspective projection matrix, then the new matrix will beM * P
. So when transforming a vectorv
with the new matrix by usingM * 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 thanPI
)aspect
 the aspect ratio (i.e. width / height; must be greater than zero)zNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 righthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andF
the frustum matrix, then the new matrix will beM * F
. So when transforming a vectorv
with the new matrix by usingM * F * v
, the frustum transformation will be applied first!Reference: http://www.songho.ca
 Parameters:
left
 the distance along the xaxis to the left frustum edgeright
 the distance along the xaxis to the right frustum edgebottom
 the distance along the yaxis to the bottom frustum edgetop
 the distance along the yaxis to the top frustum edgezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.zZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
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 righthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andF
the frustum matrix, then the new matrix will beM * F
. So when transforming a vectorv
with the new matrix by usingM * F * v
, the frustum transformation will be applied first!Reference: http://www.songho.ca
 Parameters:
left
 the distance along the xaxis to the left frustum edgeright
 the distance along the xaxis to the right frustum edgebottom
 the distance along the yaxis to the bottom frustum edgetop
 the distance along the yaxis to the top frustum edgezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.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 lefthanded coordinate system using the given NDC z range to this matrix and store the result indest
.If
M
isthis
matrix andF
the frustum matrix, then the new matrix will beM * F
. So when transforming a vectorv
with the new matrix by usingM * F * v
, the frustum transformation will be applied first!Reference: http://www.songho.ca
 Parameters:
left
 the distance along the xaxis to the left frustum edgeright
 the distance along the xaxis to the right frustum edgebottom
 the distance along the yaxis to the bottom frustum edgetop
 the distance along the yaxis to the top frustum edgezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.zZeroToOne
 whether to use Vulkan's and Direct3D's NDC z range of[0..+1]
whentrue
or whether to use OpenGL's NDC z range of[1..+1]
whenfalse
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 lefthanded coordinate system using OpenGL's NDC z range of[1..+1]
to this matrix and store the result indest
.If
M
isthis
matrix andF
the frustum matrix, then the new matrix will beM * F
. So when transforming a vectorv
with the new matrix by usingM * F * v
, the frustum transformation will be applied first!Reference: http://www.songho.ca
 Parameters:
left
 the distance along the xaxis to the left frustum edgeright
 the distance along the xaxis to the right frustum edgebottom
 the distance along the yaxis to the bottom frustum edgetop
 the distance along the yaxis to the top frustum edgezNear
 near clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the near clipping plane will be at positive infinity. In that case,zFar
may not also beDouble.POSITIVE_INFINITY
.zFar
 far clipping plane distance. If the special valueDouble.POSITIVE_INFINITY
is used, the far clipping plane will be at positive infinity. In that case,zNear
may not also beDouble.POSITIVE_INFINITY
.dest
 will hold the result Returns:
 dest

frustumPlane
Calculate a frustum plane ofthis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givendest
.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 givenVector4d
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 usinga*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 axisaligned boxes.Reference: Fast Extraction of Viewing Frustum Planes from the WorldViewProjection Matrix

frustumCorner
Compute the corner coordinates of the frustum defined bythis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givenpoint
.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 WorldViewProjection Matrix
 Parameters:
corner
 one of the eight possible corners, given as numeric constantsCORNER_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
Compute the eye/origin of the perspective frustum transformation defined bythis
matrix, which can be a projection matrix or a combined modelviewprojection matrix, and store the result in the givenorigin
.Note that this method will only work using perspective projections obtained via one of the perspective methods, such as
perspective()
orfrustum()
.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 ofthis
matrix, the methodperspectiveInvOrigin(Vector3d)
on the inverse of the matrix should be used instead.Reference: http://geomalgorithms.com
Reference: Fast Extraction of Viewing Frustum Planes from the WorldViewProjection Matrix
 Parameters:
origin
 will hold the origin of the coordinate system before applyingthis
perspective projection transformation Returns:
 origin

perspectiveInvOrigin
Compute the eye/origin of the inverse of the perspective frustum transformation defined bythis
matrix, which can be the inverse of a projection matrix or the inverse of a combined modelviewprojection matrix, and store the result in the givendest
.Note that this method will only work using perspective projections obtained via one of the perspective methods, such as
perspective()
orfrustum()
.If the inverse of the modelviewprojection matrix is not available, then calling
perspectiveOrigin(Vector3d)
on the original modelviewprojection matrix is preferred. Parameters:
dest
 will hold the result Returns:
 dest
 See Also:
perspectiveOrigin(Vector3d)

perspectiveFov
double perspectiveFov()Return the vertical fieldofview 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()
orfrustum()
.For orthogonal transformations this method will return
0.0
.Reference: Fast Extraction of Viewing Frustum Planes from the WorldViewProjection Matrix
 Returns:
 the vertical fieldofview angle in radians

perspectiveNear
double perspectiveNear()Extract the near clip plane distance fromthis
perspective projection matrix.This method only works if
this
is a perspective projection matrix, for example obtained viaperspective(double, double, double, double, Matrix4d)
. Returns:
 the near clip plane distance

perspectiveFar
double perspectiveFar()Extract the far clip plane distance fromthis
perspective projection matrix.This method only works if
this
is a perspective projection matrix, for example obtained viaperspective(double, double, double, double, Matrix4d)
. Returns:
 the far clip plane distance

frustumRayDir
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 beforethis
transformation was applied to it in order to yield homogeneous clipping space.The parameters
x
andy
are used to interpolate the generated ray direction from the bottomleft to the topright 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 theFrustumRayBuilder
.Reference: Fast Extraction of Viewing Frustum Planes from the WorldViewProjection Matrix
 Parameters:
x
 the interpolation factor along the lefttoright frustum planes, within[0..1]
y
 the interpolation factor along the bottomtotop 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 usingthis
matrix Returns:
 dir

positiveZ
Obtain the direction of+Z
before the transformation represented bythis
matrix is applied.This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to
+Z
bythis
matrix.This method is equivalent to the following code:
Matrix4d inv = new Matrix4d(this).invert(); inv.transformDirection(dir.set(0, 0, 1)).normalize();
Ifthis
is already an orthogonal matrix, then consider usingnormalizedPositiveZ(Vector3d)
instead.Reference: http://www.euclideanspace.com
 Parameters:
dir
 will hold the direction of+Z
 Returns:
 dir

normalizedPositiveZ
Obtain the direction of+Z
before the transformation represented bythis
orthogonal matrix is applied. This method only produces correct results ifthis
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
bythis
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
Obtain the direction of+X
before the transformation represented bythis
matrix is applied.This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to
+X
bythis
matrix.This method is equivalent to the following code:
Matrix4d inv = new Matrix4d(this).invert(); inv.transformDirection(dir.set(1, 0, 0)).normalize();
Ifthis
is already an orthogonal matrix, then consider usingnormalizedPositiveX(Vector3d)
instead.Reference: http://www.euclideanspace.com
 Parameters:
dir
 will hold the direction of+X
 Returns:
 dir

normalizedPositiveX
Obtain the direction of+X
before the transformation represented bythis
orthogonal matrix is applied. This method only produces correct results ifthis
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
bythis
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
Obtain the direction of+Y
before the transformation represented bythis
matrix is applied.This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to
+Y
bythis
matrix.This method is equivalent to the following code:
Matrix4d inv = new Matrix4d(this).invert(); inv.transformDirection(dir.set(0, 1, 0)).normalize();
Ifthis
is already an orthogonal matrix, then consider usingnormalizedPositiveY(Vector3d)
instead.Reference: http://www.euclideanspace.com
 Parameters:
dir
 will hold the direction of+Y
 Returns:
 dir

normalizedPositiveY
Obtain the direction of+Y
before the transformation represented bythis
orthogonal matrix is applied. This method only produces correct results ifthis
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
bythis
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
Obtain the position that gets transformed to the origin bythis
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
Obtain the position that gets transformed to the origin bythis
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
Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equationx*a + y*b + z*c + d = 0
as if casting a shadow from a given light position/directionlight
and store the result indest
.If
light.w
is0.0
the light is being treated as a directional light; if it is1.0
it is a point light.If
M
isthis
matrix andS
the shadow matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the reflection will be applied first!Reference: ftp.sgi.com
 Parameters:
light
 the light's vectora
 the x factor in the plane equationb
 the y factor in the plane equationc
 the z factor in the plane equationd
 the constant in the plane equationdest
 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 equationx*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 indest
.If
lightW
is0.0
the light is being treated as a directional light; if it is1.0
it is a point light.If
M
isthis
matrix andS
the shadow matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the reflection will be applied first!Reference: ftp.sgi.com
 Parameters:
lightX
 the xcomponent of the light's vectorlightY
 the ycomponent of the light's vectorlightZ
 the zcomponent of the light's vectorlightW
 the wcomponent of the light's vectora
 the x factor in the plane equationb
 the y factor in the plane equationc
 the z factor in the plane equationd
 the constant in the plane equationdest
 will hold the result Returns:
 dest

shadow
Apply a projection transformation to this matrix that projects onto the plane with the general plane equationy = 0
as if casting a shadow from a given light position/directionlight
and store the result indest
.Before the shadow projection is applied, the plane is transformed via the specified
planeTransformation
.If
light.w
is0.0
the light is being treated as a directional light; if it is1.0
it is a point light.If
M
isthis
matrix andS
the shadow matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the reflection will be applied first! Parameters:
light
 the light's vectorplaneTransform
 the transformation to transform the implied planey = 0
before applying the projectiondest
 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 equationy = 0
as if casting a shadow from a given light position/direction(lightX, lightY, lightZ, lightW)
and store the result indest
.Before the shadow projection is applied, the plane is transformed via the specified
planeTransformation
.If
lightW
is0.0
the light is being treated as a directional light; if it is1.0
it is a point light.If
M
isthis
matrix andS
the shadow matrix, then the new matrix will beM * S
. So when transforming a vectorv
with the new matrix by usingM * S * v
, the reflection will be applied first! Parameters:
lightX
 the xcomponent of the light vectorlightY
 the ycomponent of the light vectorlightZ
 the zcomponent of the light vectorlightW
 the wcomponent of the light vectorplaneTransform
 the transformation to transform the implied planey = 0
before applying the projectiondest
 will hold the result Returns:
 dest

pick
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 indest
. Parameters:
x
 the x coordinate of the picking region center in window coordinatesy
 the y coordinate of the picking region center in window coordinateswidth
 the width of the picking region in window coordinatesheight
 the height of the picking region in window coordinatesviewport
 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 givenradius
and center(centerX, centerY, centerZ)
position of the arcball and the specified X and Y rotation angles, and store the result indest
.This method is equivalent to calling:
translate(0, 0, radius, dest).rotateX(angleX).rotateY(angleY).translate(centerX, centerY, centerZ)
 Parameters:
radius
 the arcball radiuscenterX
 the x coordinate of the center position of the arcballcenterY
 the y coordinate of the center position of the arcballcenterZ
 the z coordinate of the center position of the arcballangleX
 the rotation angle around the X axis in radiansangleY
 the rotation angle around the Y axis in radiansdest
 will hold the result Returns:
 dest

arcball
Apply an arcball view transformation to this matrix with the givenradius
andcenter
position of the arcball and the specified X and Y rotation angles, and store the result indest
.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 radiuscenter
 the center position of the arcballangleX
 the rotation angle around the X axis in radiansangleY
 the rotation angle around the Y axis in radiansdest
 will hold the result Returns:
 dest

projectedGridRange
Compute the range matrix for the Projected Grid transformation as described in chapter "2.4.2 Creating the range conversion matrix" of the paper Realtime water rendering  Introducing the projected grid concept based on the inverse of the viewprojection matrix which is assumed to bethis
, and store that range matrix intodest
.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 viewprojection transformationsLower
 the lower (smallest) Ycoordinate which any transformed vertex might have while still being visible on the projected gridsUpper
 the upper (highest) Ycoordinate which any transformed vertex might have while still being visible on the projected griddest
 will hold the resulting range matrix Returns:
 the computed range matrix; or
null
if the projected grid will not be visible

perspectiveFrustumSlice
Change the near and far clip plane distances ofthis
perspective frustum transformation matrix and store the result indest
.This method only works if
this
is a perspective projection frustum transformation, for example obtained viaperspective()
orfrustum()
. Parameters:
near
 the new near clip plane distancefar
 the new far clip plane distancedest
 will hold the resulting matrix Returns:
 dest
 See Also:
perspective(double, double, double, double, Matrix4d)
,frustum(double, double, double, double, double, double, Matrix4d)

orthoCrop
Build an ortographic projection transformation that fits the viewprojection transformation represented bythis
into the given affineview
transformation.The transformation represented by
this
must be given as theinverse
of a typical combined camera viewprojection transformation, whose projection can be either orthographic or perspective.The
view
must be anaffine
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 vialookAt()
.Reference: OpenGL SDK  Cascaded Shadow Maps
 Parameters:
view
 the view transformation to build a corresponding orthographic projection to fit the frustum ofthis
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 axisaligned box given as the minimum corner(minX, minY, minZ)
and maximum corner(maxX, maxY, maxZ)
bythis
affine
matrix and compute the axisaligned box of the result whose minimum corner is stored inoutMin
and maximum corner stored inoutMax
.Reference: http://dev.theomader.com
 Parameters:
minX
 the x coordinate of the minimum corner of the axisaligned boxminY
 the y coordinate of the minimum corner of the axisaligned boxminZ
 the z coordinate of the minimum corner of the axisaligned boxmaxX
 the x coordinate of the maximum corner of the axisaligned boxmaxY
 the y coordinate of the maximum corner of the axisaligned boxmaxZ
 the y coordinate of the maximum corner of the axisaligned boxoutMin
 will hold the minimum corner of the resulting axisaligned boxoutMax
 will hold the maximum corner of the resulting axisaligned box Returns:
 this

transformAab
Transform the axisaligned box given as the minimum cornermin
and maximum cornermax
bythis
affine
matrix and compute the axisaligned box of the result whose minimum corner is stored inoutMin
and maximum corner stored inoutMax
. Parameters:
min
 the minimum corner of the axisaligned boxmax
 the maximum corner of the axisaligned boxoutMin
 will hold the minimum corner of the resulting axisaligned boxoutMax
 will hold the maximum corner of the resulting axisaligned box Returns:
 this

lerp
Linearly interpolatethis
andother
using the given interpolation factort
and store the result indest
.If
t
is0.0
then the result isthis
. If the interpolation factor is1.0
then the result isother
. Parameters:
other
 the other matrixt
 the interpolation factor between 0.0 and 1.0dest
 will hold the result Returns:
 dest

rotateTowards
Apply a model transformation to this matrix for a righthanded coordinate system, that aligns the local+Z
axis withdirection
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * 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 towardsup
 the up vectordest
 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 righthanded coordinate system, that aligns the local+Z
axis withdir
and store the result indest
.If
M
isthis
matrix andL
the lookat matrix, then the new matrix will beM * L
. So when transforming a vectorv
with the new matrix by usingM * 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 xcoordinate of the direction to rotate towardsdirY
 the ycoordinate of the direction to rotate towardsdirZ
 the zcoordinate of the direction to rotate towardsupX
 the xcoordinate of the up vectorupY
 the ycoordinate of the up vectorupZ
 the zcoordinate of the up vectordest
 will hold the result Returns:
 dest
 See Also:
rotateTowards(Vector3dc, Vector3dc, Matrix4d)

getEulerAnglesZYX
Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix ofthis
and store the extracted Euler angles indest
.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 callingrotateZYX(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 matrixm2
should be identical tom
(disregarding possible floatingpoint 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 bythis
matrix.This method assumes
this
matrix to be a transformation from any arbitrary coordinate system/spaceM
into standard OpenGL clip space and tests whether the given point with the coordinates(x, y, z)
given in spaceM
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 WorldViewProjection Matrix
 Parameters:
x
 the xcoordinate of the pointy
 the ycoordinate of the pointz
 the zcoordinate 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 bythis
matrix.This method assumes
this
matrix to be a transformation from any arbitrary coordinate system/spaceM
into standard OpenGL clip space and tests whether the given sphere with the coordinates(x, y, z)
given in spaceM
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 WorldViewProjection Matrix
 Parameters:
x
 the xcoordinate of the sphere's centery
 the ycoordinate of the sphere's centerz
 the zcoordinate of the sphere's centerr
 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 axisaligned box is partly or completely within or outside of the frustum defined bythis
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/spaceM
into standard OpenGL clip space and tests whether the given axisaligned box with its minimum corner coordinates(minX, minY, minZ)
and maximum corner coordinates(maxX, maxY, maxZ)
given in spaceM
is within the clip space.When testing multiple axisaligned 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 WorldViewProjection Matrix Parameters:
minX
 the xcoordinate of the minimum cornerminY
 the ycoordinate of the minimum cornerminZ
 the zcoordinate of the minimum cornermaxX
 the xcoordinate of the maximum cornermaxY
 the ycoordinate of the maximum cornermaxZ
 the zcoordinate of the maximum corner Returns:
true
if the axisaligned box is completely or partly inside of the frustum;false
otherwise

obliqueZ
Apply an oblique projection transformation to this matrix with the given values fora
andb
and store the result indest
.If
M
isthis
matrix andO
the oblique transformation matrix, then the new matrix will beM * O
. So when transforming a vectorv
with the new matrix by usingM * 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 xb
 the value for the z factor that applies to ydest
 will hold the result Returns:
 dest

withLookAtUp
Apply a transformation to this matrix to ensure that the local Y axis (as obtained bypositiveY(Vector3d)
) will be coplanar to the plane spanned by the local Z axis (as obtained bypositiveZ(Vector3d)
) and the given vectorup
, and store the result indest
.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 byoriginAffine(Vector3d)
), the sum of this position and the negated local Z axis as well as the given vectorup
.This method must only be called on
isAffine()
matrices. Parameters:
up
 the up vectordest
 will hold the result Returns:
 this

withLookAtUp
Apply a transformation to this matrix to ensure that the local Y axis (as obtained bypositiveY(Vector3d)
) will be coplanar to the plane spanned by the local Z axis (as obtained bypositiveZ(Vector3d)
) and the given vector(upX, upY, upZ)
, and store the result indest
.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 byoriginAffine(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 vectorupY
 the y coordinate of the up vectorupZ
 the z coordinate of the up vectordest
 will hold the result Returns:
 this

equals
Compare the matrix elements ofthis
matrix with the given matrix using the givendelta
and return whether all of them are equal within a maximum difference ofdelta
.Please note that this method is not used by any data structure such as
ArrayList
HashSet
orHashMap
and their operations, such asArrayList.contains(Object)
orHashSet.remove(Object)
, since those data structures only use theObject.equals(Object)
andObject.hashCode()
methods. Parameters:
m
 the other matrixdelta
 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 floatingpoint values, that is, they are notNaN
and notinfinity
. Returns:
true
if all components are finite floatingpoint values;false
otherwise
