Package org.joml

## Interface Matrix4dc

• All Known Implementing Classes:
`Matrix4d`, `Matrix4dStack`

`public interface Matrix4dc`
Interface to a read-only view of a 4x4 matrix of double-precision floats.
Author:
Kai Burjack
• ### Method Summary

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

• #### m00

`double m00()`
Return the value of the matrix element at column 0 and row 0.
Returns:
the value of the matrix element
• #### m01

`double m01()`
Return the value of the matrix element at column 0 and row 1.
Returns:
the value of the matrix element
• #### m02

`double m02()`
Return the value of the matrix element at column 0 and row 2.
Returns:
the value of the matrix element
• #### m03

`double m03()`
Return the value of the matrix element at column 0 and row 3.
Returns:
the value of the matrix element
• #### m10

`double m10()`
Return the value of the matrix element at column 1 and row 0.
Returns:
the value of the matrix element
• #### m11

`double m11()`
Return the value of the matrix element at column 1 and row 1.
Returns:
the value of the matrix element
• #### m12

`double m12()`
Return the value of the matrix element at column 1 and row 2.
Returns:
the value of the matrix element
• #### m13

`double m13()`
Return the value of the matrix element at column 1 and row 3.
Returns:
the value of the matrix element
• #### m20

`double m20()`
Return the value of the matrix element at column 2 and row 0.
Returns:
the value of the matrix element
• #### m21

`double m21()`
Return the value of the matrix element at column 2 and row 1.
Returns:
the value of the matrix element
• #### m22

`double m22()`
Return the value of the matrix element at column 2 and row 2.
Returns:
the value of the matrix element
• #### m23

`double m23()`
Return the value of the matrix element at column 2 and row 3.
Returns:
the value of the matrix element
• #### m30

`double m30()`
Return the value of the matrix element at column 3 and row 0.
Returns:
the value of the matrix element
• #### m31

`double m31()`
Return the value of the matrix element at column 3 and row 1.
Returns:
the value of the matrix element
• #### m32

`double m32()`
Return the value of the matrix element at column 3 and row 2.
Returns:
the value of the matrix element
• #### m33

`double m33()`
Return the value of the matrix element at column 3 and row 3.
Returns:
the value of the matrix element
• #### mul

```Matrix4d mul​(Matrix4dc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix and store the result in `dest`.

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

Parameters:
`right` - the right operand of the multiplication
`dest` - will hold the result
Returns:
dest
• #### mulLocal

```Matrix4d mulLocal​(Matrix4dc left,
Matrix4d dest)```
Pre-multiply this matrix by the supplied `left` matrix and store the result in `dest`.

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

Parameters:
`left` - the left operand of the matrix multiplication
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mulLocalAffine

```Matrix4d mulLocalAffine​(Matrix4dc left,
Matrix4d dest)```
Pre-multiply this matrix by the supplied `left` matrix, both of which are assumed to be `affine`, and store the result in `dest`.

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

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

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

Parameters:
`left` - the left operand of the matrix multiplication (the last row is assumed to be `(0, 0, 0, 1)`)
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mul

```Matrix4d mul​(Matrix3x2dc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix and store the result in `dest`.

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

Parameters:
`right` - the right operand of the matrix multiplication
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mul

```Matrix4d mul​(Matrix3x2fc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix and store the result in `dest`.

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

Parameters:
`right` - the right operand of the matrix multiplication
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mul

```Matrix4d mul​(Matrix4x3dc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix and store the result in `dest`.

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

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

Parameters:
`right` - the right operand of the matrix multiplication
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mul

```Matrix4d mul​(Matrix4x3fc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix and store the result in `dest`.

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

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

Parameters:
`right` - the right operand of the matrix multiplication
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mul

```Matrix4d mul​(Matrix4fc right,
Matrix4d dest)```
Multiply this matrix by the supplied parameter matrix and store the result in `dest`.

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

Parameters:
`right` - the right operand of the multiplication
`dest` - will hold the result
Returns:
dest
• #### mulPerspectiveAffine

```Matrix4d mulPerspectiveAffine​(Matrix4dc view,
Matrix4d dest)```
Multiply `this` symmetric perspective projection matrix by the supplied `affine` `view` matrix and store the result in `dest`.

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

Parameters:
`view` - the `affine` matrix to multiply `this` symmetric perspective projection matrix by
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mulAffineR

```Matrix4d mulAffineR​(Matrix4dc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix, which is assumed to be `affine`, and store the result in `dest`.

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

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

Parameters:
`right` - the right operand of the matrix multiplication (the last row is assumed to be `(0, 0, 0, 1)`)
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mulAffine

```Matrix4d mulAffine​(Matrix4dc right,
Matrix4d dest)```
Multiply this matrix by the supplied `right` matrix, both of which are assumed to be `affine`, and store the result in `dest`.

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

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

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

Parameters:
`right` - the right operand of the matrix multiplication (the last row is assumed to be `(0, 0, 0, 1)`)
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mulTranslationAffine

```Matrix4d mulTranslationAffine​(Matrix4dc right,
Matrix4d dest)```
Multiply this matrix, which is assumed to only contain a translation, by the supplied `right` matrix, which is assumed to be `affine`, and store the result in `dest`.

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

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

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

Parameters:
`right` - the right operand of the matrix multiplication (the last row is assumed to be `(0, 0, 0, 1)`)
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### mulOrthoAffine

```Matrix4d mulOrthoAffine​(Matrix4dc view,
Matrix4d dest)```
Multiply `this` orthographic projection matrix by the supplied `affine` `view` matrix and store the result in `dest`.

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

Parameters:
`view` - the affine matrix which to multiply `this` with
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### fma4x3

```Matrix4d fma4x3​(Matrix4dc other,
double otherFactor,
Matrix4d dest)```
Component-wise add the upper 4x3 submatrices of `this` and `other` by first multiplying each component of `other`'s 4x3 submatrix by `otherFactor`, adding that to `this` and storing the final result in `dest`.

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

The matrices `this` and `other` will not be changed.

Parameters:
`other` - the other matrix
`otherFactor` - the factor to multiply each of the other matrix's 4x3 components
`dest` - will hold the result
Returns:
dest

```Matrix4d add​(Matrix4dc other,
Matrix4d dest)```
Component-wise add `this` and `other` and store the result in `dest`.
Parameters:
`other` - the other addend
`dest` - will hold the result
Returns:
dest
• #### sub

```Matrix4d sub​(Matrix4dc subtrahend,
Matrix4d dest)```
Component-wise subtract `subtrahend` from `this` and store the result in `dest`.
Parameters:
`subtrahend` - the subtrahend
`dest` - will hold the result
Returns:
dest
• #### mulComponentWise

```Matrix4d mulComponentWise​(Matrix4dc other,
Matrix4d dest)```
Component-wise multiply `this` by `other` and store the result in `dest`.
Parameters:
`other` - the other matrix
`dest` - will hold the result
Returns:
dest

```Matrix4d add4x3​(Matrix4dc other,
Matrix4d dest)```
Component-wise add the upper 4x3 submatrices of `this` and `other` and store the result in `dest`.

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

Parameters:
`other` - the other addend
`dest` - will hold the result
Returns:
dest

```Matrix4d add4x3​(Matrix4fc other,
Matrix4d dest)```
Component-wise add the upper 4x3 submatrices of `this` and `other` and store the result in `dest`.

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

Parameters:
`other` - the other addend
`dest` - will hold the result
Returns:
dest
• #### sub4x3

```Matrix4d sub4x3​(Matrix4dc subtrahend,
Matrix4d dest)```
Component-wise subtract the upper 4x3 submatrices of `subtrahend` from `this` and store the result in `dest`.

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

Parameters:
`subtrahend` - the subtrahend
`dest` - will hold the result
Returns:
dest
• #### mul4x3ComponentWise

```Matrix4d mul4x3ComponentWise​(Matrix4dc other,
Matrix4d dest)```
Component-wise multiply the upper 4x3 submatrices of `this` by `other` and store the result in `dest`.

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

Parameters:
`other` - the other matrix
`dest` - will hold the result
Returns:
dest
• #### determinant

`double determinant()`
Return the determinant of this matrix.

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

Returns:
the determinant
`determinantAffine()`
• #### determinant3x3

`double determinant3x3()`
Return the determinant of the upper left 3x3 submatrix of this matrix.
Returns:
the determinant
• #### determinantAffine

`double determinantAffine()`
Return the determinant of this matrix by assuming that it represents an `affine` transformation and thus its last row is equal to `(0, 0, 0, 1)`.
Returns:
the determinant
• #### invert

`Matrix4d invert​(Matrix4d dest)`
Invert `this` matrix and store the result in `dest`.

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

Parameters:
`dest` - will hold the result
Returns:
dest
`invertAffine(Matrix4d)`
• #### invertPerspective

`Matrix4d invertPerspective​(Matrix4d dest)`
If `this` is a perspective projection matrix obtained via one of the `perspective()` methods, that is, if `this` is a symmetrical perspective frustum transformation, then this method builds the inverse of `this` and stores it into the given `dest`.

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

Parameters:
`dest` - will hold the inverse of `this`
Returns:
dest
`perspective(double, double, double, double, Matrix4d)`
• #### invertOrtho

`Matrix4d invertOrtho​(Matrix4d dest)`
Invert `this` orthographic projection matrix and store the result into the given `dest`.

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

Parameters:
`dest` - will hold the inverse of `this`
Returns:
dest
• #### invertPerspectiveView

```Matrix4d invertPerspectiveView​(Matrix4dc view,
Matrix4d dest)```
If `this` is a perspective projection matrix obtained via one of the `perspective()` methods, that is, if `this` is a symmetrical perspective frustum transformation and the given `view` matrix is `affine` and has unit scaling (for example by being obtained via `lookAt()`), then this method builds the inverse of `this * view` and stores it into the given `dest`.

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

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

``` dest.set(this).mul(view).invert();
```
Parameters:
`view` - the view transformation (must be `affine` and have unit scaling)
`dest` - will hold the inverse of `this * view`
Returns:
dest
• #### invertPerspectiveView

```Matrix4d invertPerspectiveView​(Matrix4x3dc view,
Matrix4d dest)```
If `this` is a perspective projection matrix obtained via one of the `perspective()` methods, that is, if `this` is a symmetrical perspective frustum transformation and the given `view` matrix has unit scaling, then this method builds the inverse of `this * view` and stores it into the given `dest`.

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

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

``` dest.set(this).mul(view).invert();
```
Parameters:
`view` - the view transformation (must have unit scaling)
`dest` - will hold the inverse of `this * view`
Returns:
dest
• #### invertAffine

`Matrix4d invertAffine​(Matrix4d dest)`
Invert this matrix by assuming that it is an `affine` transformation (i.e. its last row is equal to `(0, 0, 0, 1)`) and write the result into `dest`.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### transpose

`Matrix4d transpose​(Matrix4d dest)`
Transpose `this` matrix and store the result into `dest`.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### transpose3x3

`Matrix4d transpose3x3​(Matrix4d dest)`
Transpose only the upper left 3x3 submatrix of this matrix and store the result in `dest`.

All other matrix elements are left unchanged.

Parameters:
`dest` - will hold the result
Returns:
dest
• #### transpose3x3

`Matrix3d transpose3x3​(Matrix3d dest)`
Transpose only the upper left 3x3 submatrix of this matrix and store the result in `dest`.
Parameters:
`dest` - will hold the result
Returns:
dest
• #### getTranslation

`Vector3d getTranslation​(Vector3d dest)`
Get only the translation components `(m30, m31, m32)` of this matrix and store them in the given vector `xyz`.
Parameters:
`dest` - will hold the translation components of this matrix
Returns:
dest
• #### getScale

`Vector3d getScale​(Vector3d dest)`
Get the scaling factors of `this` matrix for the three base axes.
Parameters:
`dest` - will hold the scaling factors for `x`, `y` and `z`
Returns:
dest
• #### get

`Matrix4d get​(Matrix4d dest)`
Get the current values of `this` matrix and store them into `dest`.
Parameters:
`dest` - the destination matrix
Returns:
the passed in destination
• #### get4x3

`Matrix4x3d get4x3​(Matrix4x3d dest)`
Get the current values of the upper 4x3 submatrix of `this` matrix and store them into `dest`.
Parameters:
`dest` - the destination matrix
Returns:
the passed in destination
• #### get3x3

`Matrix3d get3x3​(Matrix3d dest)`
Get the current values of the upper left 3x3 submatrix of `this` matrix and store them into `dest`.
Parameters:
`dest` - the destination matrix
Returns:
the passed in destination
• #### getUnnormalizedRotation

`Quaternionf getUnnormalizedRotation​(Quaternionf dest)`
Get the current values of `this` matrix and store the represented rotation into the given `Quaternionf`.

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

Parameters:
`dest` - the destination `Quaternionf`
Returns:
the passed in destination
`Quaternionf.setFromUnnormalized(Matrix4dc)`
• #### getNormalizedRotation

`Quaternionf getNormalizedRotation​(Quaternionf dest)`
Get the current values of `this` matrix and store the represented rotation into the given `Quaternionf`.

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

Parameters:
`dest` - the destination `Quaternionf`
Returns:
the passed in destination
`Quaternionf.setFromNormalized(Matrix4dc)`
• #### getUnnormalizedRotation

`Quaterniond getUnnormalizedRotation​(Quaterniond dest)`
Get the current values of `this` matrix and store the represented rotation into the given `Quaterniond`.

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

Parameters:
`dest` - the destination `Quaterniond`
Returns:
the passed in destination
`Quaterniond.setFromUnnormalized(Matrix4dc)`
• #### getNormalizedRotation

`Quaterniond getNormalizedRotation​(Quaterniond dest)`
Get the current values of `this` matrix and store the represented rotation into the given `Quaterniond`.

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

Parameters:
`dest` - the destination `Quaterniond`
Returns:
the passed in destination
`Quaterniond.setFromNormalized(Matrix4dc)`
• #### get

`java.nio.DoubleBuffer get​(java.nio.DoubleBuffer buffer)`
Store this matrix in column-major order into the supplied `DoubleBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of this matrix in column-major order at its current position
Returns:
the passed in buffer
`get(int, DoubleBuffer)`
• #### get

```java.nio.DoubleBuffer get​(int index,
java.nio.DoubleBuffer buffer)```
Store this matrix in column-major order into the supplied `DoubleBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the `DoubleBuffer`
`buffer` - will receive the values of this matrix in column-major order
Returns:
the passed in buffer
• #### get

`java.nio.FloatBuffer get​(java.nio.FloatBuffer buffer)`
Store this matrix in column-major order into the supplied `FloatBuffer` at the current buffer `position`.

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

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

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

Parameters:
`buffer` - will receive the values of this matrix in column-major order at its current position
Returns:
the passed in buffer
`get(int, FloatBuffer)`
• #### get

```java.nio.FloatBuffer get​(int index,
java.nio.FloatBuffer buffer)```
Store this matrix in column-major order into the supplied `FloatBuffer` starting at the specified absolute buffer position/index.

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

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

Parameters:
`index` - the absolute position into the FloatBuffer
`buffer` - will receive the values of this matrix in column-major order
Returns:
the passed in buffer
• #### get

`java.nio.ByteBuffer get​(java.nio.ByteBuffer buffer)`
Store this matrix in column-major order into the supplied `ByteBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of this matrix in column-major order at its current position
Returns:
the passed in buffer
`get(int, ByteBuffer)`
• #### get

```java.nio.ByteBuffer get​(int index,
java.nio.ByteBuffer buffer)```
Store this matrix in column-major order into the supplied `ByteBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the ByteBuffer
`buffer` - will receive the values of this matrix in column-major order
Returns:
the passed in buffer

`Matrix4dc getToAddress​(long address)`
Store this matrix in column-major order at the given off-heap address.

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

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

Parameters:
`address` - the off-heap address where to store this matrix
Returns:
this
• #### getFloats

`java.nio.ByteBuffer getFloats​(java.nio.ByteBuffer buffer)`
Store the elements of this matrix as float values in column-major order into the supplied `ByteBuffer` at the current buffer `position`.

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

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

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

Parameters:
`buffer` - will receive the elements of this matrix as float values in column-major order at its current position
Returns:
the passed in buffer
`getFloats(int, ByteBuffer)`
• #### getFloats

```java.nio.ByteBuffer getFloats​(int index,
java.nio.ByteBuffer buffer)```
Store the elements of this matrix as float values in column-major order into the supplied `ByteBuffer` starting at the specified absolute buffer position/index.

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

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

Parameters:
`index` - the absolute position into the ByteBuffer
`buffer` - will receive the elements of this matrix as float values in column-major order
Returns:
the passed in buffer
• #### get

```double[] get​(double[] arr,
int offset)```
Store this matrix into the supplied double array in column-major order at the given offset.
Parameters:
`arr` - the array to write the matrix values into
`offset` - the offset into the array
Returns:
the passed in array
• #### get

`double[] get​(double[] arr)`
Store this matrix into the supplied double array in column-major order.

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

Parameters:
`arr` - the array to write the matrix values into
Returns:
the passed in array
`get(double[], int)`
• #### get

```float[] get​(float[] arr,
int offset)```
Store the elements of this matrix as float values in column-major order into the supplied float array at the given offset.

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

Parameters:
`arr` - the array to write the matrix values into
`offset` - the offset into the array
Returns:
the passed in array
• #### get

`float[] get​(float[] arr)`
Store the elements of this matrix as float values in column-major order into the supplied float array.

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

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

Parameters:
`arr` - the array to write the matrix values into
Returns:
the passed in array
`get(float[], int)`
• #### getTransposed

`java.nio.DoubleBuffer getTransposed​(java.nio.DoubleBuffer buffer)`
Store the transpose of this matrix in column-major order into the supplied `DoubleBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of this matrix in column-major order at its current position
Returns:
the passed in buffer
`getTransposed(int, DoubleBuffer)`
• #### getTransposed

```java.nio.DoubleBuffer getTransposed​(int index,
java.nio.DoubleBuffer buffer)```
Store the transpose of this matrix in column-major order into the supplied `DoubleBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the DoubleBuffer
`buffer` - will receive the values of this matrix in column-major order
Returns:
the passed in buffer
• #### getTransposed

`java.nio.ByteBuffer getTransposed​(java.nio.ByteBuffer buffer)`
Store the transpose of this matrix in column-major order into the supplied `ByteBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of this matrix in column-major order at its current position
Returns:
the passed in buffer
`getTransposed(int, ByteBuffer)`
• #### getTransposed

```java.nio.ByteBuffer getTransposed​(int index,
java.nio.ByteBuffer buffer)```
Store the transpose of this matrix in column-major order into the supplied `ByteBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the ByteBuffer
`buffer` - will receive the values of this matrix in column-major order
Returns:
the passed in buffer
• #### get4x3Transposed

`java.nio.DoubleBuffer get4x3Transposed​(java.nio.DoubleBuffer buffer)`
Store the upper 4x3 submatrix of `this` matrix in row-major order into the supplied `DoubleBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of the upper 4x3 submatrix in row-major order at its current position
Returns:
the passed in buffer
`get4x3Transposed(int, DoubleBuffer)`
• #### get4x3Transposed

```java.nio.DoubleBuffer get4x3Transposed​(int index,
java.nio.DoubleBuffer buffer)```
Store the upper 4x3 submatrix of `this` matrix in row-major order into the supplied `DoubleBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the DoubleBuffer
`buffer` - will receive the values of the upper 4x3 submatrix in row-major order
Returns:
the passed in buffer
• #### get4x3Transposed

`java.nio.ByteBuffer get4x3Transposed​(java.nio.ByteBuffer buffer)`
Store the upper 4x3 submatrix of `this` matrix in row-major order into the supplied `ByteBuffer` at the current buffer `position`.

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

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

Parameters:
`buffer` - will receive the values of the upper 4x3 submatrix in row-major order at its current position
Returns:
the passed in buffer
`get4x3Transposed(int, ByteBuffer)`
• #### get4x3Transposed

```java.nio.ByteBuffer get4x3Transposed​(int index,
java.nio.ByteBuffer buffer)```
Store the upper 4x3 submatrix of `this` matrix in row-major order into the supplied `ByteBuffer` starting at the specified absolute buffer position/index.

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

Parameters:
`index` - the absolute position into the ByteBuffer
`buffer` - will receive the values of the upper 4x3 submatrix in row-major order
Returns:
the passed in buffer
• #### transform

`Vector4d transform​(Vector4d v)`
Transform/multiply the given vector by this matrix and store the result in that vector.
Parameters:
`v` - the vector to transform and to hold the final result
Returns:
v
`Vector4d.mul(Matrix4dc)`
• #### transform

```Vector4d transform​(Vector4dc v,
Vector4d dest)```
Transform/multiply the given vector by this matrix and store the result in `dest`.
Parameters:
`v` - the vector to transform
`dest` - will contain the result
Returns:
dest
`Vector4d.mul(Matrix4dc, Vector4d)`
• #### transform

```Vector4d transform​(double x,
double y,
double z,
double w,
Vector4d dest)```
Transform/multiply the vector `(x, y, z, w)` by this matrix and store the result in `dest`.
Parameters:
`x` - the x coordinate of the vector to transform
`y` - the y coordinate of the vector to transform
`z` - the z coordinate of the vector to transform
`w` - the w coordinate of the vector to transform
`dest` - will contain the result
Returns:
dest
• #### transformProject

`Vector4d transformProject​(Vector4d v)`
Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
Parameters:
`v` - the vector to transform and to hold the final result
Returns:
v
`Vector4d.mulProject(Matrix4dc)`
• #### transformProject

```Vector4d transformProject​(Vector4dc v,
Vector4d dest)```
Transform/multiply the given vector by this matrix, perform perspective divide and store the result in `dest`.
Parameters:
`v` - the vector to transform
`dest` - will contain the result
Returns:
dest
`Vector4d.mulProject(Matrix4dc, Vector4d)`
• #### transformProject

```Vector4d transformProject​(double x,
double y,
double z,
double w,
Vector4d dest)```
Transform/multiply the vector `(x, y, z, w)` by this matrix, perform perspective divide and store the result in `dest`.
Parameters:
`x` - the x coordinate of the direction to transform
`y` - the y coordinate of the direction to transform
`z` - the z coordinate of the direction to transform
`w` - the w coordinate of the direction to transform
`dest` - will contain the result
Returns:
dest
• #### transformProject

`Vector3d transformProject​(Vector3d v)`
Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.

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

Parameters:
`v` - the vector to transform and to hold the final result
Returns:
v
`Vector3d.mulProject(Matrix4dc)`
• #### transformProject

```Vector3d transformProject​(Vector3dc v,
Vector3d dest)```
Transform/multiply the given vector by this matrix, perform perspective divide and store the result in `dest`.

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

Parameters:
`v` - the vector to transform
`dest` - will contain the result
Returns:
dest
`Vector3d.mulProject(Matrix4dc, Vector3d)`
• #### transformProject

```Vector3d transformProject​(double x,
double y,
double z,
Vector3d dest)```
Transform/multiply the vector `(x, y, z)` by this matrix, perform perspective divide and store the result in `dest`.

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

Parameters:
`x` - the x coordinate of the vector to transform
`y` - the y coordinate of the vector to transform
`z` - the z coordinate of the vector to transform
`dest` - will contain the result
Returns:
dest
• #### transformDirection

`Vector3d transformDirection​(Vector3d v)`
Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.

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

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

Parameters:
`v` - the vector to transform and to hold the final result
Returns:
v
• #### transformDirection

```Vector3d transformDirection​(Vector3dc v,
Vector3d dest)```
Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in `dest`.

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

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

Parameters:
`v` - the vector to transform and to hold the final result
`dest` - will hold the result
Returns:
dest
• #### transformDirection

`Vector3f transformDirection​(Vector3f v)`
Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in that vector.

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

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

Parameters:
`v` - the vector to transform and to hold the final result
Returns:
v
• #### transformDirection

```Vector3f transformDirection​(Vector3fc v,
Vector3f dest)```
Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by this matrix and store the result in `dest`.

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

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

Parameters:
`v` - the vector to transform and to hold the final result
`dest` - will hold the result
Returns:
dest
• #### transformDirection

```Vector3d transformDirection​(double x,
double y,
double z,
Vector3d dest)```
Transform/multiply the 3D-vector `(x, y, z)`, as if it was a 4D-vector with w=0, by this matrix and store the result in `dest`.

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

Parameters:
`x` - the x coordinate of the direction to transform
`y` - the y coordinate of the direction to transform
`z` - the z coordinate of the direction to transform
`dest` - will hold the result
Returns:
dest
• #### transformAffine

```Vector4d transformAffine​(Vector4dc v,
Vector4d dest)```
Transform/multiply the given 4D-vector by assuming that `this` matrix represents an `affine` transformation (i.e. its last row is equal to `(0, 0, 0, 1)`) and store the result in `dest`.

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

Parameters:
`v` - the vector to transform and to hold the final result
`dest` - will hold the result
Returns:
dest
`transformAffine(Vector4d)`
• #### transformAffine

```Vector4d transformAffine​(double x,
double y,
double z,
double w,
Vector4d dest)```
Transform/multiply the 4D-vector `(x, y, z, w)` by assuming that `this` matrix represents an `affine` transformation (i.e. its last row is equal to `(0, 0, 0, 1)`) and store the result in `dest`.
Parameters:
`x` - the x coordinate of the direction to transform
`y` - the y coordinate of the direction to transform
`z` - the z coordinate of the direction to transform
`w` - the w coordinate of the direction to transform
`dest` - will hold the result
Returns:
dest
• #### scale

```Matrix4d scale​(Vector3dc xyz,
Matrix4d dest)```
Apply scaling to `this` matrix by scaling the base axes by the given `xyz.x`, `xyz.y` and `xyz.z` factors, respectively and store the result in `dest`.

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

Parameters:
`xyz` - the factors of the x, y and z component, respectively
`dest` - will hold the result
Returns:
dest
• #### scale

```Matrix4d scale​(double x,
double y,
double z,
Matrix4d dest)```
Apply scaling to `this` matrix by scaling the base axes by the given x, y and z factors and store the result in `dest`.

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

Parameters:
`x` - the factor of the x component
`y` - the factor of the y component
`z` - the factor of the z component
`dest` - will hold the result
Returns:
dest
• #### scale

```Matrix4d scale​(double xyz,
Matrix4d dest)```
Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor and store the result in `dest`.

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

Parameters:
`xyz` - the factor for all components
`dest` - will hold the result
Returns:
dest
`scale(double, double, double, Matrix4d)`
• #### scaleAround

```Matrix4d scaleAround​(double sx,
double sy,
double sz,
double ox,
double oy,
double oz,
Matrix4d dest)```
Apply scaling to `this` matrix by scaling the base axes by the given sx, sy and sz factors while using `(ox, oy, oz)` as the scaling origin, and store the result in `dest`.

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

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

Parameters:
`sx` - the scaling factor of the x component
`sy` - the scaling factor of the y component
`sz` - the scaling factor of the z component
`ox` - the x coordinate of the scaling origin
`oy` - the y coordinate of the scaling origin
`oz` - the z coordinate of the scaling origin
`dest` - will hold the result
Returns:
dest
• #### scaleAround

```Matrix4d scaleAround​(double factor,
double ox,
double oy,
double oz,
Matrix4d dest)```
Apply scaling to this matrix by scaling all three base axes by the given `factor` while using `(ox, oy, oz)` as the scaling origin, and store the result in `dest`.

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

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

Parameters:
`factor` - the scaling factor for all three axes
`ox` - the x coordinate of the scaling origin
`oy` - the y coordinate of the scaling origin
`oz` - the z coordinate of the scaling origin
`dest` - will hold the result
Returns:
this
• #### scaleLocal

```Matrix4d scaleLocal​(double xyz,
Matrix4d dest)```
Pre-multiply scaling to `this` matrix by scaling all base axes by the given `xyz` factor, and store the result in `dest`.

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

Parameters:
`xyz` - the factor to scale all three base axes by
`dest` - will hold the result
Returns:
dest
• #### scaleLocal

```Matrix4d scaleLocal​(double x,
double y,
double z,
Matrix4d dest)```
Pre-multiply scaling to `this` matrix by scaling the base axes by the given x, y and z factors and store the result in `dest`.

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

Parameters:
`x` - the factor of the x component
`y` - the factor of the y component
`z` - the factor of the z component
`dest` - will hold the result
Returns:
dest
• #### scaleAroundLocal

```Matrix4d scaleAroundLocal​(double sx,
double sy,
double sz,
double ox,
double oy,
double oz,
Matrix4d dest)```
Pre-multiply scaling to `this` matrix by scaling the base axes by the given sx, sy and sz factors while using the given `(ox, oy, oz)` as the scaling origin, and store the result in `dest`.

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

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

Parameters:
`sx` - the scaling factor of the x component
`sy` - the scaling factor of the y component
`sz` - the scaling factor of the z component
`ox` - the x coordinate of the scaling origin
`oy` - the y coordinate of the scaling origin
`oz` - the z coordinate of the scaling origin
`dest` - will hold the result
Returns:
dest
• #### scaleAroundLocal

```Matrix4d scaleAroundLocal​(double factor,
double ox,
double oy,
double oz,
Matrix4d dest)```
Pre-multiply scaling to this matrix by scaling all three base axes by the given `factor` while using `(ox, oy, oz)` as the scaling origin, and store the result in `dest`.

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

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

Parameters:
`factor` - the scaling factor for all three axes
`ox` - the x coordinate of the scaling origin
`oy` - the y coordinate of the scaling origin
`oz` - the z coordinate of the scaling origin
`dest` - will hold the result
Returns:
this
• #### rotate

```Matrix4d rotate​(double ang,
double x,
double y,
double z,
Matrix4d dest)```
Apply rotation to this matrix by rotating the given amount of radians about the given axis specified as x, y and z components and store the result in `dest`.

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

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

Parameters:
`ang` - the angle is in radians
`x` - the x component of the axis
`y` - the y component of the axis
`z` - the z component of the axis
`dest` - will hold the result
Returns:
dest
• #### rotateTranslation

```Matrix4d rotateTranslation​(double ang,
double x,
double y,
double z,
Matrix4d dest)```
Apply rotation to this matrix, which is assumed to only contain a translation, by rotating the given amount of radians about the specified `(x, y, z)` axis and store the result in `dest`.

This method assumes `this` to only contain a translation.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`x` - the x component of the axis
`y` - the y component of the axis
`z` - the z component of the axis
`dest` - will hold the result
Returns:
dest
• #### rotateAffine

```Matrix4d rotateAffine​(double ang,
double x,
double y,
double z,
Matrix4d dest)```
Apply rotation to this `affine` matrix by rotating the given amount of radians about the specified `(x, y, z)` axis and store the result in `dest`.

This method assumes `this` to be `affine`.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`x` - the x component of the axis
`y` - the y component of the axis
`z` - the z component of the axis
`dest` - will hold the result
Returns:
dest
• #### rotateAroundAffine

```Matrix4d rotateAroundAffine​(Quaterniondc quat,
double ox,
double oy,
double oz,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this `affine` matrix while using `(ox, oy, oz)` as the rotation origin, and store the result in `dest`.

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

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`ox` - the x coordinate of the rotation origin
`oy` - the y coordinate of the rotation origin
`oz` - the z coordinate of the rotation origin
`dest` - will hold the result
Returns:
dest
• #### rotateAround

```Matrix4d rotateAround​(Quaterniondc quat,
double ox,
double oy,
double oz,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this matrix while using `(ox, oy, oz)` as the rotation origin, and store the result in `dest`.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`ox` - the x coordinate of the rotation origin
`oy` - the y coordinate of the rotation origin
`oz` - the z coordinate of the rotation origin
`dest` - will hold the result
Returns:
dest
• #### rotateLocal

```Matrix4d rotateLocal​(double ang,
double x,
double y,
double z,
Matrix4d dest)```
Pre-multiply a rotation to this matrix by rotating the given amount of radians about the specified `(x, y, z)` axis and store the result in `dest`.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`x` - the x component of the axis
`y` - the y component of the axis
`z` - the z component of the axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalX

```Matrix4d rotateLocalX​(double ang,
Matrix4d dest)```
Pre-multiply a rotation around the X axis to this matrix by rotating the given amount of radians about the X axis and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians to rotate about the X axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalY

```Matrix4d rotateLocalY​(double ang,
Matrix4d dest)```
Pre-multiply a rotation around the Y axis to this matrix by rotating the given amount of radians about the Y axis and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians to rotate about the Y axis
`dest` - will hold the result
Returns:
dest
• #### rotateLocalZ

```Matrix4d rotateLocalZ​(double ang,
Matrix4d dest)```
Pre-multiply a rotation around the Z axis to this matrix by rotating the given amount of radians about the Z axis and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians to rotate about the Z axis
`dest` - will hold the result
Returns:
dest
• #### rotateAroundLocal

```Matrix4d rotateAroundLocal​(Quaterniondc quat,
double ox,
double oy,
double oz,
Matrix4d dest)```
Pre-multiply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this matrix while using `(ox, oy, oz)` as the rotation origin, and store the result in `dest`.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`ox` - the x coordinate of the rotation origin
`oy` - the y coordinate of the rotation origin
`oz` - the z coordinate of the rotation origin
`dest` - will hold the result
Returns:
dest
• #### translate

```Matrix4d translate​(Vector3dc offset,
Matrix4d dest)```
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`offset` - the number of units in x, y and z by which to translate
`dest` - will hold the result
Returns:
dest
• #### translate

```Matrix4d translate​(Vector3fc offset,
Matrix4d dest)```
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`offset` - the number of units in x, y and z by which to translate
`dest` - will hold the result
Returns:
dest
• #### translate

```Matrix4d translate​(double x,
double y,
double z,
Matrix4d dest)```
Apply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`x` - the offset to translate in x
`y` - the offset to translate in y
`z` - the offset to translate in z
`dest` - will hold the result
Returns:
dest
• #### translateLocal

```Matrix4d translateLocal​(Vector3fc offset,
Matrix4d dest)```
Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`offset` - the number of units in x, y and z by which to translate
`dest` - will hold the result
Returns:
dest
• #### translateLocal

```Matrix4d translateLocal​(Vector3dc offset,
Matrix4d dest)```
Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`offset` - the number of units in x, y and z by which to translate
`dest` - will hold the result
Returns:
dest
• #### translateLocal

```Matrix4d translateLocal​(double x,
double y,
double z,
Matrix4d dest)```
Pre-multiply a translation to this matrix by translating by the given number of units in x, y and z and store the result in `dest`.

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

Parameters:
`x` - the offset to translate in x
`y` - the offset to translate in y
`z` - the offset to translate in z
`dest` - will hold the result
Returns:
dest
• #### rotateX

```Matrix4d rotateX​(double ang,
Matrix4d dest)```
Apply rotation about the X axis to this matrix by rotating the given amount of radians and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`dest` - will hold the result
Returns:
dest
• #### rotateY

```Matrix4d rotateY​(double ang,
Matrix4d dest)```
Apply rotation about the Y axis to this matrix by rotating the given amount of radians and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`dest` - will hold the result
Returns:
dest
• #### rotateZ

```Matrix4d rotateZ​(double ang,
Matrix4d dest)```
Apply rotation about the Z axis to this matrix by rotating the given amount of radians and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`ang` - the angle in radians
`dest` - will hold the result
Returns:
dest
• #### rotateTowardsXY

```Matrix4d rotateTowardsXY​(double dirX,
double dirY,
Matrix4d dest)```
Apply rotation about the Z axis to align the local `+X` towards `(dirX, dirY)` and store the result in `dest`.

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

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

Parameters:
`dirX` - the x component of the normalized direction
`dirY` - the y component of the normalized direction
`dest` - will hold the result
Returns:
this
• #### rotateXYZ

```Matrix4d rotateXYZ​(double angleX,
double angleY,
double angleZ,
Matrix4d dest)```
Apply rotation of `angleX` radians about the X axis, followed by a rotation of `angleY` radians about the Y axis and followed by a rotation of `angleZ` radians about the Z axis and store the result in `dest`.

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

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

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

Parameters:
`angleX` - the angle to rotate about X
`angleY` - the angle to rotate about Y
`angleZ` - the angle to rotate about Z
`dest` - will hold the result
Returns:
dest
• #### rotateAffineXYZ

```Matrix4d rotateAffineXYZ​(double angleX,
double angleY,
double angleZ,
Matrix4d dest)```
Apply rotation of `angleX` radians about the X axis, followed by a rotation of `angleY` radians about the Y axis and followed by a rotation of `angleZ` radians about the Z axis and store the result in `dest`.

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

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

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

Parameters:
`angleX` - the angle to rotate about X
`angleY` - the angle to rotate about Y
`angleZ` - the angle to rotate about Z
`dest` - will hold the result
Returns:
dest
• #### rotateZYX

```Matrix4d rotateZYX​(double angleZ,
double angleY,
double angleX,
Matrix4d dest)```
Apply rotation of `angleZ` radians about the Z axis, followed by a rotation of `angleY` radians about the Y axis and followed by a rotation of `angleX` radians about the X axis and store the result in `dest`.

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

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

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

Parameters:
`angleZ` - the angle to rotate about Z
`angleY` - the angle to rotate about Y
`angleX` - the angle to rotate about X
`dest` - will hold the result
Returns:
dest
• #### rotateAffineZYX

```Matrix4d rotateAffineZYX​(double angleZ,
double angleY,
double angleX,
Matrix4d dest)```
Apply rotation of `angleZ` radians about the Z axis, followed by a rotation of `angleY` radians about the Y axis and followed by a rotation of `angleX` radians about the X axis and store the result in `dest`.

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

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

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

Parameters:
`angleZ` - the angle to rotate about Z
`angleY` - the angle to rotate about Y
`angleX` - the angle to rotate about X
`dest` - will hold the result
Returns:
dest
• #### rotateYXZ

```Matrix4d rotateYXZ​(double angleY,
double angleX,
double angleZ,
Matrix4d dest)```
Apply rotation of `angleY` radians about the Y axis, followed by a rotation of `angleX` radians about the X axis and followed by a rotation of `angleZ` radians about the Z axis and store the result in `dest`.

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

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

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

Parameters:
`angleY` - the angle to rotate about Y
`angleX` - the angle to rotate about X
`angleZ` - the angle to rotate about Z
`dest` - will hold the result
Returns:
dest
• #### rotateAffineYXZ

```Matrix4d rotateAffineYXZ​(double angleY,
double angleX,
double angleZ,
Matrix4d dest)```
Apply rotation of `angleY` radians about the Y axis, followed by a rotation of `angleX` radians about the X axis and followed by a rotation of `angleZ` radians about the Z axis and store the result in `dest`.

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

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

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

Parameters:
`angleY` - the angle to rotate about Y
`angleX` - the angle to rotate about X
`angleZ` - the angle to rotate about Z
`dest` - will hold the result
Returns:
dest
• #### rotate

```Matrix4d rotate​(Quaterniondc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this matrix and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`dest` - will hold the result
Returns:
dest
• #### rotate

```Matrix4d rotate​(Quaternionfc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaternionfc` to this matrix and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaternionfc`
`dest` - will hold the result
Returns:
dest
• #### rotateAffine

```Matrix4d rotateAffine​(Quaterniondc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this `affine` matrix and store the result in `dest`.

This method assumes `this` to be `affine`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`dest` - will hold the result
Returns:
dest
• #### rotateTranslation

```Matrix4d rotateTranslation​(Quaterniondc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this matrix, which is assumed to only contain a translation, and store the result in `dest`.

This method assumes `this` to only contain a translation.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`dest` - will hold the result
Returns:
dest
• #### rotateTranslation

```Matrix4d rotateTranslation​(Quaternionfc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaternionfc` to this matrix, which is assumed to only contain a translation, and store the result in `dest`.

This method assumes `this` to only contain a translation.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaternionfc`
`dest` - will hold the result
Returns:
dest
• #### rotateLocal

```Matrix4d rotateLocal​(Quaterniondc quat,
Matrix4d dest)```
Pre-multiply the rotation - and possibly scaling - transformation of the given `Quaterniondc` to this matrix and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaterniondc`
`dest` - will hold the result
Returns:
dest
• #### rotateAffine

```Matrix4d rotateAffine​(Quaternionfc quat,
Matrix4d dest)```
Apply the rotation - and possibly scaling - transformation of the given `Quaternionfc` to this `affine` matrix and store the result in `dest`.

This method assumes `this` to be `affine`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaternionfc`
`dest` - will hold the result
Returns:
dest
• #### rotateLocal

```Matrix4d rotateLocal​(Quaternionfc quat,
Matrix4d dest)```
Pre-multiply the rotation - and possibly scaling - transformation of the given `Quaternionfc` to this matrix and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`quat` - the `Quaternionfc`
`dest` - will hold the result
Returns:
dest
• #### rotate

```Matrix4d rotate​(AxisAngle4f axisAngle,
Matrix4d dest)```
Apply a rotation transformation, rotating about the given `AxisAngle4f` and store the result in `dest`.

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

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

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

Reference: http://en.wikipedia.org

Parameters:
`axisAngle` - the `AxisAngle4f` (needs to be `normalized`)
`dest` - will hold the result
Returns:
dest
`rotate(double, double, double, double, Matrix4d)`
• #### rotate

```Matrix4d rotate​(AxisAngle4d axisAngle,
Matrix4d dest)```
Apply a rotation transformation, rotating about the given `AxisAngle4d` and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`axisAngle` - the `AxisAngle4d` (needs to be `normalized`)
`dest` - will hold the result
Returns:
dest
`rotate(double, double, double, double, Matrix4d)`
• #### rotate

```Matrix4d rotate​(double angle,
Vector3dc axis,
Matrix4d dest)```
Apply a rotation transformation, rotating the given radians about the specified axis and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`angle` - the angle in radians
`axis` - the rotation axis (needs to be `normalized`)
`dest` - will hold the result
Returns:
dest
`rotate(double, double, double, double, Matrix4d)`
• #### rotate

```Matrix4d rotate​(double angle,
Vector3fc axis,
Matrix4d dest)```
Apply a rotation transformation, rotating the given radians about the specified axis and store the result in `dest`.

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

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

Reference: http://en.wikipedia.org

Parameters:
`angle` - the angle in radians
`axis` - the rotation axis (needs to be `normalized`)
`dest` - will hold the result
Returns:
dest
`rotate(double, double, double, double, Matrix4d)`
• #### getRow

```Vector4d getRow​(int row,
Vector4d dest)
throws java.lang.IndexOutOfBoundsException```
Get the row at the given `row` index, starting with `0`.
Parameters:
`row` - the row index in `[0..3]`
`dest` - will hold the row components
Returns:
the passed in destination
Throws:
`java.lang.IndexOutOfBoundsException` - if `row` is not in `[0..3]`
• #### getRow

```Vector3d getRow​(int row,
Vector3d dest)
throws java.lang.IndexOutOfBoundsException```
Get the first three components of the row at the given `row` index, starting with `0`.
Parameters:
`row` - the row index in `[0..3]`
`dest` - will hold the first three row components
Returns:
the passed in destination
Throws:
`java.lang.IndexOutOfBoundsException` - if `row` is not in `[0..3]`
• #### getColumn

```Vector4d getColumn​(int column,
Vector4d dest)
throws java.lang.IndexOutOfBoundsException```
Get the column at the given `column` index, starting with `0`.
Parameters:
`column` - the column index in `[0..3]`
`dest` - will hold the column components
Returns:
the passed in destination
Throws:
`java.lang.IndexOutOfBoundsException` - if `column` is not in `[0..3]`
• #### getColumn

```Vector3d getColumn​(int column,
Vector3d dest)
throws java.lang.IndexOutOfBoundsException```
Get the first three components of the column at the given `column` index, starting with `0`.
Parameters:
`column` - the column index in `[0..3]`
`dest` - will hold the first three column components
Returns:
the passed in destination
Throws:
`java.lang.IndexOutOfBoundsException` - if `column` is not in `[0..3]`
• #### normal

`Matrix4d normal​(Matrix4d dest)`
Compute a normal matrix from the upper left 3x3 submatrix of `this` and store it into the upper left 3x3 submatrix of `dest`. All other values of `dest` will be set to identity.

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

Parameters:
`dest` - will hold the result
Returns:
dest
• #### normal

`Matrix3d normal​(Matrix3d dest)`
Compute a normal matrix from the upper left 3x3 submatrix of `this` and store it into `dest`.

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

Parameters:
`dest` - will hold the result
Returns:
dest
`get3x3(Matrix3d)`
• #### normalize3x3

`Matrix4d normalize3x3​(Matrix4d dest)`
Normalize the upper left 3x3 submatrix of this matrix and store the result in `dest`.

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

Parameters:
`dest` - will hold the result
Returns:
dest
• #### normalize3x3

`Matrix3d normalize3x3​(Matrix3d dest)`
Normalize the upper left 3x3 submatrix of this matrix and store the result in `dest`.

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

Parameters:
`dest` - will hold the result
Returns:
dest
• #### unproject

```Vector4d unproject​(double winX,
double winY,
double winZ,
int[] viewport,
Vector4d dest)```
Unproject the given window coordinates `(winX, winY, winZ)` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`winZ` - the z-coordinate, which is the depth value in `[0..1]`
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unprojectInv(double, double, double, int[], Vector4d)`, `invert(Matrix4d)`
• #### unproject

```Vector3d unproject​(double winX,
double winY,
double winZ,
int[] viewport,
Vector3d dest)```
Unproject the given window coordinates `(winX, winY, winZ)` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`winZ` - the z-coordinate, which is the depth value in `[0..1]`
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unprojectInv(double, double, double, int[], Vector3d)`, `invert(Matrix4d)`
• #### unproject

```Vector4d unproject​(Vector3dc winCoords,
int[] viewport,
Vector4d dest)```
Unproject the given window coordinates `winCoords` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unprojectInv(double, double, double, int[], Vector4d)`, `unproject(double, double, double, int[], Vector4d)`, `invert(Matrix4d)`
• #### unproject

```Vector3d unproject​(Vector3dc winCoords,
int[] viewport,
Vector3d dest)```
Unproject the given window coordinates `winCoords` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unprojectInv(double, double, double, int[], Vector4d)`, `unproject(double, double, double, int[], Vector4d)`, `invert(Matrix4d)`
• #### unprojectRay

```Matrix4d unprojectRay​(double winX,
double winY,
int[] viewport,
Vector3d originDest,
Vector3d dirDest)```
Unproject the given 2D window coordinates `(winX, winY)` by `this` matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC `z = -1.0` and goes through NDC `z = +1.0`.

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

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`viewport` - the viewport described by `[x, y, width, height]`
`originDest` - will hold the ray origin
`dirDest` - will hold the (unnormalized) ray direction
Returns:
this
`unprojectInvRay(double, double, int[], Vector3d, Vector3d)`, `invert(Matrix4d)`
• #### unprojectRay

```Matrix4d unprojectRay​(Vector2dc winCoords,
int[] viewport,
Vector3d originDest,
Vector3d dirDest)```
Unproject the given 2D window coordinates `winCoords` by `this` matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC `z = -1.0` and goes through NDC `z = +1.0`.

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

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`originDest` - will hold the ray origin
`dirDest` - will hold the (unnormalized) ray direction
Returns:
this
`unprojectInvRay(double, double, int[], Vector3d, Vector3d)`, `unprojectRay(double, double, int[], Vector3d, Vector3d)`, `invert(Matrix4d)`
• #### unprojectInv

```Vector4d unprojectInv​(Vector3dc winCoords,
int[] viewport,
Vector4d dest)```
Unproject the given window coordinates `winCoords` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unproject(Vector3dc, int[], Vector4d)`
• #### unprojectInv

```Vector4d unprojectInv​(double winX,
double winY,
double winZ,
int[] viewport,
Vector4d dest)```
Unproject the given window coordinates `(winX, winY, winZ)` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`winZ` - the z-coordinate, which is the depth value in `[0..1]`
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unproject(double, double, double, int[], Vector4d)`
• #### unprojectInv

```Vector3d unprojectInv​(Vector3dc winCoords,
int[] viewport,
Vector3d dest)```
Unproject the given window coordinates `winCoords` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unproject(Vector3dc, int[], Vector3d)`
• #### unprojectInv

```Vector3d unprojectInv​(double winX,
double winY,
double winZ,
int[] viewport,
Vector3d dest)```
Unproject the given window coordinates `(winX, winY, winZ)` by `this` matrix using the specified viewport.

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

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

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`winZ` - the z-coordinate, which is the depth value in `[0..1]`
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - will hold the unprojected position
Returns:
dest
`unproject(double, double, double, int[], Vector3d)`
• #### unprojectInvRay

```Matrix4d unprojectInvRay​(Vector2dc winCoords,
int[] viewport,
Vector3d originDest,
Vector3d dirDest)```
Unproject the given window coordinates `winCoords` by `this` matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC `z = -1.0` and goes through NDC `z = +1.0`.

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

Parameters:
`winCoords` - the window coordinates to unproject
`viewport` - the viewport described by `[x, y, width, height]`
`originDest` - will hold the ray origin
`dirDest` - will hold the (unnormalized) ray direction
Returns:
this
`unprojectRay(Vector2dc, int[], Vector3d, Vector3d)`
• #### unprojectInvRay

```Matrix4d unprojectInvRay​(double winX,
double winY,
int[] viewport,
Vector3d originDest,
Vector3d dirDest)```
Unproject the given 2D window coordinates `(winX, winY)` by `this` matrix using the specified viewport and compute the origin and the direction of the resulting ray which starts at NDC `z = -1.0` and goes through NDC `z = +1.0`.

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

Parameters:
`winX` - the x-coordinate in window coordinates (pixels)
`winY` - the y-coordinate in window coordinates (pixels)
`viewport` - the viewport described by `[x, y, width, height]`
`originDest` - will hold the ray origin
`dirDest` - will hold the (unnormalized) ray direction
Returns:
this
`unprojectRay(double, double, int[], Vector3d, Vector3d)`
• #### project

```Vector4d project​(double x,
double y,
double z,
int[] viewport,
Vector4d winCoordsDest)```
Project the given `(x, y, z)` position via `this` matrix using the specified viewport and store the resulting window coordinates in `winCoordsDest`.

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

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

Parameters:
`x` - the x-coordinate of the position to project
`y` - the y-coordinate of the position to project
`z` - the z-coordinate of the position to project
`viewport` - the viewport described by `[x, y, width, height]`
`winCoordsDest` - will hold the projected window coordinates
Returns:
winCoordsDest
• #### project

```Vector3d project​(double x,
double y,
double z,
int[] viewport,
Vector3d winCoordsDest)```
Project the given `(x, y, z)` position via `this` matrix using the specified viewport and store the resulting window coordinates in `winCoordsDest`.

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

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

Parameters:
`x` - the x-coordinate of the position to project
`y` - the y-coordinate of the position to project
`z` - the z-coordinate of the position to project
`viewport` - the viewport described by `[x, y, width, height]`
`winCoordsDest` - will hold the projected window coordinates
Returns:
winCoordsDest
• #### project

```Vector4d project​(Vector3dc position,
int[] viewport,
Vector4d winCoordsDest)```
Project the given `position` via `this` matrix using the specified viewport and store the resulting window coordinates in `winCoordsDest`.

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

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

Parameters:
`position` - the position to project into window coordinates
`viewport` - the viewport described by `[x, y, width, height]`
`winCoordsDest` - will hold the projected window coordinates
Returns:
winCoordsDest
`project(double, double, double, int[], Vector4d)`
• #### project

```Vector3d project​(Vector3dc position,
int[] viewport,
Vector3d winCoordsDest)```
Project the given `position` via `this` matrix using the specified viewport and store the resulting window coordinates in `winCoordsDest`.

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

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

Parameters:
`position` - the position to project into window coordinates
`viewport` - the viewport described by `[x, y, width, height]`
`winCoordsDest` - will hold the projected window coordinates
Returns:
winCoordsDest
`project(double, double, double, int[], Vector4d)`
• #### reflect

```Matrix4d reflect​(double a,
double b,
double c,
double d,
Matrix4d dest)```
Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the equation `x*a + y*b + z*c + d = 0` and store the result in `dest`.

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

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

Reference: msdn.microsoft.com

Parameters:
`a` - the x factor in the plane equation
`b` - the y factor in the plane equation
`c` - the z factor in the plane equation
`d` - the constant in the plane equation
`dest` - will hold the result
Returns:
dest
• #### reflect

```Matrix4d reflect​(double nx,
double ny,
double nz,
double px,
double py,
double pz,
Matrix4d dest)```
Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in `dest`.

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

Parameters:
`nx` - the x-coordinate of the plane normal
`ny` - the y-coordinate of the plane normal
`nz` - the z-coordinate of the plane normal
`px` - the x-coordinate of a point on the plane
`py` - the y-coordinate of a point on the plane
`pz` - the z-coordinate of a point on the plane
`dest` - will hold the result
Returns:
dest
• #### reflect

```Matrix4d reflect​(Quaterniondc orientation,
Vector3dc point,
Matrix4d dest)```
Apply a mirror/reflection transformation to this matrix that reflects about a plane specified via the plane orientation and a point on the plane, and store the result in `dest`.

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

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

Parameters:
`orientation` - the plane orientation
`point` - a point on the plane
`dest` - will hold the result
Returns:
dest
• #### reflect

```Matrix4d reflect​(Vector3dc normal,
Vector3dc point,
Matrix4d dest)```
Apply a mirror/reflection transformation to this matrix that reflects about the given plane specified via the plane normal and a point on the plane, and store the result in `dest`.

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

Parameters:
`normal` - the plane normal
`point` - a point on the plane
`dest` - will hold the result
Returns:
dest
• #### ortho

```Matrix4d ortho​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply an orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
`dest` - will hold the result
Returns:
dest
• #### ortho

```Matrix4d ortho​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
Matrix4d dest)```
Apply an orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
Returns:
dest
• #### orthoLH

```Matrix4d orthoLH​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply an orthographic projection transformation for a left-handed coordiante system using the given NDC z range to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
`dest` - will hold the result
Returns:
dest
• #### orthoLH

```Matrix4d orthoLH​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
Matrix4d dest)```
Apply an orthographic projection transformation for a left-handed coordiante system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
Returns:
dest
• #### orthoSymmetric

```Matrix4d orthoSymmetric​(double width,
double height,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply a symmetric orthographic projection transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`width` - the distance between the right and left frustum edges
`height` - the distance between the top and bottom frustum edges
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
Returns:
dest
• #### orthoSymmetric

```Matrix4d orthoSymmetric​(double width,
double height,
double zNear,
double zFar,
Matrix4d dest)```
Apply a symmetric orthographic projection transformation for a right-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`width` - the distance between the right and left frustum edges
`height` - the distance between the top and bottom frustum edges
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
Returns:
dest
• #### orthoSymmetricLH

```Matrix4d orthoSymmetricLH​(double width,
double height,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply a symmetric orthographic projection transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`width` - the distance between the right and left frustum edges
`height` - the distance between the top and bottom frustum edges
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
Returns:
dest
• #### orthoSymmetricLH

```Matrix4d orthoSymmetricLH​(double width,
double height,
double zNear,
double zFar,
Matrix4d dest)```
Apply a symmetric orthographic projection transformation for a left-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`width` - the distance between the right and left frustum edges
`height` - the distance between the top and bottom frustum edges
`zNear` - near clipping plane distance
`zFar` - far clipping plane distance
`dest` - will hold the result
Returns:
dest
• #### ortho2D

```Matrix4d ortho2D​(double left,
double right,
double bottom,
double top,
Matrix4d dest)```
Apply an orthographic projection transformation for a right-handed coordinate system to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`dest` - will hold the result
Returns:
dest
`ortho(double, double, double, double, double, double, Matrix4d)`
• #### ortho2DLH

```Matrix4d ortho2DLH​(double left,
double right,
double bottom,
double top,
Matrix4d dest)```
Apply an orthographic projection transformation for a left-handed coordinate system to this matrix and store the result in `dest`.

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

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance from the center to the left frustum edge
`right` - the distance from the center to the right frustum edge
`bottom` - the distance from the center to the bottom frustum edge
`top` - the distance from the center to the top frustum edge
`dest` - will hold the result
Returns:
dest
`orthoLH(double, double, double, double, double, double, Matrix4d)`
• #### lookAlong

```Matrix4d lookAlong​(Vector3dc dir,
Vector3dc up,
Matrix4d dest)```
Apply a rotation transformation to this matrix to make `-z` point along `dir` and store the result in `dest`.

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

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

Parameters:
`dir` - the direction in space to look along
`up` - the direction of 'up'
`dest` - will hold the result
Returns:
dest
`lookAlong(double, double, double, double, double, double, Matrix4d)`, `lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)`
• #### lookAlong

```Matrix4d lookAlong​(double dirX,
double dirY,
double dirZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a rotation transformation to this matrix to make `-z` point along `dir` and store the result in `dest`.

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

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

Parameters:
`dirX` - the x-coordinate of the direction to look along
`dirY` - the y-coordinate of the direction to look along
`dirZ` - the z-coordinate of the direction to look along
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
`lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)`
• #### lookAt

```Matrix4d lookAt​(Vector3dc eye,
Vector3dc center,
Vector3dc up,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns `-z` with `center - eye` and store the result in `dest`.

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

Parameters:
`eye` - the position of the camera
`center` - the point in space to look at
`up` - the direction of 'up'
`dest` - will hold the result
Returns:
dest
`lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)`
• #### lookAt

```Matrix4d lookAt​(double eyeX,
double eyeY,
double eyeZ,
double centerX,
double centerY,
double centerZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns `-z` with `center - eye` and store the result in `dest`.

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

Parameters:
`eyeX` - the x-coordinate of the eye/camera location
`eyeY` - the y-coordinate of the eye/camera location
`eyeZ` - the z-coordinate of the eye/camera location
`centerX` - the x-coordinate of the point to look at
`centerY` - the y-coordinate of the point to look at
`centerZ` - the z-coordinate of the point to look at
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
`lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)`
• #### lookAtPerspective

```Matrix4d lookAtPerspective​(double eyeX,
double eyeY,
double eyeZ,
double centerX,
double centerY,
double centerZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a right-handed coordinate system, that aligns `-z` with `center - eye` and store the result in `dest`.

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

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

Parameters:
`eyeX` - the x-coordinate of the eye/camera location
`eyeY` - the y-coordinate of the eye/camera location
`eyeZ` - the z-coordinate of the eye/camera location
`centerX` - the x-coordinate of the point to look at
`centerY` - the y-coordinate of the point to look at
`centerZ` - the z-coordinate of the point to look at
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
• #### lookAtLH

```Matrix4d lookAtLH​(Vector3dc eye,
Vector3dc center,
Vector3dc up,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns `+z` with `center - eye` and store the result in `dest`.

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

Parameters:
`eye` - the position of the camera
`center` - the point in space to look at
`up` - the direction of 'up'
`dest` - will hold the result
Returns:
dest
• #### lookAtLH

```Matrix4d lookAtLH​(double eyeX,
double eyeY,
double eyeZ,
double centerX,
double centerY,
double centerZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns `+z` with `center - eye` and store the result in `dest`.

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

Parameters:
`eyeX` - the x-coordinate of the eye/camera location
`eyeY` - the y-coordinate of the eye/camera location
`eyeZ` - the z-coordinate of the eye/camera location
`centerX` - the x-coordinate of the point to look at
`centerY` - the y-coordinate of the point to look at
`centerZ` - the z-coordinate of the point to look at
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
`lookAtLH(Vector3dc, Vector3dc, Vector3dc, Matrix4d)`
• #### lookAtPerspectiveLH

```Matrix4d lookAtPerspectiveLH​(double eyeX,
double eyeY,
double eyeZ,
double centerX,
double centerY,
double centerZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a "lookat" transformation to this matrix for a left-handed coordinate system, that aligns `+z` with `center - eye` and store the result in `dest`.

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

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

Parameters:
`eyeX` - the x-coordinate of the eye/camera location
`eyeY` - the y-coordinate of the eye/camera location
`eyeZ` - the z-coordinate of the eye/camera location
`centerX` - the x-coordinate of the point to look at
`centerY` - the y-coordinate of the point to look at
`centerZ` - the z-coordinate of the point to look at
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
• #### perspective

```Matrix4d perspective​(double fovy,
double aspect,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

Parameters:
`fovy` - the vertical field of view in radians (must be greater than zero and less than `PI`)
`aspect` - the aspect ratio (i.e. width / height; must be greater than zero)
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`dest` - will hold the result
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
Returns:
dest
• #### perspective

```Matrix4d perspective​(double fovy,
double aspect,
double zNear,
double zFar,
Matrix4d dest)```
Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Parameters:
`fovy` - the vertical field of view in radians (must be greater than zero and less than `PI`)
`aspect` - the aspect ratio (i.e. width / height; must be greater than zero)
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`dest` - will hold the result
Returns:
dest
• #### perspectiveLH

```Matrix4d perspectiveLH​(double fovy,
double aspect,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

Parameters:
`fovy` - the vertical field of view in radians (must be greater than zero and less than `PI`)
`aspect` - the aspect ratio (i.e. width / height; must be greater than zero)
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
`dest` - will hold the result
Returns:
dest
• #### perspectiveLH

```Matrix4d perspectiveLH​(double fovy,
double aspect,
double zNear,
double zFar,
Matrix4d dest)```
Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Parameters:
`fovy` - the vertical field of view in radians (must be greater than zero and less than `PI`)
`aspect` - the aspect ratio (i.e. width / height; must be greater than zero)
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`dest` - will hold the result
Returns:
dest
• #### frustum

```Matrix4d frustum​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance along the x-axis to the left frustum edge
`right` - the distance along the x-axis to the right frustum edge
`bottom` - the distance along the y-axis to the bottom frustum edge
`top` - the distance along the y-axis to the top frustum edge
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
`dest` - will hold the result
Returns:
dest
• #### frustum

```Matrix4d frustum​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
Matrix4d dest)```
Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance along the x-axis to the left frustum edge
`right` - the distance along the x-axis to the right frustum edge
`bottom` - the distance along the y-axis to the bottom frustum edge
`top` - the distance along the y-axis to the top frustum edge
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`dest` - will hold the result
Returns:
dest
• #### frustumLH

```Matrix4d frustumLH​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
boolean zZeroToOne,
Matrix4d dest)```
Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using the given NDC z range to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance along the x-axis to the left frustum edge
`right` - the distance along the x-axis to the right frustum edge
`bottom` - the distance along the y-axis to the bottom frustum edge
`top` - the distance along the y-axis to the top frustum edge
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`zZeroToOne` - whether to use Vulkan's and Direct3D's NDC z range of `[0..+1]` when `true` or whether to use OpenGL's NDC z range of `[-1..+1]` when `false`
`dest` - will hold the result
Returns:
dest
• #### frustumLH

```Matrix4d frustumLH​(double left,
double right,
double bottom,
double top,
double zNear,
double zFar,
Matrix4d dest)```
Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system using OpenGL's NDC z range of `[-1..+1]` to this matrix and store the result in `dest`.

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

Reference: http://www.songho.ca

Parameters:
`left` - the distance along the x-axis to the left frustum edge
`right` - the distance along the x-axis to the right frustum edge
`bottom` - the distance along the y-axis to the bottom frustum edge
`top` - the distance along the y-axis to the top frustum edge
`zNear` - near clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the near clipping plane will be at positive infinity. In that case, `zFar` may not also be `Double.POSITIVE_INFINITY`.
`zFar` - far clipping plane distance. If the special value `Double.POSITIVE_INFINITY` is used, the far clipping plane will be at positive infinity. In that case, `zNear` may not also be `Double.POSITIVE_INFINITY`.
`dest` - will hold the result
Returns:
dest
• #### frustumPlane

```Vector4d frustumPlane​(int plane,
Vector4d planeEquation)```
Calculate a frustum plane of `this` matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given `planeEquation`.

Generally, this method computes the frustum plane in the local frame of any coordinate system that existed before `this` transformation was applied to it in order to yield homogeneous clipping space.

The frustum plane will be given in the form of a general plane equation: `a*x + b*y + c*z + d = 0`, where the given `Vector4d` components will hold the `(a, b, c, d)` values of the equation.

The plane normal, which is `(a, b, c)`, is directed "inwards" of the frustum. Any plane/point test using `a*x + b*y + c*z + d` therefore will yield a result greater than zero if the point is within the frustum (i.e. at the positive side of the frustum plane).

For performing frustum culling, the class `FrustumIntersection` should be used instead of manually obtaining the frustum planes and testing them against points, spheres or axis-aligned boxes.

Parameters:
`plane` - one of the six possible planes, given as numeric constants `PLANE_NX`, `PLANE_PX`, `PLANE_NY`, `PLANE_PY`, `PLANE_NZ` and `PLANE_PZ`
`planeEquation` - will hold the computed plane equation. The plane equation will be normalized, meaning that `(a, b, c)` will be a unit vector
Returns:
planeEquation
• #### frustumPlane

```Planed frustumPlane​(int plane,
Planed planeEquation)```
Calculate a frustum plane of `this` matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given `plane`.

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 plane normal, which is `(a, b, c)`, is directed "inwards" of the frustum. Any plane/point test using `a*x + b*y + c*z + d` therefore will yield a result greater than zero if the point is within the frustum (i.e. at the positive side of the frustum plane).

For performing frustum culling, the class `FrustumIntersection` should be used instead of manually obtaining the frustum planes and testing them against points, spheres or axis-aligned boxes.

Parameters:
`plane` - one of the six possible planes, given as numeric constants `PLANE_NX`, `PLANE_PX`, `PLANE_NY`, `PLANE_PY`, `PLANE_NZ` and `PLANE_PZ`
`planeEquation` - will hold the computed plane equation. The plane equation will be normalized, meaning that `(a, b, c)` will be a unit vector
Returns:
planeEquation
• #### perspectiveOrigin

`Vector3d perspectiveOrigin​(Vector3d origin)`
Compute the eye/origin of the perspective frustum transformation defined by `this` matrix, which can be a projection matrix or a combined modelview-projection matrix, and store the result in the given `origin`.

Note that this method will only work using perspective projections obtained via one of the perspective methods, such as `perspective()` or `frustum()`.

Generally, this method computes the origin in the local frame of any coordinate system that existed before `this` transformation was applied to it in order to yield homogeneous clipping space.

Reference: http://geomalgorithms.com

Parameters:
`origin` - will hold the origin of the coordinate system before applying `this` perspective projection transformation
Returns:
origin
• #### perspectiveFov

`double perspectiveFov()`
Return the vertical field-of-view angle in radians of this perspective transformation matrix.

Note that this method will only work using perspective projections obtained via one of the perspective methods, such as `perspective()` or `frustum()`.

For orthogonal transformations this method will return `0.0`.

Returns:
the vertical field-of-view angle in radians
• #### perspectiveNear

`double perspectiveNear()`
Extract the near clip plane distance from `this` perspective projection matrix.

This method only works if `this` is a perspective projection matrix, for example obtained via `perspective(double, double, double, double, Matrix4d)`.

Returns:
the near clip plane distance
• #### perspectiveFar

`double perspectiveFar()`
Extract the far clip plane distance from `this` perspective projection matrix.

This method only works if `this` is a perspective projection matrix, for example obtained via `perspective(double, double, double, double, Matrix4d)`.

Returns:
the far clip plane distance
• #### frustumRayDir

```Vector3d frustumRayDir​(double x,
double y,
Vector3d dir)```
Obtain the direction of a ray starting at the center of the coordinate system and going through the near frustum plane.

This method computes the `dir` vector in the local frame of any coordinate system that existed before `this` transformation was applied to it in order to yield homogeneous clipping space.

The parameters `x` and `y` are used to interpolate the generated ray direction from the bottom-left to the top-right frustum corners.

For optimal efficiency when building many ray directions over the whole frustum, it is recommended to use this method only in order to compute the four corner rays at `(0, 0)`, `(1, 0)`, `(0, 1)` and `(1, 1)` and then bilinearly interpolating between them; or to use the `FrustumRayBuilder`.

Parameters:
`x` - the interpolation factor along the left-to-right frustum planes, within `[0..1]`
`y` - the interpolation factor along the bottom-to-top frustum planes, within `[0..1]`
`dir` - will hold the normalized ray direction in the local frame of the coordinate system before transforming to homogeneous clipping space using `this` matrix
Returns:
dir
• #### positiveZ

`Vector3d positiveZ​(Vector3d dir)`
Obtain the direction of `+Z` before the transformation represented by `this` matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+Z` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).invert();
inv.transformDirection(dir.set(0, 0, 1)).normalize();
```
If `this` is already an orthogonal matrix, then consider using `normalizedPositiveZ(Vector3d)` instead.

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+Z`
Returns:
dir
• #### normalizedPositiveZ

`Vector3d normalizedPositiveZ​(Vector3d dir)`
Obtain the direction of `+Z` before the transformation represented by `this` orthogonal matrix is applied. This method only produces correct results if `this` is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+Z` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).transpose();
inv.transformDirection(dir.set(0, 0, 1));
```

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+Z`
Returns:
dir
• #### positiveX

`Vector3d positiveX​(Vector3d dir)`
Obtain the direction of `+X` before the transformation represented by `this` matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+X` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).invert();
inv.transformDirection(dir.set(1, 0, 0)).normalize();
```
If `this` is already an orthogonal matrix, then consider using `normalizedPositiveX(Vector3d)` instead.

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+X`
Returns:
dir
• #### normalizedPositiveX

`Vector3d normalizedPositiveX​(Vector3d dir)`
Obtain the direction of `+X` before the transformation represented by `this` orthogonal matrix is applied. This method only produces correct results if `this` is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+X` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).transpose();
inv.transformDirection(dir.set(1, 0, 0));
```

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+X`
Returns:
dir
• #### positiveY

`Vector3d positiveY​(Vector3d dir)`
Obtain the direction of `+Y` before the transformation represented by `this` matrix is applied.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+Y` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).invert();
inv.transformDirection(dir.set(0, 1, 0)).normalize();
```
If `this` is already an orthogonal matrix, then consider using `normalizedPositiveY(Vector3d)` instead.

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+Y`
Returns:
dir
• #### normalizedPositiveY

`Vector3d normalizedPositiveY​(Vector3d dir)`
Obtain the direction of `+Y` before the transformation represented by `this` orthogonal matrix is applied. This method only produces correct results if `this` is an orthogonal matrix.

This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction that is transformed to `+Y` by `this` matrix.

This method is equivalent to the following code:

``` Matrix4d inv = new Matrix4d(this).transpose();
inv.transformDirection(dir.set(0, 1, 0));
```

Reference: http://www.euclideanspace.com

Parameters:
`dir` - will hold the direction of `+Y`
Returns:
dir
• #### originAffine

`Vector3d originAffine​(Vector3d origin)`
Obtain the position that gets transformed to the origin by `this` `affine` matrix. This can be used to get the position of the "camera" from a given view transformation matrix.

This method only works with `affine` matrices.

This method is equivalent to the following code:

``` Matrix4f inv = new Matrix4f(this).invertAffine();
inv.transformPosition(origin.set(0, 0, 0));
```
Parameters:
`origin` - will hold the position transformed to the origin
Returns:
origin
• #### origin

`Vector3d origin​(Vector3d origin)`
Obtain the position that gets transformed to the origin by `this` matrix. This can be used to get the position of the "camera" from a given view/projection transformation matrix.

This method is equivalent to the following code:

``` Matrix4f inv = new Matrix4f(this).invert();
inv.transformPosition(origin.set(0, 0, 0));
```
Parameters:
`origin` - will hold the position transformed to the origin
Returns:
origin

```Matrix4d shadow​(Vector4dc light,
double a,
double b,
double c,
double d,
Matrix4d dest)```
Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation `x*a + y*b + z*c + d = 0` as if casting a shadow from a given light position/direction `light` and store the result in `dest`.

If `light.w` is `0.0` the light is being treated as a directional light; if it is `1.0` it is a point light.

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

Reference: ftp.sgi.com

Parameters:
`light` - the light's vector
`a` - the x factor in the plane equation
`b` - the y factor in the plane equation
`c` - the z factor in the plane equation
`d` - the constant in the plane equation
`dest` - will hold the result
Returns:
dest

```Matrix4d shadow​(double lightX,
double lightY,
double lightZ,
double lightW,
double a,
double b,
double c,
double d,
Matrix4d dest)```
Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation `x*a + y*b + z*c + d = 0` as if casting a shadow from a given light position/direction `(lightX, lightY, lightZ, lightW)` and store the result in `dest`.

If `lightW` is `0.0` the light is being treated as a directional light; if it is `1.0` it is a point light.

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

Reference: ftp.sgi.com

Parameters:
`lightX` - the x-component of the light's vector
`lightY` - the y-component of the light's vector
`lightZ` - the z-component of the light's vector
`lightW` - the w-component of the light's vector
`a` - the x factor in the plane equation
`b` - the y factor in the plane equation
`c` - the z factor in the plane equation
`d` - the constant in the plane equation
`dest` - will hold the result
Returns:
dest

```Matrix4d shadow​(Vector4dc light,
Matrix4dc planeTransform,
Matrix4d dest)```
Apply a projection transformation to this matrix that projects onto the plane with the general plane equation `y = 0` as if casting a shadow from a given light position/direction `light` and store the result in `dest`.

Before the shadow projection is applied, the plane is transformed via the specified `planeTransformation`.

If `light.w` is `0.0` the light is being treated as a directional light; if it is `1.0` it is a point light.

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

Parameters:
`light` - the light's vector
`planeTransform` - the transformation to transform the implied plane `y = 0` before applying the projection
`dest` - will hold the result
Returns:
dest

```Matrix4d shadow​(double lightX,
double lightY,
double lightZ,
double lightW,
Matrix4dc planeTransform,
Matrix4d dest)```
Apply a projection transformation to this matrix that projects onto the plane with the general plane equation `y = 0` as if casting a shadow from a given light position/direction `(lightX, lightY, lightZ, lightW)` and store the result in `dest`.

Before the shadow projection is applied, the plane is transformed via the specified `planeTransformation`.

If `lightW` is `0.0` the light is being treated as a directional light; if it is `1.0` it is a point light.

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

Parameters:
`lightX` - the x-component of the light vector
`lightY` - the y-component of the light vector
`lightZ` - the z-component of the light vector
`lightW` - the w-component of the light vector
`planeTransform` - the transformation to transform the implied plane `y = 0` before applying the projection
`dest` - will hold the result
Returns:
dest
• #### pick

```Matrix4d pick​(double x,
double y,
double width,
double height,
int[] viewport,
Matrix4d dest)```
Apply a picking transformation to this matrix using the given window coordinates `(x, y)` as the pick center and the given `(width, height)` as the size of the picking region in window coordinates, and store the result in `dest`.
Parameters:
`x` - the x coordinate of the picking region center in window coordinates
`y` - the y coordinate of the picking region center in window coordinates
`width` - the width of the picking region in window coordinates
`height` - the height of the picking region in window coordinates
`viewport` - the viewport described by `[x, y, width, height]`
`dest` - the destination matrix, which will hold the result
Returns:
dest
• #### isAffine

`boolean isAffine()`
Determine whether this matrix describes an affine transformation. This is the case iff its last row is equal to `(0, 0, 0, 1)`.
Returns:
`true` iff this matrix is affine; `false` otherwise
• #### arcball

```Matrix4d arcball​(double radius,
double centerX,
double centerY,
double centerZ,
double angleX,
double angleY,
Matrix4d dest)```
Apply an arcball view transformation to this matrix with the given `radius` and center `(centerX, centerY, centerZ)` position of the arcball and the specified X and Y rotation angles, and store the result in `dest`.

This method is equivalent to calling: `translate(0, 0, -radius).rotateX(angleX).rotateY(angleY).translate(-centerX, -centerY, -centerZ)`

Parameters:
`radius` - the arcball radius
`centerX` - the x coordinate of the center position of the arcball
`centerY` - the y coordinate of the center position of the arcball
`centerZ` - the z coordinate of the center position of the arcball
`angleX` - the rotation angle around the X axis in radians
`angleY` - the rotation angle around the Y axis in radians
`dest` - will hold the result
Returns:
dest
• #### arcball

```Matrix4d arcball​(double radius,
Vector3dc center,
double angleX,
double angleY,
Matrix4d dest)```
Apply an arcball view transformation to this matrix with the given `radius` and `center` position of the arcball and the specified X and Y rotation angles, and store the result in `dest`.

This method is equivalent to calling: `translate(0, 0, -radius).rotateX(angleX).rotateY(angleY).translate(-center.x, -center.y, -center.z)`

Parameters:
`radius` - the arcball radius
`center` - the center position of the arcball
`angleX` - the rotation angle around the X axis in radians
`angleY` - the rotation angle around the Y axis in radians
`dest` - will hold the result
Returns:
dest
• #### projectedGridRange

```Matrix4d projectedGridRange​(Matrix4dc projector,
double sLower,
double sUpper,
Matrix4d dest)```
Compute the range matrix for the Projected Grid transformation as described in chapter "2.4.2 Creating the range conversion matrix" of the paper Real-time water rendering - Introducing the projected grid concept based on the inverse of the view-projection matrix which is assumed to be `this`, and store that range matrix into `dest`.

If the projected grid will not be visible then this method returns `null`.

This method uses the `y = 0` plane for the projection.

Parameters:
`projector` - the projector view-projection transformation
`sLower` - the lower (smallest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid
`sUpper` - the upper (highest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid
`dest` - will hold the resulting range matrix
Returns:
the computed range matrix; or `null` if the projected grid will not be visible
• #### orthoCrop

```Matrix4d orthoCrop​(Matrix4dc view,
Matrix4d dest)```
Build an ortographic projection transformation that fits the view-projection transformation represented by `this` into the given affine `view` transformation.

The transformation represented by `this` must be given as the `inverse` of a typical combined camera view-projection transformation, whose projection can be either orthographic or perspective.

The `view` must be an `affine` transformation which in the application of Cascaded Shadow Maps is usually the light view transformation. It be obtained via any affine transformation or for example via `lookAt()`.

Parameters:
`view` - the view transformation to build a corresponding orthographic projection to fit the frustum of `this`
`dest` - will hold the crop projection transformation
Returns:
dest
• #### transformAab

```Matrix4d transformAab​(double minX,
double minY,
double minZ,
double maxX,
double maxY,
double maxZ,
Vector3d outMin,
Vector3d outMax)```
Transform the axis-aligned box given as the minimum corner `(minX, minY, minZ)` and maximum corner `(maxX, maxY, maxZ)` by `this` `affine` matrix and compute the axis-aligned box of the result whose minimum corner is stored in `outMin` and maximum corner stored in `outMax`.

Parameters:
`minX` - the x coordinate of the minimum corner of the axis-aligned box
`minY` - the y coordinate of the minimum corner of the axis-aligned box
`minZ` - the z coordinate of the minimum corner of the axis-aligned box
`maxX` - the x coordinate of the maximum corner of the axis-aligned box
`maxY` - the y coordinate of the maximum corner of the axis-aligned box
`maxZ` - the y coordinate of the maximum corner of the axis-aligned box
`outMin` - will hold the minimum corner of the resulting axis-aligned box
`outMax` - will hold the maximum corner of the resulting axis-aligned box
Returns:
this
• #### transformAab

```Matrix4d transformAab​(Vector3dc min,
Vector3dc max,
Vector3d outMin,
Vector3d outMax)```
Transform the axis-aligned box given as the minimum corner `min` and maximum corner `max` by `this` `affine` matrix and compute the axis-aligned box of the result whose minimum corner is stored in `outMin` and maximum corner stored in `outMax`.
Parameters:
`min` - the minimum corner of the axis-aligned box
`max` - the maximum corner of the axis-aligned box
`outMin` - will hold the minimum corner of the resulting axis-aligned box
`outMax` - will hold the maximum corner of the resulting axis-aligned box
Returns:
this
• #### lerp

```Matrix4d lerp​(Matrix4dc other,
double t,
Matrix4d dest)```
Linearly interpolate `this` and `other` using the given interpolation factor `t` and store the result in `dest`.

If `t` is `0.0` then the result is `this`. If the interpolation factor is `1.0` then the result is `other`.

Parameters:
`other` - the other matrix
`t` - the interpolation factor between 0.0 and 1.0
`dest` - will hold the result
Returns:
dest
• #### rotateTowards

```Matrix4d rotateTowards​(Vector3dc direction,
Vector3dc up,
Matrix4d dest)```
Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local `+Z` axis with `direction` and store the result in `dest`.

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

This method is equivalent to calling: `mulAffine(new Matrix4d().lookAt(new Vector3d(), new Vector3d(dir).negate(), up).invertAffine(), dest)`

Parameters:
`direction` - the direction to rotate towards
`up` - the up vector
`dest` - will hold the result
Returns:
dest
`rotateTowards(double, double, double, double, double, double, Matrix4d)`
• #### rotateTowards

```Matrix4d rotateTowards​(double dirX,
double dirY,
double dirZ,
double upX,
double upY,
double upZ,
Matrix4d dest)```
Apply a model transformation to this matrix for a right-handed coordinate system, that aligns the local `+Z` axis with `dir` and store the result in `dest`.

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

This method is equivalent to calling: `mulAffine(new Matrix4d().lookAt(0, 0, 0, -dirX, -dirY, -dirZ, upX, upY, upZ).invertAffine(), dest)`

Parameters:
`dirX` - the x-coordinate of the direction to rotate towards
`dirY` - the y-coordinate of the direction to rotate towards
`dirZ` - the z-coordinate of the direction to rotate towards
`upX` - the x-coordinate of the up vector
`upY` - the y-coordinate of the up vector
`upZ` - the z-coordinate of the up vector
`dest` - will hold the result
Returns:
dest
`rotateTowards(Vector3dc, Vector3dc, Matrix4d)`
• #### getEulerAnglesZYX

`Vector3d getEulerAnglesZYX​(Vector3d dest)`
Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of `this` and store the extracted Euler angles in `dest`.

This method assumes that the upper left of `this` only represents a rotation without scaling.

Note that the returned Euler angles must be applied in the order `Z * Y * X` to obtain the identical matrix. This means that calling `rotateZYX(double, double, double, Matrix4d)` using the obtained Euler angles will yield the same rotation as the original matrix from which the Euler angles were obtained, so in the below code the matrix `m2` should be identical to `m` (disregarding possible floating-point inaccuracies).

``` Matrix4d m = ...; // <- matrix only representing rotation
Matrix4d n = new Matrix4d();
n.rotateZYX(m.getEulerAnglesZYX(new Vector3d()));
```

Reference: http://nghiaho.com/

Parameters:
`dest` - will hold the extracted Euler angles
Returns:
dest
• #### testPoint

```boolean testPoint​(double x,
double y,
double z)```
Test whether the given point `(x, y, z)` is within the frustum defined by `this` matrix.

This method assumes `this` matrix to be a transformation from any arbitrary coordinate system/space `M` into standard OpenGL clip space and tests whether the given point with the coordinates `(x, y, z)` given in space `M` is within the clip space.

When testing multiple points using the same transformation matrix, `FrustumIntersection` should be used instead.

Parameters:
`x` - the x-coordinate of the point
`y` - the y-coordinate of the point
`z` - the z-coordinate of the point
Returns:
`true` if the given point is inside the frustum; `false` otherwise
• #### testSphere

```boolean testSphere​(double x,
double y,
double z,
double r)```
Test whether the given sphere is partly or completely within or outside of the frustum defined by `this` matrix.

This method assumes `this` matrix to be a transformation from any arbitrary coordinate system/space `M` into standard OpenGL clip space and tests whether the given sphere with the coordinates `(x, y, z)` given in space `M` is within the clip space.

When testing multiple spheres using the same transformation matrix, or more sophisticated/optimized intersection algorithms are required, `FrustumIntersection` should be used instead.

The algorithm implemented by this method is conservative. This means that in certain circumstances a false positive can occur, when the method returns `true` for spheres that are actually not visible. See iquilezles.org for an examination of this problem.

Parameters:
`x` - the x-coordinate of the sphere's center
`y` - the y-coordinate of the sphere's center
`z` - the z-coordinate of the sphere's center
`r` - the sphere's radius
Returns:
`true` if the given sphere is partly or completely inside the frustum; `false` otherwise
• #### testAab

```boolean testAab​(double minX,
double minY,
double minZ,
double maxX,
double maxY,
double maxZ)```
Test whether the given axis-aligned box is partly or completely within or outside of the frustum defined by `this` matrix. The box is specified via its min and max corner coordinates.

This method assumes `this` matrix to be a transformation from any arbitrary coordinate system/space `M` into standard OpenGL clip space and tests whether the given axis-aligned box with its minimum corner coordinates `(minX, minY, minZ)` and maximum corner coordinates `(maxX, maxY, maxZ)` given in space `M` is within the clip space.

When testing multiple axis-aligned boxes using the same transformation matrix, or more sophisticated/optimized intersection algorithms are required, `FrustumIntersection` should be used instead.

The algorithm implemented by this method is conservative. This means that in certain circumstances a false positive can occur, when the method returns `-1` for boxes that are actually not visible/do not intersect the frustum. See iquilezles.org for an examination of this problem.

Parameters:
`minX` - the x-coordinate of the minimum corner
`minY` - the y-coordinate of the minimum corner
`minZ` - the z-coordinate of the minimum corner
`maxX` - the x-coordinate of the maximum corner
`maxY` - the y-coordinate of the maximum corner
`maxZ` - the z-coordinate of the maximum corner
Returns:
`true` if the axis-aligned box is completely or partly inside of the frustum; `false` otherwise
• #### obliqueZ

```Matrix4d obliqueZ​(double a,
double b,
Matrix4d dest)```
Apply an oblique projection transformation to this matrix with the given values for `a` and `b` and store the result in `dest`.

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

The oblique transformation is defined as:

``` x' = x + a*z
y' = y + a*z
z' = z
```
or in matrix form:
``` 1 0 a 0
0 1 b 0
0 0 1 0
0 0 0 1
```
Parameters:
`a` - the value for the z factor that applies to x
`b` - the value for the z factor that applies to y
`dest` - will hold the result
Returns:
dest
• #### equals

```boolean equals​(Matrix4dc m,
double delta)```
Compare the matrix elements of `this` matrix with the given matrix using the given `delta` and return whether all of them are equal within a maximum difference of `delta`.

Please note that this method is not used by any data structure such as `ArrayList` `HashSet` or `HashMap` and their operations, such as `ArrayList.contains(Object)` or `HashSet.remove(Object)`, since those data structures only use the `Object.equals(Object)` and `Object.hashCode()` methods.

Parameters:
`m` - the other matrix
`delta` - the allowed maximum difference
Returns:
`true` whether all of the matrix elements are equal; `false` otherwise