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 Instance Methods Abstract 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
      • add

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

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

        Matrix4d mulComponentWise​(Matrix4dc other,
                                  Matrix4d dest)
        Component-wise multiply this by other and store the result in dest.
        Parameters:
        other - the other matrix
        dest - will hold the result
        Returns:
        dest
      • add4x3

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

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

        Parameters:
        other - the other addend
        dest - will hold the result
        Returns:
        dest
      • add4x3

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

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

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

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

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

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

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

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

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

        double determinant()
        Return the determinant of this matrix.

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

        Returns:
        the determinant
        See Also:
        determinantAffine()
      • determinant3x3

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

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

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

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

        Parameters:
        dest - will hold the result
        Returns:
        dest
        See Also:
        invertAffine(Matrix4d)
      • invertPerspective

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        All other matrix elements are left unchanged.

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

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

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

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

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

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

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

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

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

        Parameters:
        dest - the destination Quaternionf
        Returns:
        the passed in destination
        See Also:
        Quaternionf.setFromUnnormalized(Matrix4dc)
      • getUnnormalizedRotation

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

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

        Parameters:
        dest - the destination Quaterniond
        Returns:
        the passed in destination
        See Also:
        Quaterniond.setFromUnnormalized(Matrix4dc)
      • 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
        See Also:
        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
        See Also:
        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
        See Also:
        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
      • getToAddress

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

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

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

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

        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
        See Also:
        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
        See Also:
        get(double[], int)
      • get

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

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

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

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

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

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

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

        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
        See Also:
        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
        See Also:
        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
        See Also:
        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
        See Also:
        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
        See Also:
        Vector4d.mul(Matrix4dc)
      • 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
        See Also:
        Vector4d.mulProject(Matrix4dc)
      • transformProject

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

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

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

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

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

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

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

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

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

        Parameters:
        x - the x coordinate of the vector to transform
        y - the y coordinate of the vector to transform
        z - the z coordinate of the vector to transform
        dest - will contain the result
        Returns:
        dest
      • 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
        See Also:
        transformAffine(Vector4d)
      • transformAffine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        This method assumes this to only contain a translation.

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

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

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

        Reference: http://en.wikipedia.org

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

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

        This method assumes this to be affine.

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

        This method assumes this to be affine.

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

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

        Reference: http://en.wikipedia.org

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

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

        This method assumes this to only contain a translation.

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

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

        Reference: http://en.wikipedia.org

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

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

        This method assumes this to only contain a translation.

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

        This method assumes this to be affine.

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

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

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

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

        Reference: http://en.wikipedia.org

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

        Vector4d getRow​(int row,
                        Vector4d dest)
                 throws 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
        See Also:
        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
        See Also:
        unprojectInv(double, double, double, int[], Vector4d), invert(Matrix4d)
      • unproject

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: msdn.microsoft.com

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

        Reference: http://www.songho.ca

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

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

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

        Reference: http://www.songho.ca

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

        Reference: http://www.songho.ca

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

        Parameters:
        plane - one of the six possible planes, given as numeric constants PLANE_NX, PLANE_PX, PLANE_NY, PLANE_PY, PLANE_NZ and PLANE_PZ
        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.

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

        Parameters:
        plane - one of the six possible planes, given as numeric constants PLANE_NX, PLANE_PX, PLANE_NY, PLANE_PY, PLANE_NZ and PLANE_PZ
        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

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

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

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

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

        Returns:
        the near clip plane distance
      • perspectiveFar

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

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

        Returns:
        the far clip plane distance
      • frustumRayDir

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

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

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

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

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

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

        This method is equivalent to the following code:

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

        Reference: http://www.euclideanspace.com

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

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

        This method only works with affine matrices.

        This method is equivalent to the following code:

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

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

        This method is equivalent to the following code:

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

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

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

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

        Reference: ftp.sgi.com

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

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

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

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

        Reference: ftp.sgi.com

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        This method is equivalent to calling: translate(0, 0, -radius).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().

        Reference: OpenGL SDK - Cascaded Shadow Maps

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

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

        Reference: http://dev.theomader.com

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        Reference: http://nghiaho.com/

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

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

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

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

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

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

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

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

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

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

        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

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

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

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

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

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

        Reference: Efficient View Frustum Culling
        Reference: Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix

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

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

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

        The oblique transformation is defined as:

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