org.joml.Matrix4fc Maven / Gradle / Ivy
/*
* The MIT License
*
* Copyright (c) 2016-2020 JOML
*
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*
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package org.joml;
import java.nio.ByteBuffer;
import java.nio.FloatBuffer;
import java.util.*;
/**
* Interface to a read-only view of a 4x4 matrix of single-precision floats.
*
* @author Kai Burjack
*/
public interface Matrix4fc {
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation x=-1 when using the identity matrix.
*/
int PLANE_NX = 0;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation x=1 when using the identity matrix.
*/
int PLANE_PX = 1;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation y=-1 when using the identity matrix.
*/
int PLANE_NY = 2;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation y=1 when using the identity matrix.
*/
int PLANE_PY = 3;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation z=-1 when using the identity matrix.
*/
int PLANE_NZ = 4;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4f)} and
* {@link #frustumPlane(int, Planef)}
* identifying the plane with equation z=1 when using the identity matrix.
*/
int PLANE_PZ = 5;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (-1, -1, -1) when using the identity matrix.
*/
int CORNER_NXNYNZ = 0;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (1, -1, -1) when using the identity matrix.
*/
int CORNER_PXNYNZ = 1;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (1, 1, -1) when using the identity matrix.
*/
int CORNER_PXPYNZ = 2;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (-1, 1, -1) when using the identity matrix.
*/
int CORNER_NXPYNZ = 3;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (1, -1, 1) when using the identity matrix.
*/
int CORNER_PXNYPZ = 4;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (-1, -1, 1) when using the identity matrix.
*/
int CORNER_NXNYPZ = 5;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (-1, 1, 1) when using the identity matrix.
*/
int CORNER_NXPYPZ = 6;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3f)}
* identifying the corner (1, 1, 1) when using the identity matrix.
*/
int CORNER_PXPYPZ = 7;
/**
* Bit returned by {@link #properties()} to indicate that the matrix represents a perspective transformation.
*/
byte PROPERTY_PERSPECTIVE = 1<<0;
/**
* Bit returned by {@link #properties()} to indicate that the matrix represents an affine transformation.
*/
byte PROPERTY_AFFINE = 1<<1;
/**
* Bit returned by {@link #properties()} to indicate that the matrix represents the identity transformation.
*/
byte PROPERTY_IDENTITY = 1<<2;
/**
* Bit returned by {@link #properties()} to indicate that the matrix represents a pure translation transformation.
*/
byte PROPERTY_TRANSLATION = 1<<3;
/**
* Bit returned by {@link #properties()} to indicate that the upper-left 3x3 submatrix represents an orthogonal
* matrix (i.e. orthonormal basis). For practical reasons, this property also always implies
* {@link #PROPERTY_AFFINE} in this implementation.
*/
byte PROPERTY_ORTHONORMAL = 1<<4;
/**
* Return the assumed properties of this matrix. This is a bit-combination of
* {@link #PROPERTY_IDENTITY}, {@link #PROPERTY_AFFINE},
* {@link #PROPERTY_TRANSLATION} and {@link #PROPERTY_PERSPECTIVE}.
*
* @return the properties of the matrix
*/
int properties();
/**
* Return the value of the matrix element at column 0 and row 0.
*
* @return the value of the matrix element
*/
float m00();
/**
* Return the value of the matrix element at column 0 and row 1.
*
* @return the value of the matrix element
*/
float m01();
/**
* Return the value of the matrix element at column 0 and row 2.
*
* @return the value of the matrix element
*/
float m02();
/**
* Return the value of the matrix element at column 0 and row 3.
*
* @return the value of the matrix element
*/
float m03();
/**
* Return the value of the matrix element at column 1 and row 0.
*
* @return the value of the matrix element
*/
float m10();
/**
* Return the value of the matrix element at column 1 and row 1.
*
* @return the value of the matrix element
*/
float m11();
/**
* Return the value of the matrix element at column 1 and row 2.
*
* @return the value of the matrix element
*/
float m12();
/**
* Return the value of the matrix element at column 1 and row 3.
*
* @return the value of the matrix element
*/
float m13();
/**
* Return the value of the matrix element at column 2 and row 0.
*
* @return the value of the matrix element
*/
float m20();
/**
* Return the value of the matrix element at column 2 and row 1.
*
* @return the value of the matrix element
*/
float m21();
/**
* Return the value of the matrix element at column 2 and row 2.
*
* @return the value of the matrix element
*/
float m22();
/**
* Return the value of the matrix element at column 2 and row 3.
*
* @return the value of the matrix element
*/
float m23();
/**
* Return the value of the matrix element at column 3 and row 0.
*
* @return the value of the matrix element
*/
float m30();
/**
* Return the value of the matrix element at column 3 and row 1.
*
* @return the value of the matrix element
*/
float m31();
/**
* Return the value of the matrix element at column 3 and row 2.
*
* @return the value of the matrix element
*/
float m32();
/**
* Return the value of the matrix element at column 3 and row 3.
*
* @return the value of the matrix element
*/
float m33();
/**
* 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!
*
* @param right
* the right operand of the matrix multiplication
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mul(Matrix4fc right, Matrix4f dest);
/**
* Multiply this matrix by the supplied right matrix and store the result in dest.
*
* If M is this matrix and R the right matrix,
* then the new matrix will be M * R. So when transforming a
* vector v with the new matrix by using M * R * v, the
* transformation of the right matrix will be applied first!
*
* This method neither assumes nor checks for any matrix properties of this or right
* and will always perform a complete 4x4 matrix multiplication. This method should only be used whenever the
* multiplied matrices do not have any properties for which there are optimized multiplication methods available.
*
* @param right
* the right operand of the matrix multiplication
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mul0(Matrix4fc right, Matrix4f dest);
/**
* Multiply this matrix by the matrix with the supplied elements and store the result in dest.
*
* If M is this matrix and R the right matrix whose
* elements are supplied via the parameters, then the new matrix will be M * R.
* So when transforming a vector v with the new matrix by using M * R * v, the
* transformation of the right matrix will be applied first!
*
* @param r00
* the m00 element of the right matrix
* @param r01
* the m01 element of the right matrix
* @param r02
* the m02 element of the right matrix
* @param r03
* the m03 element of the right matrix
* @param r10
* the m10 element of the right matrix
* @param r11
* the m11 element of the right matrix
* @param r12
* the m12 element of the right matrix
* @param r13
* the m13 element of the right matrix
* @param r20
* the m20 element of the right matrix
* @param r21
* the m21 element of the right matrix
* @param r22
* the m22 element of the right matrix
* @param r23
* the m23 element of the right matrix
* @param r30
* the m30 element of the right matrix
* @param r31
* the m31 element of the right matrix
* @param r32
* the m32 element of the right matrix
* @param r33
* the m33 element of the right matrix
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mul(
float r00, float r01, float r02, float r03,
float r10, float r11, float r12, float r13,
float r20, float r21, float r22, float r23,
float r30, float r31, float r32, float r33, Matrix4f dest);
/**
* Multiply this matrix by the 3x3 matrix with the supplied elements expanded to a 4x4 matrix with
* all other matrix elements set to identity, and store the result in dest.
*
* If M is this matrix and R the right matrix whose
* elements are supplied via the parameters, then the new matrix will be M * R.
* So when transforming a vector v with the new matrix by using M * R * v, the
* transformation of the right matrix will be applied first!
*
* @param r00
* the m00 element of the right matrix
* @param r01
* the m01 element of the right matrix
* @param r02
* the m02 element of the right matrix
* @param r10
* the m10 element of the right matrix
* @param r11
* the m11 element of the right matrix
* @param r12
* the m12 element of the right matrix
* @param r20
* the m20 element of the right matrix
* @param r21
* the m21 element of the right matrix
* @param r22
* the m22 element of the right matrix
* @param dest
* the destination matrix, which will hold the result
* @return this
*/
Matrix4f mul3x3(
float r00, float r01, float r02,
float r10, float r11, float r12,
float r20, float r21, float r22, Matrix4f 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!
*
* @param left
* the left operand of the matrix multiplication
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulLocal(Matrix4fc left, Matrix4f dest);
/**
* Pre-multiply this matrix by the supplied left matrix, both of which are assumed to be {@link #isAffine() affine}, and store the result in dest.
*
* This method assumes that this matrix and the given left matrix both represent an {@link #isAffine() 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!
*
* @param left
* the left operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulLocalAffine(Matrix4fc left, Matrix4f 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!
*
* @param right
* the right operand of the matrix multiplication
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mul(Matrix3x2fc right, Matrix4f 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!
*
* @param right
* the right operand of the matrix multiplication
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mul(Matrix4x3fc right, Matrix4f dest);
/**
* Multiply this symmetric perspective projection matrix by the supplied {@link #isAffine() 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!
*
* @param view
* the {@link #isAffine() affine} matrix to multiply this symmetric perspective projection matrix by
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulPerspectiveAffine(Matrix4fc view, Matrix4f dest);
/**
* Multiply this symmetric perspective projection matrix by the supplied view matrix and store the result in dest.
*
* If P is this matrix and V the view matrix,
* then the new matrix will be P * V. So when transforming a
* vector v with the new matrix by using P * V * v, the
* transformation of the view matrix will be applied first!
*
* @param view
* the matrix to multiply this symmetric perspective projection matrix by
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulPerspectiveAffine(Matrix4x3fc view, Matrix4f dest);
/**
* Multiply this matrix by the supplied right matrix, which is assumed to be {@link #isAffine() affine}, and store the result in dest.
*
* This method assumes that the given right matrix represents an {@link #isAffine() 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!
*
* @param right
* the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulAffineR(Matrix4fc right, Matrix4f dest);
/**
* Multiply this matrix by the supplied right matrix, both of which are assumed to be {@link #isAffine() affine}, and store the result in dest.
*
* This method assumes that this matrix and the given right matrix both represent an {@link #isAffine() 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!
*
* @param right
* the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulAffine(Matrix4fc right, Matrix4f dest);
/**
* Multiply this matrix, which is assumed to only contain a translation, by the supplied right matrix, which is assumed to be {@link #isAffine() 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 {@link #isAffine() 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!
*
* @param right
* the right operand of the matrix multiplication (the last row is assumed to be (0, 0, 0, 1))
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulTranslationAffine(Matrix4fc right, Matrix4f dest);
/**
* Multiply this orthographic projection matrix by the supplied {@link #isAffine() 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!
*
* @param view
* the affine matrix which to multiply this with
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f mulOrthoAffine(Matrix4fc view, Matrix4f 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.
*
* @param other
* the other matrix
* @param otherFactor
* the factor to multiply each of the other matrix's 4x3 components
* @param dest
* will hold the result
* @return dest
*/
Matrix4f fma4x3(Matrix4fc other, float otherFactor, Matrix4f dest);
/**
* Component-wise add this and other and store the result in dest.
*
* @param other
* the other addend
* @param dest
* will hold the result
* @return dest
*/
Matrix4f add(Matrix4fc other, Matrix4f dest);
/**
* Component-wise subtract subtrahend from this and store the result in dest.
*
* @param subtrahend
* the subtrahend
* @param dest
* will hold the result
* @return dest
*/
Matrix4f sub(Matrix4fc subtrahend, Matrix4f dest);
/**
* Component-wise multiply this by other and store the result in dest.
*
* @param other
* the other matrix
* @param dest
* will hold the result
* @return dest
*/
Matrix4f mulComponentWise(Matrix4fc other, Matrix4f 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.
*
* @param other
* the other addend
* @param dest
* will hold the result
* @return dest
*/
Matrix4f add4x3(Matrix4fc other, Matrix4f 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.
*
* @param subtrahend
* the subtrahend
* @param dest
* will hold the result
* @return dest
*/
Matrix4f sub4x3(Matrix4fc subtrahend, Matrix4f 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.
*
* @param other
* the other matrix
* @param dest
* will hold the result
* @return dest
*/
Matrix4f mul4x3ComponentWise(Matrix4fc other, Matrix4f dest);
/**
* Return the determinant of this matrix.
*
* If this matrix represents an {@link #isAffine() affine} transformation, such as translation, rotation, scaling and shearing,
* and thus its last row is equal to (0, 0, 0, 1), then {@link #determinantAffine()} can be used instead of this method.
*
* @see #determinantAffine()
*
* @return the determinant
*/
float determinant();
/**
* Return the determinant of the upper left 3x3 submatrix of this matrix.
*
* @return the determinant
*/
float determinant3x3();
/**
* Return the determinant of this matrix by assuming that it represents an {@link #isAffine() affine} transformation and thus
* its last row is equal to (0, 0, 0, 1).
*
* @return the determinant
*/
float determinantAffine();
/**
* Invert this matrix and write the result into dest.
*
* If this matrix represents an {@link #isAffine() affine} transformation, such as translation, rotation, scaling and shearing,
* and thus its last row is equal to (0, 0, 0, 1), then {@link #invertAffine(Matrix4f)} can be used instead of this method.
*
* @see #invertAffine(Matrix4f)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f invert(Matrix4f dest);
/**
* If this is a perspective projection matrix obtained via one of the {@link #perspective(float, float, float, float, Matrix4f) 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 {@link #perspective(float, float, float, float, Matrix4f) perspective()}.
*
* @see #perspective(float, float, float, float, Matrix4f)
*
* @param dest
* will hold the inverse of this
* @return dest
*/
Matrix4f invertPerspective(Matrix4f dest);
/**
* If this is an arbitrary perspective projection matrix obtained via one of the {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()} methods,
* then this method builds the inverse of this and stores it into the given dest.
*
* This method can be used to quickly obtain the inverse of a perspective projection matrix.
*
* If this matrix represents a symmetric perspective frustum transformation, as obtained via {@link #perspective(float, float, float, float, Matrix4f) perspective()}, then
* {@link #invertPerspective(Matrix4f)} should be used instead.
*
* @see #frustum(float, float, float, float, float, float, Matrix4f)
* @see #invertPerspective(Matrix4f)
*
* @param dest
* will hold the inverse of this
* @return dest
*/
Matrix4f invertFrustum(Matrix4f 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.
*
* @param dest
* will hold the inverse of this
* @return dest
*/
Matrix4f invertOrtho(Matrix4f dest);
/**
* If this is a perspective projection matrix obtained via one of the {@link #perspective(float, float, float, float, Matrix4f) perspective()} methods,
* that is, if this is a symmetrical perspective frustum transformation
* and the given view matrix is {@link #isAffine() affine} and has unit scaling (for example by being obtained via {@link #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f) 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 {@link #perspective(float, float, float, float, Matrix4f) perspective()} and {@link #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f) lookAt()} or
* other methods, that build affine matrices, such as {@link #translate(float, float, float, Matrix4f) translate} and {@link #rotate(float, float, float, float, Matrix4f)}, except for {@link #scale(float, float, float, Matrix4f) 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();
*
*
* @param view
* the view transformation (must be {@link #isAffine() affine} and have unit scaling)
* @param dest
* will hold the inverse of this * view
* @return dest
*/
Matrix4f invertPerspectiveView(Matrix4fc view, Matrix4f dest);
/**
* If this is a perspective projection matrix obtained via one of the {@link #perspective(float, float, float, float, Matrix4f) 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 {@link #perspective(float, float, float, float, Matrix4f) perspective()} and {@link #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f) lookAt()} or
* other methods, that build affine matrices, such as {@link #translate(float, float, float, Matrix4f) translate} and {@link #rotate(float, float, float, float, Matrix4f)}, except for {@link #scale(float, float, float, Matrix4f) 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();
*
*
* @param view
* the view transformation (must have unit scaling)
* @param dest
* will hold the inverse of this * view
* @return dest
*/
Matrix4f invertPerspectiveView(Matrix4x3fc view, Matrix4f dest);
/**
* Invert this matrix by assuming that it is an {@link #isAffine() affine} transformation (i.e. its last row is equal to (0, 0, 0, 1))
* and write the result into dest.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f invertAffine(Matrix4f dest);
/**
* Transpose this matrix and store the result in dest.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f transpose(Matrix4f dest);
/**
* Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
*
* All other matrix elements are left unchanged.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f transpose3x3(Matrix4f dest);
/**
* Transpose only the upper left 3x3 submatrix of this matrix and store the result in dest.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3f transpose3x3(Matrix3f dest);
/**
* Get only the translation components (m30, m31, m32) of this matrix and store them in the given vector xyz.
*
* @param dest
* will hold the translation components of this matrix
* @return dest
*/
Vector3f getTranslation(Vector3f dest);
/**
* Get the scaling factors of this matrix for the three base axes.
*
* @param dest
* will hold the scaling factors for x, y and z
* @return dest
*/
Vector3f getScale(Vector3f dest);
/**
* Get the current values of this matrix and store them into
* dest.
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix4f get(Matrix4f dest);
/**
* Get the current values of the upper 4x3 submatrix of this matrix and store them into
* dest.
*
* @see Matrix4x3f#set(Matrix4fc)
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix4x3f get4x3(Matrix4x3f dest);
/**
* Get the current values of this matrix and store them into
* dest.
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix4d get(Matrix4d dest);
/**
* Get the current values of the upper left 3x3 submatrix of this matrix and store them into
* dest.
*
* @see Matrix3f#set(Matrix4fc)
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix3f get3x3(Matrix3f dest);
/**
* Get the current values of the upper left 3x3 submatrix of this matrix and store them into
* dest.
*
* @see Matrix3d#set(Matrix4fc)
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix3d get3x3(Matrix3d dest);
/**
* Get the rotational component of this matrix and store the represented rotation
* into the given {@link AxisAngle4f}.
*
* @see AxisAngle4f#set(Matrix4fc)
*
* @param dest
* the destination {@link AxisAngle4f}
* @return the passed in destination
*/
AxisAngle4f getRotation(AxisAngle4f dest);
/**
* Get the rotational component of this matrix and store the represented rotation
* into the given {@link AxisAngle4d}.
*
* @see AxisAngle4f#set(Matrix4fc)
*
* @param dest
* the destination {@link AxisAngle4d}
* @return the passed in destination
*/
AxisAngle4d getRotation(AxisAngle4d dest);
/**
* Get the current values of this matrix and store the represented rotation
* into the given {@link 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.
*
* @see Quaternionf#setFromUnnormalized(Matrix4fc)
*
* @param dest
* the destination {@link Quaternionf}
* @return the passed in destination
*/
Quaternionf getUnnormalizedRotation(Quaternionf dest);
/**
* Get the current values of this matrix and store the represented rotation
* into the given {@link Quaternionf}.
*
* This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
*
* @see Quaternionf#setFromNormalized(Matrix4fc)
*
* @param dest
* the destination {@link Quaternionf}
* @return the passed in destination
*/
Quaternionf getNormalizedRotation(Quaternionf dest);
/**
* Get the current values of this matrix and store the represented rotation
* into the given {@link 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.
*
* @see Quaterniond#setFromUnnormalized(Matrix4fc)
*
* @param dest
* the destination {@link Quaterniond}
* @return the passed in destination
*/
Quaterniond getUnnormalizedRotation(Quaterniond dest);
/**
* Get the current values of this matrix and store the represented rotation
* into the given {@link Quaterniond}.
*
* This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
*
* @see Quaterniond#setFromNormalized(Matrix4fc)
*
* @param dest
* the destination {@link Quaterniond}
* @return the passed in destination
*/
Quaterniond getNormalizedRotation(Quaterniond dest);
/**
* Store this matrix in column-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() 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 {@link #get(int, FloatBuffer)}, taking
* the absolute position as parameter.
*
* @see #get(int, FloatBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
FloatBuffer get(FloatBuffer buffer);
/**
* Store this matrix in column-major order into the supplied {@link FloatBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given FloatBuffer.
*
* @param index
* the absolute position into the FloatBuffer
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
FloatBuffer get(int index, FloatBuffer buffer);
/**
* Store this matrix in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() 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 {@link #get(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #get(int, ByteBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
ByteBuffer get(ByteBuffer buffer);
/**
* Store this matrix in column-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
ByteBuffer get(int index, ByteBuffer buffer);
/**
* Store the upper 4x3 submatrix in column-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() 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 {@link #get(int, FloatBuffer)}, taking
* the absolute position as parameter.
*
* @see #get(int, FloatBuffer)
*
* @param buffer
* will receive the values of the upper 4x3 submatrix in column-major order at its current position
* @return the passed in buffer
*/
FloatBuffer get4x3(FloatBuffer buffer);
/**
* Store the upper 4x3 submatrix in column-major order into the supplied {@link FloatBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given FloatBuffer.
*
* @param index
* the absolute position into the FloatBuffer
* @param buffer
* will receive the values of the upper 4x3 submatrix in column-major order
* @return the passed in buffer
*/
FloatBuffer get4x3(int index, FloatBuffer buffer);
/**
* Store the upper 4x3 submatrix in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() 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 {@link #get(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #get(int, ByteBuffer)
*
* @param buffer
* will receive the values of the upper 4x3 submatrix in column-major order at its current position
* @return the passed in buffer
*/
ByteBuffer get4x3(ByteBuffer buffer);
/**
* Store the upper 4x3 submatrix in column-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the values of the upper 4x3 submatrix in column-major order
* @return the passed in buffer
*/
ByteBuffer get4x3(int index, ByteBuffer buffer);
/**
* Store the left 3x4 submatrix in column-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() 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 {@link #get3x4(int, FloatBuffer)}, taking
* the absolute position as parameter.
*
* @see #get3x4(int, FloatBuffer)
*
* @param buffer
* will receive the values of the left 3x4 submatrix in column-major order at its current position
* @return the passed in buffer
*/
FloatBuffer get3x4(FloatBuffer buffer);
/**
* Store the left 3x4 submatrix in column-major order into the supplied {@link FloatBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given FloatBuffer.
*
* @param index
* the absolute position into the FloatBuffer
* @param buffer
* will receive the values of the left 3x4 submatrix in column-major order
* @return the passed in buffer
*/
FloatBuffer get3x4(int index, FloatBuffer buffer);
/**
* Store the left 3x4 submatrix in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() 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 {@link #get3x4(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #get3x4(int, ByteBuffer)
*
* @param buffer
* will receive the values of the left 3x4 submatrix in column-major order at its current position
* @return the passed in buffer
*/
ByteBuffer get3x4(ByteBuffer buffer);
/**
* Store the left 3x4 submatrix in column-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the values of the left 3x4 submatrix in column-major order
* @return the passed in buffer
*/
ByteBuffer get3x4(int index, ByteBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() 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 {@link #getTransposed(int, FloatBuffer)}, taking
* the absolute position as parameter.
*
* @see #getTransposed(int, FloatBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
FloatBuffer getTransposed(FloatBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link FloatBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given FloatBuffer.
*
* @param index
* the absolute position into the FloatBuffer
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
FloatBuffer getTransposed(int index, FloatBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() 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 {@link #getTransposed(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #getTransposed(int, ByteBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
ByteBuffer getTransposed(ByteBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
ByteBuffer getTransposed(int index, ByteBuffer buffer);
/**
* Store the upper 4x3 submatrix of this matrix in row-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() 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 {@link #get4x3Transposed(int, FloatBuffer)}, taking
* the absolute position as parameter.
*
* @see #get4x3Transposed(int, FloatBuffer)
*
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order at its current position
* @return the passed in buffer
*/
FloatBuffer get4x3Transposed(FloatBuffer buffer);
/**
* Store the upper 4x3 submatrix of this matrix in row-major order into the supplied {@link FloatBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given FloatBuffer.
*
* @param index
* the absolute position into the FloatBuffer
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order
* @return the passed in buffer
*/
FloatBuffer get4x3Transposed(int index, FloatBuffer buffer);
/**
* Store the upper 4x3 submatrix of this matrix in row-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() 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 {@link #get4x3Transposed(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #get4x3Transposed(int, ByteBuffer)
*
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order at its current position
* @return the passed in buffer
*/
ByteBuffer get4x3Transposed(ByteBuffer buffer);
/**
* Store the upper 4x3 submatrix of this matrix in row-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
*
* This method will not increment the position of the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order
* @return the passed in buffer
*/
ByteBuffer get4x3Transposed(int index, ByteBuffer buffer);
/**
* Store this matrix in column-major order at the given off-heap address.
*
* This method will throw an {@link 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.
*
* @param address
* the off-heap address where to store this matrix
* @return this
*/
Matrix4fc getToAddress(long address);
/**
* Store this matrix into the supplied float array in column-major order at the given offset.
*
* @param arr
* the array to write the matrix values into
* @param offset
* the offset into the array
* @return the passed in array
*/
float[] get(float[] arr, int offset);
/**
* Store this matrix into the supplied float array in column-major order.
*
* In order to specify an explicit offset into the array, use the method {@link #get(float[], int)}.
*
* @see #get(float[], int)
*
* @param arr
* the array to write the matrix values into
* @return the passed in array
*/
float[] get(float[] arr);
/**
* Transform/multiply the given vector by this matrix and store the result in that vector.
*
* @see Vector4f#mul(Matrix4fc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4f transform(Vector4f v);
/**
* Transform/multiply the given vector by this matrix and store the result in dest.
*
* @see Vector4f#mul(Matrix4fc, Vector4f)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transform(Vector4fc v, Vector4f dest);
/**
* Transform/multiply the vector (x, y, z, w) by this matrix and store the result in dest.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param w
* the w coordinate of the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transform(float x, float y, float z, float w, Vector4f dest);
/**
* Transform/multiply the given vector by the transpose of this matrix and store the result in that vector.
*
* @see Vector4f#mulTranspose(Matrix4fc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4f transformTranspose(Vector4f v);
/**
* Transform/multiply the given vector by the transpose of this matrix and store the result in dest.
*
* @see Vector4f#mulTranspose(Matrix4fc, Vector4f)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transformTranspose(Vector4fc v, Vector4f dest);
/**
* Transform/multiply the vector (x, y, z, w) by the transpose of this matrix and store the result in dest.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param w
* the w coordinate of the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transformTranspose(float x, float y, float z, float w, Vector4f dest);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
*
* @see Vector4f#mulProject(Matrix4fc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4f transformProject(Vector4f v);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in dest.
*
* @see Vector4f#mulProject(Matrix4fc, Vector4f)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transformProject(Vector4fc v, Vector4f dest);
/**
* Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store the result in dest.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param w
* the w coordinate of the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4f transformProject(float x, float y, float z, float w, Vector4f dest);
/**
* 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.
*
* @see Vector3f#mulProject(Matrix4fc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector3f transformProject(Vector3f v);
/**
* 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.
*
* @see Vector3f#mulProject(Matrix4fc, Vector3f)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector3f transformProject(Vector3fc v, Vector3f 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.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector3f transformProject(float x, float y, float z, Vector3f dest);
/**
* Transform/multiply the vector (x, y, z, w) by this matrix, perform perspective divide and store
* (x, y, z) of the result in dest.
*
* @param x
* the x coordinate of the vector to transform
* @param y
* the y coordinate of the vector to transform
* @param z
* the z coordinate of the vector to transform
* @param w
* the w coordinate of the vector to transform
* @param dest
* will contain the (x, y, z) components of the result
* @return dest
*/
Vector3f transformProject(float x, float y, float z, float w, Vector3f dest);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by
* this matrix and store the result in that vector.
*
* The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it
* will represent a position/location in 3D-space rather than a direction. This method is therefore
* not suited for perspective projection transformations as it will not save the
* w component of the transformed vector.
* For perspective projection use {@link #transform(Vector4f)} or {@link #transformProject(Vector3f)}
* when perspective divide should be applied, too.
*
* In order to store the result in another vector, use {@link #transformPosition(Vector3fc, Vector3f)}.
*
* @see #transformPosition(Vector3fc, Vector3f)
* @see #transform(Vector4f)
* @see #transformProject(Vector3f)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector3f transformPosition(Vector3f 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 dest.
*
* The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it
* will represent a position/location in 3D-space rather than a direction. This method is therefore
* not suited for perspective projection transformations as it will not save the
* w component of the transformed vector.
* For perspective projection use {@link #transform(Vector4fc, Vector4f)} or
* {@link #transformProject(Vector3fc, Vector3f)} when perspective divide should be applied, too.
*
* In order to store the result in the same vector, use {@link #transformPosition(Vector3f)}.
*
* @see #transformPosition(Vector3f)
* @see #transform(Vector4fc, Vector4f)
* @see #transformProject(Vector3fc, Vector3f)
*
* @param v
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3f transformPosition(Vector3fc v, Vector3f dest);
/**
* Transform/multiply the 3D-vector (x, y, z), as if it was a 4D-vector with w=1, by
* this matrix and store the result in dest.
*
* The given 3D-vector is treated as a 4D-vector with its w-component being 1.0, so it
* will represent a position/location in 3D-space rather than a direction. This method is therefore
* not suited for perspective projection transformations as it will not save the
* w component of the transformed vector.
* For perspective projection use {@link #transform(float, float, float, float, Vector4f)} or
* {@link #transformProject(float, float, float, Vector3f)} when perspective divide should be applied, too.
*
* @see #transform(float, float, float, float, Vector4f)
* @see #transformProject(float, float, float, Vector3f)
*
* @param x
* the x coordinate of the position
* @param y
* the y coordinate of the position
* @param z
* the z coordinate of the position
* @param dest
* will hold the result
* @return dest
*/
Vector3f transformPosition(float x, float y, float z, 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 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 {@link #transformDirection(Vector3fc, Vector3f)}.
*
* @see #transformDirection(Vector3fc, Vector3f)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
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 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 {@link #transformDirection(Vector3f)}.
*
* @see #transformDirection(Vector3f)
*
* @param v
* the vector to transform and to hold the final result
* @param dest
* will hold the result
* @return dest
*/
Vector3f transformDirection(Vector3fc v, Vector3f dest);
/**
* Transform/multiply the given 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.
*
* @param x
* the x coordinate of the direction to transform
* @param y
* the y coordinate of the direction to transform
* @param z
* the z coordinate of the direction to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3f transformDirection(float x, float y, float z, Vector3f dest);
/**
* Transform/multiply the given 4D-vector by assuming that this matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to (0, 0, 0, 1)).
*
* In order to store the result in another vector, use {@link #transformAffine(Vector4fc, Vector4f)}.
*
* @see #transformAffine(Vector4fc, Vector4f)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4f transformAffine(Vector4f v);
/**
* Transform/multiply the given 4D-vector by assuming that this matrix represents an {@link #isAffine() 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 {@link #transformAffine(Vector4f)}.
*
* @see #transformAffine(Vector4f)
*
* @param v
* the vector to transform and to hold the final result
* @param dest
* will hold the result
* @return dest
*/
Vector4f transformAffine(Vector4fc v, Vector4f dest);
/**
* Transform/multiply the 4D-vector (x, y, z, w) by assuming that this matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to (0, 0, 0, 1)) and store the result in dest.
*
* @param x
* the x coordinate of the direction to transform
* @param y
* the y coordinate of the direction to transform
* @param z
* the z coordinate of the direction to transform
* @param w
* the w coordinate of the direction to transform
* @param dest
* will hold the result
* @return dest
*/
Vector4f transformAffine(float x, float y, float z, float w, Vector4f 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!
*
* @param xyz
* the factors of the x, y and z component, respectively
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scale(Vector3fc xyz, Matrix4f 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!
*
* Individual scaling of all three axes can be applied using {@link #scale(float, float, float, Matrix4f)}.
*
* @see #scale(float, float, float, Matrix4f)
*
* @param xyz
* the factor for all components
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scale(float xyz, Matrix4f dest);
/**
* Apply scaling to this matrix by by scaling the X axis by x and the Y axis by y
* and store the result in dest.
*
* If M is this matrix and S the scaling matrix,
* then the new matrix will be M * S. So when transforming a
* vector v with the new matrix by using M * S * v, the
* scaling will be applied first!
*
* @param x
* the factor of the x component
* @param y
* the factor of the y component
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scaleXY(float x, float y, Matrix4f 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!
*
* @param x
* the factor of the x component
* @param y
* the factor of the y component
* @param z
* the factor of the z component
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scale(float x, float y, float z, Matrix4f 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)
*
* @param sx
* the scaling factor of the x component
* @param sy
* the scaling factor of the y component
* @param sz
* the scaling factor of the z component
* @param ox
* the x coordinate of the scaling origin
* @param oy
* the y coordinate of the scaling origin
* @param oz
* the z coordinate of the scaling origin
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scaleAround(float sx, float sy, float sz, float ox, float oy, float oz, Matrix4f 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)
*
* @param factor
* the scaling factor for all three axes
* @param ox
* the x coordinate of the scaling origin
* @param oy
* the y coordinate of the scaling origin
* @param oz
* the z coordinate of the scaling origin
* @param dest
* will hold the result
* @return this
*/
Matrix4f scaleAround(float factor, float ox, float oy, float oz, Matrix4f 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!
*
* @param xyz
* the factor to scale all three base axes by
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scaleLocal(float xyz, Matrix4f 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!
*
* @param x
* the factor of the x component
* @param y
* the factor of the y component
* @param z
* the factor of the z component
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scaleLocal(float x, float y, float z, Matrix4f 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 Matrix4f().translate(ox, oy, oz).scale(sx, sy, sz).translate(-ox, -oy, -oz).mul(this, dest)
*
* @param sx
* the scaling factor of the x component
* @param sy
* the scaling factor of the y component
* @param sz
* the scaling factor of the z component
* @param ox
* the x coordinate of the scaling origin
* @param oy
* the y coordinate of the scaling origin
* @param oz
* the z coordinate of the scaling origin
* @param dest
* will hold the result
* @return dest
*/
Matrix4f scaleAroundLocal(float sx, float sy, float sz, float ox, float oy, float oz, Matrix4f 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 Matrix4f().translate(ox, oy, oz).scale(factor).translate(-ox, -oy, -oz).mul(this, dest)
*
* @param factor
* the scaling factor for all three axes
* @param ox
* the x coordinate of the scaling origin
* @param oy
* the y coordinate of the scaling origin
* @param oz
* the z coordinate of the scaling origin
* @param dest
* will hold the result
* @return this
*/
Matrix4f scaleAroundLocal(float factor, float ox, float oy, float oz, Matrix4f 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
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateX(float ang, Matrix4f 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
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateY(float ang, Matrix4f 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
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateZ(float ang, Matrix4f 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.
*
* @param dirX
* the x component of the normalized direction
* @param dirY
* the y component of the normalized direction
* @param dest
* will hold the result
* @return this
*/
Matrix4f rotateTowardsXY(float dirX, float dirY, Matrix4f 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)
*
* @param angleX
* the angle to rotate about X
* @param angleY
* the angle to rotate about Y
* @param angleZ
* the angle to rotate about Z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateXYZ(float angleX, float angleY, float angleZ, Matrix4f 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 {@link #isAffine() 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!
*
* @param angleX
* the angle to rotate about X
* @param angleY
* the angle to rotate about Y
* @param angleZ
* the angle to rotate about Z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAffineXYZ(float angleX, float angleY, float angleZ, Matrix4f 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)
*
* @param angleZ
* the angle to rotate about Z
* @param angleY
* the angle to rotate about Y
* @param angleX
* the angle to rotate about X
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateZYX(float angleZ, float angleY, float angleX, Matrix4f 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 {@link #isAffine() 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!
*
* @param angleZ
* the angle to rotate about Z
* @param angleY
* the angle to rotate about Y
* @param angleX
* the angle to rotate about X
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAffineZYX(float angleZ, float angleY, float angleX, Matrix4f 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)
*
* @param angleY
* the angle to rotate about Y
* @param angleX
* the angle to rotate about X
* @param angleZ
* the angle to rotate about Z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateYXZ(float angleY, float angleX, float angleZ, Matrix4f 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 {@link #isAffine() 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!
*
* @param angleY
* the angle to rotate about Y
* @param angleX
* the angle to rotate about X
* @param angleZ
* the angle to rotate about Z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAffineYXZ(float angleY, float angleX, float angleZ, Matrix4f dest);
/**
* Apply 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 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
*
* @param ang
* the angle in radians
* @param x
* the x component of the axis
* @param y
* the y component of the axis
* @param z
* the z component of the axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotate(float ang, float x, float y, float z, Matrix4f 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
*
* @param ang
* the angle in radians
* @param x
* the x component of the axis
* @param y
* the y component of the axis
* @param z
* the z component of the axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateTranslation(float ang, float x, float y, float z, Matrix4f dest);
/**
* Apply rotation to this {@link #isAffine() 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 {@link #isAffine() 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
*
* @param ang
* the angle in radians
* @param x
* the x component of the axis
* @param y
* the y component of the axis
* @param z
* the z component of the axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAffine(float ang, float x, float y, float z, Matrix4f 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
*
* @param ang
* the angle in radians
* @param x
* the x component of the axis
* @param y
* the y component of the axis
* @param z
* the z component of the axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateLocal(float ang, float x, float y, float z, Matrix4f 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
*
* @param ang
* the angle in radians to rotate about the X axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateLocalX(float ang, Matrix4f 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
*
* @param ang
* the angle in radians to rotate about the Y axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateLocalY(float ang, Matrix4f 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
*
* @param ang
* the angle in radians to rotate about the Z axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateLocalZ(float ang, Matrix4f 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!
*
* @param offset
* the number of units in x, y and z by which to translate
* @param dest
* will hold the result
* @return dest
*/
Matrix4f translate(Vector3fc offset, Matrix4f 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!
*
* @param x
* the offset to translate in x
* @param y
* the offset to translate in y
* @param z
* the offset to translate in z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f translate(float x, float y, float z, Matrix4f 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!
*
* @param offset
* the number of units in x, y and z by which to translate
* @param dest
* will hold the result
* @return dest
*/
Matrix4f translateLocal(Vector3fc offset, Matrix4f 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!
*
* @param x
* the offset to translate in x
* @param y
* the offset to translate in y
* @param z
* the offset to translate in z
* @param dest
* will hold the result
* @return dest
*/
Matrix4f translateLocal(float x, float y, float z, Matrix4f 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
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param 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
* @param dest
* will hold the result
* @return dest
*/
Matrix4f ortho(float left, float right, float bottom, float top, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @return dest
*/
Matrix4f ortho(float left, float right, float bottom, float top, float zNear, float zFar, Matrix4f 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
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param 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
* @param dest
* will hold the result
* @return dest
*/
Matrix4f orthoLH(float left, float right, float bottom, float top, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @return dest
*/
Matrix4f orthoLH(float left, float right, float bottom, float top, float zNear, float zFar, Matrix4f 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 {@link #ortho(float, float, float, float, float, float, boolean, Matrix4f) 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
*
* @param width
* the distance between the right and left frustum edges
* @param height
* the distance between the top and bottom frustum edges
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @param 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
* @return dest
*/
Matrix4f orthoSymmetric(float width, float height, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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 {@link #ortho(float, float, float, float, float, float, Matrix4f) 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
*
* @param width
* the distance between the right and left frustum edges
* @param height
* the distance between the top and bottom frustum edges
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @return dest
*/
Matrix4f orthoSymmetric(float width, float height, float zNear, float zFar, Matrix4f 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 {@link #orthoLH(float, float, float, float, float, float, boolean, Matrix4f) 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
*
* @param width
* the distance between the right and left frustum edges
* @param height
* the distance between the top and bottom frustum edges
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @param 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
* @return dest
*/
Matrix4f orthoSymmetricLH(float width, float height, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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 {@link #orthoLH(float, float, float, float, float, float, Matrix4f) 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
*
* @param width
* the distance between the right and left frustum edges
* @param height
* the distance between the top and bottom frustum edges
* @param zNear
* near clipping plane distance
* @param zFar
* far clipping plane distance
* @param dest
* will hold the result
* @return dest
*/
Matrix4f orthoSymmetricLH(float width, float height, float zNear, float zFar, Matrix4f 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 {@link #ortho(float, float, float, float, float, float, Matrix4f) 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
*
* @see #ortho(float, float, float, float, float, float, Matrix4f)
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param dest
* will hold the result
* @return dest
*/
Matrix4f ortho2D(float left, float right, float bottom, float top, Matrix4f 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 {@link #orthoLH(float, float, float, float, float, float, Matrix4f) 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
*
* @see #orthoLH(float, float, float, float, float, float, Matrix4f)
*
* @param left
* the distance from the center to the left frustum edge
* @param right
* the distance from the center to the right frustum edge
* @param bottom
* the distance from the center to the bottom frustum edge
* @param top
* the distance from the center to the top frustum edge
* @param dest
* will hold the result
* @return dest
*/
Matrix4f ortho2DLH(float left, float right, float bottom, float top, Matrix4f 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
* {@link #lookAt(Vector3fc, Vector3fc, Vector3fc, Matrix4f) lookAt}
* with eye = (0, 0, 0) and center = dir.
*
* @see #lookAlong(float, float, float, float, float, float, Matrix4f)
* @see #lookAt(Vector3fc, Vector3fc, Vector3fc, Matrix4f)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAlong(Vector3fc dir, Vector3fc up, Matrix4f 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
* {@link #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f) lookAt()}
* with eye = (0, 0, 0) and center = dir.
*
* @see #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f)
*
* @param dirX
* the x-coordinate of the direction to look along
* @param dirY
* the y-coordinate of the direction to look along
* @param dirZ
* the z-coordinate of the direction to look along
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAlong(float dirX, float dirY, float dirZ, float upX, float upY, float upZ, Matrix4f 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!
*
* @see #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f)
*
* @param eye
* the position of the camera
* @param center
* the point in space to look at
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAt(Vector3fc eye, Vector3fc center, Vector3fc up, Matrix4f 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!
*
* @see #lookAt(Vector3fc, Vector3fc, Vector3fc, Matrix4f)
*
* @param eyeX
* the x-coordinate of the eye/camera location
* @param eyeY
* the y-coordinate of the eye/camera location
* @param eyeZ
* the z-coordinate of the eye/camera location
* @param centerX
* the x-coordinate of the point to look at
* @param centerY
* the y-coordinate of the point to look at
* @param centerZ
* the z-coordinate of the point to look at
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAt(float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ, Matrix4f 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
* {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()} or {@link #perspective(float, float, float, float, Matrix4f) 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!
*
* @param eyeX
* the x-coordinate of the eye/camera location
* @param eyeY
* the y-coordinate of the eye/camera location
* @param eyeZ
* the z-coordinate of the eye/camera location
* @param centerX
* the x-coordinate of the point to look at
* @param centerY
* the y-coordinate of the point to look at
* @param centerZ
* the z-coordinate of the point to look at
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAtPerspective(float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ, Matrix4f 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!
*
* @see #lookAtLH(float, float, float, float, float, float, float, float, float, Matrix4f)
*
* @param eye
* the position of the camera
* @param center
* the point in space to look at
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAtLH(Vector3fc eye, Vector3fc center, Vector3fc up, Matrix4f 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!
*
* @see #lookAtLH(Vector3fc, Vector3fc, Vector3fc, Matrix4f)
*
* @param eyeX
* the x-coordinate of the eye/camera location
* @param eyeY
* the y-coordinate of the eye/camera location
* @param eyeZ
* the z-coordinate of the eye/camera location
* @param centerX
* the x-coordinate of the point to look at
* @param centerY
* the y-coordinate of the point to look at
* @param centerZ
* the z-coordinate of the point to look at
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAtLH(float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ, Matrix4f 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
* {@link #frustumLH(float, float, float, float, float, float, Matrix4f) frustumLH()} or {@link #perspectiveLH(float, float, float, float, Matrix4f) 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!
*
* @param eyeX
* the x-coordinate of the eye/camera location
* @param eyeY
* the y-coordinate of the eye/camera location
* @param eyeZ
* the z-coordinate of the eye/camera location
* @param centerX
* the x-coordinate of the point to look at
* @param centerY
* the y-coordinate of the point to look at
* @param centerZ
* the z-coordinate of the point to look at
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lookAtPerspectiveLH(float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ, Matrix4f 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!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @param 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
* @return dest
*/
Matrix4f perspective(float fovy, float aspect, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f perspective(float fovy, float aspect, float zNear, float zFar, Matrix4f 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!
*
* @param width
* the width of the near frustum plane
* @param height
* the height of the near frustum plane
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @param 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
* @return dest
*/
Matrix4f perspectiveRect(float width, float height, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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!
*
* @param width
* the width of the near frustum plane
* @param height
* the height of the near frustum plane
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f perspectiveRect(float width, float height, float zNear, float zFar, Matrix4f dest);
/**
* Apply a symmetric perspective projection frustum transformation using for a right-handed coordinate system
* the given NDC z range to this matrix.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param width
* the width of the near frustum plane
* @param height
* the height of the near frustum plane
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param 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
* @return this
*/
Matrix4f perspectiveRect(float width, float height, float zNear, float zFar, boolean zZeroToOne);
/**
* Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system
* using OpenGL's NDC z range of [-1..+1] to this matrix.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param width
* the width of the near frustum plane
* @param height
* the height of the near frustum plane
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @return this
*/
Matrix4f perspectiveRect(float width, float height, float zNear, float zFar);
/**
* Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system
* using the given NDC z range to this matrix and store the result in dest.
*
* The given angles offAngleX and offAngleY are the horizontal and vertical angles between
* the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY
* is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane
* is parallel to the XZ-plane.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param offAngleX
* the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param offAngleY
* the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @param 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
* @return dest
*/
Matrix4f perspectiveOffCenter(float fovy, float offAngleX, float offAngleY, float aspect, float zNear, float zFar, boolean zZeroToOne, Matrix4f dest);
/**
* Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system
* using OpenGL's NDC z range of [-1..+1] to this matrix and store the result in dest.
*
* The given angles offAngleX and offAngleY are the horizontal and vertical angles between
* the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY
* is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane
* is parallel to the XZ-plane.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param offAngleX
* the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param offAngleY
* the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f perspectiveOffCenter(float fovy, float offAngleX, float offAngleY, float aspect, float zNear, float zFar, Matrix4f dest);
/**
* Apply an asymmetric off-center perspective projection frustum transformation using for a right-handed coordinate system
* the given NDC z range to this matrix.
*
* The given angles offAngleX and offAngleY are the horizontal and vertical angles between
* the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY
* is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane
* is parallel to the XZ-plane.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param offAngleX
* the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param offAngleY
* the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param 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
* @return this
*/
Matrix4f perspectiveOffCenter(float fovy, float offAngleX, float offAngleY, float aspect, float zNear, float zFar, boolean zZeroToOne);
/**
* Apply an asymmetric off-center perspective projection frustum transformation for a right-handed coordinate system
* using OpenGL's NDC z range of [-1..+1] to this matrix.
*
* The given angles offAngleX and offAngleY are the horizontal and vertical angles between
* the line of sight and the line given by the center of the near and far frustum planes. So, when offAngleY
* is just fovy/2 then the projection frustum is rotated towards +Y and the bottom frustum plane
* is parallel to the XZ-plane.
*
* If M is this matrix and P the perspective projection matrix,
* then the new matrix will be M * P. So when transforming a
* vector v with the new matrix by using M * P * v,
* the perspective projection will be applied first!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param offAngleX
* the horizontal angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param offAngleY
* the vertical angle between the line of sight and the line crossing the center of the near and far frustum planes
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @return this
*/
Matrix4f perspectiveOffCenter(float fovy, float offAngleX, float offAngleY, float aspect, float zNear, float zFar);
/**
* 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!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param 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
* @param dest
* will hold the result
* @return dest
*/
Matrix4f perspectiveLH(float fovy, float aspect, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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!
*
* @param fovy
* the vertical field of view in radians (must be greater than zero and less than {@link Math#PI PI})
* @param aspect
* the aspect ratio (i.e. width / height; must be greater than zero)
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f perspectiveLH(float fovy, float aspect, float zNear, float zFar, Matrix4f 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
*
* @param left
* the distance along the x-axis to the left frustum edge
* @param right
* the distance along the x-axis to the right frustum edge
* @param bottom
* the distance along the y-axis to the bottom frustum edge
* @param top
* the distance along the y-axis to the top frustum edge
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param 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
* @param dest
* will hold the result
* @return dest
*/
Matrix4f frustum(float left, float right, float bottom, float top, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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
*
* @param left
* the distance along the x-axis to the left frustum edge
* @param right
* the distance along the x-axis to the right frustum edge
* @param bottom
* the distance along the y-axis to the bottom frustum edge
* @param top
* the distance along the y-axis to the top frustum edge
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f frustum(float left, float right, float bottom, float top, float zNear, float zFar, Matrix4f 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
*
* @param left
* the distance along the x-axis to the left frustum edge
* @param right
* the distance along the x-axis to the right frustum edge
* @param bottom
* the distance along the y-axis to the bottom frustum edge
* @param top
* the distance along the y-axis to the top frustum edge
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param 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
* @param dest
* will hold the result
* @return dest
*/
Matrix4f frustumLH(float left, float right, float bottom, float top, float zNear, float zFar, boolean zZeroToOne, Matrix4f 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
*
* @param left
* the distance along the x-axis to the left frustum edge
* @param right
* the distance along the x-axis to the right frustum edge
* @param bottom
* the distance along the y-axis to the bottom frustum edge
* @param top
* the distance along the y-axis to the top frustum edge
* @param zNear
* near clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, zFar may not also be {@link Float#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Float#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, zNear may not also be {@link Float#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4f frustumLH(float left, float right, float bottom, float top, float zNear, float zFar, Matrix4f dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link 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
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotate(Quaternionfc quat, Matrix4f dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this {@link #isAffine() affine} matrix and store
* the result in dest.
*
* This method assumes this to be {@link #isAffine() 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
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAffine(Quaternionfc quat, Matrix4f dest);
/**
* Apply the rotation - and possibly scaling - ransformation of the given {@link 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
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateTranslation(Quaternionfc quat, Matrix4f dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this {@link #isAffine() 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 {@link #isAffine() affine} matrix.
*
* This method is equivalent to calling: translate(ox, oy, oz, dest).rotate(quat).translate(-ox, -oy, -oz)
*
* Reference: http://en.wikipedia.org
*
* @param quat
* the {@link Quaternionfc}
* @param ox
* the x coordinate of the rotation origin
* @param oy
* the y coordinate of the rotation origin
* @param oz
* the z coordinate of the rotation origin
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAroundAffine(Quaternionfc quat, float ox, float oy, float oz, Matrix4f dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} 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
*
* @param quat
* the {@link Quaternionfc}
* @param ox
* the x coordinate of the rotation origin
* @param oy
* the y coordinate of the rotation origin
* @param oz
* the z coordinate of the rotation origin
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAround(Quaternionfc quat, float ox, float oy, float oz, Matrix4f dest);
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link 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
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateLocal(Quaternionfc quat, Matrix4f dest);
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} 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
*
* @param quat
* the {@link Quaternionfc}
* @param ox
* the x coordinate of the rotation origin
* @param oy
* the y coordinate of the rotation origin
* @param oz
* the z coordinate of the rotation origin
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateAroundLocal(Quaternionfc quat, float ox, float oy, float oz, Matrix4f dest);
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4f} 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 {@link 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 {@link AxisAngle4f} rotation will be applied first!
*
* Reference: http://en.wikipedia.org
*
* @see #rotate(float, float, float, float, Matrix4f)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotate(AxisAngle4f axisAngle, Matrix4f dest);
/**
* Apply a rotation transformation, rotating the given radians about the specified axis 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 axis-angle,
* 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
*
* @see #rotate(float, float, float, float, Matrix4f)
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis (needs to be {@link Vector3fc#normalize(Vector3f) normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotate(float angle, Vector3fc axis, Matrix4f 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInv(float, float, float, int[], Vector4f) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(float, float, float, int[], Vector4f)
* @see #invert(Matrix4f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param winZ
* the z-coordinate, which is the depth value in [0..1]
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4f unproject(float winX, float winY, float winZ, int[] viewport, Vector4f 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInv(float, float, float, int[], Vector3f) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(float, float, float, int[], Vector3f)
* @see #invert(Matrix4f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param winZ
* the z-coordinate, which is the depth value in [0..1]
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3f unproject(float winX, float winY, float winZ, int[] viewport, Vector3f 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInv(float, float, float, int[], Vector4f) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(float, float, float, int[], Vector4f)
* @see #unproject(float, float, float, int[], Vector4f)
* @see #invert(Matrix4f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4f unproject(Vector3fc winCoords, int[] viewport, Vector4f 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInv(float, float, float, int[], Vector3f) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(float, float, float, int[], Vector3f)
* @see #unproject(float, float, float, int[], Vector3f)
* @see #invert(Matrix4f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3f unproject(Vector3fc winCoords, int[] viewport, Vector3f dest);
/**
* 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInvRay(float, float, int[], Vector3f, Vector3f) unprojectInvRay()} can be invoked on it.
*
* @see #unprojectInvRay(float, float, int[], Vector3f, Vector3f)
* @see #invert(Matrix4f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param viewport
* the viewport described by [x, y, width, height]
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4f unprojectRay(float winX, float winY, int[] viewport, Vector3f originDest, Vector3f 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 {@link #invert(Matrix4f)} and then the method {@link #unprojectInvRay(float, float, int[], Vector3f, Vector3f) unprojectInvRay()} can be invoked on it.
*
* @see #unprojectInvRay(float, float, int[], Vector3f, Vector3f)
* @see #unprojectRay(float, float, int[], Vector3f, Vector3f)
* @see #invert(Matrix4f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4f unprojectRay(Vector2fc winCoords, int[] viewport, Vector3f originDest, Vector3f dirDest);
/**
* Unproject the given window coordinates winCoords by this matrix using the specified viewport.
*
* This method differs from {@link #unproject(Vector3fc, int[], Vector4f) 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.
*
* The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.
*
* This method reads the four viewport parameters from the given int[].
*
* @see #unproject(Vector3fc, int[], Vector4f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4f unprojectInv(Vector3fc winCoords, int[] viewport, Vector4f dest);
/**
* Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
*
* This method differs from {@link #unproject(float, float, float, int[], Vector4f) 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.
*
* The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.
*
* @see #unproject(float, float, float, int[], Vector4f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param winZ
* the z-coordinate, which is the depth value in [0..1]
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4f unprojectInv(float winX, float winY, float winZ, int[] viewport, Vector4f dest);
/**
* 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 {@link #unprojectRay(Vector2fc, int[], Vector3f, Vector3f) 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.
*
* @see #unprojectRay(Vector2fc, int[], Vector3f, Vector3f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4f unprojectInvRay(Vector2fc winCoords, int[] viewport, Vector3f originDest, Vector3f 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 {@link #unprojectRay(float, float, int[], Vector3f, Vector3f) 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.
*
* @see #unprojectRay(float, float, int[], Vector3f, Vector3f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param viewport
* the viewport described by [x, y, width, height]
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4f unprojectInvRay(float winX, float winY, int[] viewport, Vector3f originDest, Vector3f dirDest);
/**
* Unproject the given window coordinates winCoords by this matrix using the specified viewport.
*
* This method differs from {@link #unproject(Vector3fc, int[], Vector3f) 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.
*
* The depth range of winCoords.z is assumed to be [0..1], which is also the OpenGL default.
*
* @see #unproject(Vector3fc, int[], Vector3f)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3f unprojectInv(Vector3fc winCoords, int[] viewport, Vector3f dest);
/**
* Unproject the given window coordinates (winX, winY, winZ) by this matrix using the specified viewport.
*
* This method differs from {@link #unproject(float, float, float, int[], Vector3f) 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.
*
* The depth range of winZ is assumed to be [0..1], which is also the OpenGL default.
*
* @see #unproject(float, float, float, int[], Vector3f)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param winZ
* the z-coordinate, which is the depth value in [0..1]
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3f unprojectInv(float winX, float winY, float winZ, int[] viewport, Vector3f dest);
/**
* 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.
*
* @param x
* the x-coordinate of the position to project
* @param y
* the y-coordinate of the position to project
* @param z
* the z-coordinate of the position to project
* @param viewport
* the viewport described by [x, y, width, height]
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector4f project(float x, float y, float z, int[] viewport, Vector4f 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.
*
* @param x
* the x-coordinate of the position to project
* @param y
* the y-coordinate of the position to project
* @param z
* the z-coordinate of the position to project
* @param viewport
* the viewport described by [x, y, width, height]
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector3f project(float x, float y, float z, int[] viewport, Vector3f 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.
*
* @see #project(float, float, float, int[], Vector4f)
*
* @param position
* the position to project into window coordinates
* @param viewport
* the viewport described by [x, y, width, height]
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector4f project(Vector3fc position, int[] viewport, Vector4f 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.
*
* @see #project(float, float, float, int[], Vector4f)
*
* @param position
* the position to project into window coordinates
* @param viewport
* the viewport described by [x, y, width, height]
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector3f project(Vector3fc position, int[] viewport, Vector3f winCoordsDest);
/**
* 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
*
* @param a
* the x factor in the plane equation
* @param b
* the y factor in the plane equation
* @param c
* the z factor in the plane equation
* @param d
* the constant in the plane equation
* @param dest
* will hold the result
* @return dest
*/
Matrix4f reflect(float a, float b, float c, float d, Matrix4f 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!
*
* @param nx
* the x-coordinate of the plane normal
* @param ny
* the y-coordinate of the plane normal
* @param nz
* the z-coordinate of the plane normal
* @param px
* the x-coordinate of a point on the plane
* @param py
* the y-coordinate of a point on the plane
* @param pz
* the z-coordinate of a point on the plane
* @param dest
* will hold the result
* @return dest
*/
Matrix4f reflect(float nx, float ny, float nz, float px, float py, float pz, Matrix4f 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 {@link Quaternionfc} 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!
*
* @param orientation
* the plane orientation relative to an implied normal vector of (0, 0, 1)
* @param point
* a point on the plane
* @param dest
* will hold the result
* @return dest
*/
Matrix4f reflect(Quaternionfc orientation, Vector3fc point, Matrix4f 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!
*
* @param normal
* the plane normal
* @param point
* a point on the plane
* @param dest
* will hold the result
* @return dest
*/
Matrix4f reflect(Vector3fc normal, Vector3fc point, Matrix4f dest);
/**
* Get the row at the given row index, starting with 0.
*
* @param row
* the row index in [0..3]
* @param dest
* will hold the row components
* @return the passed in destination
* @throws IndexOutOfBoundsException if row is not in [0..3]
*/
Vector4f getRow(int row, Vector4f dest) throws IndexOutOfBoundsException;
/**
* Get the first three components of the row at the given row index, starting with 0.
*
* @param row
* the row index in [0..3]
* @param dest
* will hold the first three row components
* @return the passed in destination
* @throws IndexOutOfBoundsException if row is not in [0..3]
*/
Vector3f getRow(int row, Vector3f dest) throws IndexOutOfBoundsException;
/**
* Get the column at the given column index, starting with 0.
*
* @param column
* the column index in [0..3]
* @param dest
* will hold the column components
* @return the passed in destination
* @throws IndexOutOfBoundsException if column is not in [0..3]
*/
Vector4f getColumn(int column, Vector4f dest) throws IndexOutOfBoundsException;
/**
* Get the first three components of the column at the given column index, starting with 0.
*
* @param column
* the column index in [0..3]
* @param dest
* will hold the first three column components
* @return the passed in destination
* @throws IndexOutOfBoundsException if column is not in [0..3]
*/
Vector3f getColumn(int column, Vector3f dest) throws IndexOutOfBoundsException;
/**
* Get the matrix element value at the given column and row.
*
* @param column
* the colum index in [0..3]
* @param row
* the row index in [0..3]
* @return the element value
*/
float get(int column, int row);
/**
* Get the matrix element value at the given row and column.
*
* @param row
* the row index in [0..3]
* @param column
* the colum index in [0..3]
* @return the element value
*/
float getRowColumn(int row, int column);
/**
* 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.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f normal(Matrix4f 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.
*
* @see Matrix3f#set(Matrix4fc)
* @see #get3x3(Matrix3f)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3f normal(Matrix3f dest);
/**
* Compute the cofactor matrix of the upper left 3x3 submatrix of this
* and store it into dest.
*
* The cofactor matrix can be used instead of {@link #normal(Matrix3f)} to transform normals
* when the orientation of the normals with respect to the surface should be preserved.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3f cofactor3x3(Matrix3f dest);
/**
* Compute the cofactor matrix of the upper left 3x3 submatrix of this
* and store it into dest.
* All other values of dest will be set to identity.
*
* The cofactor matrix can be used instead of {@link #normal(Matrix4f)} to transform normals
* when the orientation of the normals with respect to the surface should be preserved.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f cofactor3x3(Matrix4f 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).
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4f normalize3x3(Matrix4f 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).
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3f normalize3x3(Matrix3f dest);
/**
* Calculate a frustum plane of this matrix, which
* can be a projection matrix or a combined modelview-projection matrix, and store the result
* in the given 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 {@link Vector4f} 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 {@link 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
*
* @param plane
* one of the six possible planes, given as numeric constants
* {@link #PLANE_NX}, {@link #PLANE_PX},
* {@link #PLANE_NY}, {@link #PLANE_PY},
* {@link #PLANE_NZ} and {@link #PLANE_PZ}
* @param planeEquation
* will hold the computed plane equation.
* The plane equation will be normalized, meaning that (a, b, c) will be a unit vector
* @return planeEquation
*/
Vector4f frustumPlane(int plane, Vector4f 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 {@link 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
*
* @param which
* one of the six possible planes, given as numeric constants
* {@link #PLANE_NX}, {@link #PLANE_PX},
* {@link #PLANE_NY}, {@link #PLANE_PY},
* {@link #PLANE_NZ} and {@link #PLANE_PZ}
* @param plane
* will hold the computed plane equation.
* The plane equation will be normalized, meaning that (a, b, c) will be a unit vector
* @return planeEquation
*/
Planef frustumPlane(int which, Planef plane);
/**
* Compute the corner coordinates of the frustum defined by this matrix, which
* can be a projection matrix or a combined modelview-projection matrix, and store the result
* in the given point.
*
* Generally, this method computes the frustum corners in the local frame of
* any coordinate system that existed before this
* transformation was applied to it in order to yield homogeneous clipping space.
*
* Reference: http://geomalgorithms.com
*
* Reference:
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
*
* @param corner
* one of the eight possible corners, given as numeric constants
* {@link #CORNER_NXNYNZ}, {@link #CORNER_PXNYNZ}, {@link #CORNER_PXPYNZ}, {@link #CORNER_NXPYNZ},
* {@link #CORNER_PXNYPZ}, {@link #CORNER_NXNYPZ}, {@link #CORNER_NXPYPZ}, {@link #CORNER_PXPYPZ}
* @param point
* will hold the resulting corner point coordinates
* @return point
*/
Vector3f frustumCorner(int corner, Vector3f point);
/**
* 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 {@link #perspective(float, float, float, float, Matrix4f) perspective()}
* or {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()}.
*
* Generally, this method computes the origin in the local frame of
* any coordinate system that existed before this
* transformation was applied to it in order to yield homogeneous clipping space.
*
* This method is equivalent to calling: invert(new Matrix4f()).transformProject(0, 0, -1, 0, origin)
* and in the case of an already available inverse of this matrix, the method {@link #perspectiveInvOrigin(Vector3f)}
* on the inverse of the matrix should be used instead.
*
* Reference: http://geomalgorithms.com
*
* Reference:
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
*
* @param origin
* will hold the origin of the coordinate system before applying this
* perspective projection transformation
* @return origin
*/
Vector3f perspectiveOrigin(Vector3f origin);
/**
* Compute the eye/origin of the inverse of the perspective frustum transformation defined by this matrix,
* which can be the inverse of a projection matrix or the inverse of a combined modelview-projection matrix, and store the result
* in the given dest.
*
* Note that this method will only work using perspective projections obtained via one of the
* perspective methods, such as {@link #perspective(float, float, float, float, Matrix4f) perspective()}
* or {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()}.
*
* If the inverse of the modelview-projection matrix is not available, then calling {@link #perspectiveOrigin(Vector3f)}
* on the original modelview-projection matrix is preferred.
*
* @see #perspectiveOrigin(Vector3f)
*
* @param dest
* will hold the result
* @return dest
*/
Vector3f perspectiveInvOrigin(Vector3f dest);
/**
* Return the vertical field-of-view angle in radians of this perspective transformation matrix.
*
* Note that this method will only work using perspective projections obtained via one of the
* perspective methods, such as {@link #perspective(float, float, float, float, Matrix4f) perspective()}
* or {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()}.
*
* For orthogonal transformations this method will return 0.0.
*
* Reference:
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
*
* @return the vertical field-of-view angle in radians
*/
float perspectiveFov();
/**
* 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 {@link #perspective(float, float, float, float, Matrix4f)}.
*
* @return the near clip plane distance
*/
float perspectiveNear();
/**
* 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 {@link #perspective(float, float, float, float, Matrix4f)}.
*
* @return the far clip plane distance
*/
float perspectiveFar();
/**
* 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 {@link FrustumRayBuilder}.
*
* Reference:
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
*
* @param x
* the interpolation factor along the left-to-right frustum planes, within [0..1]
* @param y
* the interpolation factor along the bottom-to-top frustum planes, within [0..1]
* @param dir
* will hold the normalized ray direction in the local frame of the coordinate system before
* transforming to homogeneous clipping space using this matrix
* @return dir
*/
Vector3f frustumRayDir(float x, float y, Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).invert();
* inv.transformDirection(dir.set(0, 0, 1)).normalize();
*
* If this is already an orthogonal matrix, then consider using {@link #normalizedPositiveZ(Vector3f)} instead.
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +Z
* @return dir
*/
Vector3f positiveZ(Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).transpose();
* inv.transformDirection(dir.set(0, 0, 1));
*
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +Z
* @return dir
*/
Vector3f normalizedPositiveZ(Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).invert();
* inv.transformDirection(dir.set(1, 0, 0)).normalize();
*
* If this is already an orthogonal matrix, then consider using {@link #normalizedPositiveX(Vector3f)} instead.
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +X
* @return dir
*/
Vector3f positiveX(Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).transpose();
* inv.transformDirection(dir.set(1, 0, 0));
*
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +X
* @return dir
*/
Vector3f normalizedPositiveX(Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).invert();
* inv.transformDirection(dir.set(0, 1, 0)).normalize();
*
* If this is already an orthogonal matrix, then consider using {@link #normalizedPositiveY(Vector3f)} instead.
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +Y
* @return dir
*/
Vector3f positiveY(Vector3f 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:
*
* Matrix4f inv = new Matrix4f(this).transpose();
* inv.transformDirection(dir.set(0, 1, 0));
*
*
* Reference: http://www.euclideanspace.com
*
* @param dir
* will hold the direction of +Y
* @return dir
*/
Vector3f normalizedPositiveY(Vector3f dir);
/**
* Obtain the position that gets transformed to the origin by this {@link #isAffine() affine} matrix.
* This can be used to get the position of the "camera" from a given view transformation matrix.
*
* This method only works with {@link #isAffine() affine} matrices.
*
* This method is equivalent to the following code:
*
* Matrix4f inv = new Matrix4f(this).invertAffine();
* inv.transformPosition(origin.set(0, 0, 0));
*
*
* @param origin
* will hold the position transformed to the origin
* @return origin
*/
Vector3f originAffine(Vector3f 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));
*
*
* @param origin
* will hold the position transformed to the origin
* @return origin
*/
Vector3f origin(Vector3f origin);
/**
* 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
*
* @param light
* the light's vector
* @param a
* the x factor in the plane equation
* @param b
* the y factor in the plane equation
* @param c
* the z factor in the plane equation
* @param d
* the constant in the plane equation
* @param dest
* will hold the result
* @return dest
*/
Matrix4f shadow(Vector4f light, float a, float b, float c, float d, Matrix4f 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
*
* @param lightX
* the x-component of the light's vector
* @param lightY
* the y-component of the light's vector
* @param lightZ
* the z-component of the light's vector
* @param lightW
* the w-component of the light's vector
* @param a
* the x factor in the plane equation
* @param b
* the y factor in the plane equation
* @param c
* the z factor in the plane equation
* @param d
* the constant in the plane equation
* @param dest
* will hold the result
* @return dest
*/
Matrix4f shadow(float lightX, float lightY, float lightZ, float lightW, float a, float b, float c, float d, Matrix4f 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!
*
* @param light
* the light's vector
* @param planeTransform
* the transformation to transform the implied plane y = 0 before applying the projection
* @param dest
* will hold the result
* @return dest
*/
Matrix4f shadow(Vector4f light, Matrix4fc planeTransform, Matrix4f 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!
*
* @param lightX
* the x-component of the light vector
* @param lightY
* the y-component of the light vector
* @param lightZ
* the z-component of the light vector
* @param lightW
* the w-component of the light vector
* @param planeTransform
* the transformation to transform the implied plane y = 0 before applying the projection
* @param dest
* will hold the result
* @return dest
*/
Matrix4f shadow(float lightX, float lightY, float lightZ, float lightW, Matrix4fc planeTransform, Matrix4f 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.
*
* @param x
* the x coordinate of the picking region center in window coordinates
* @param y
* the y coordinate of the picking region center in window coordinates
* @param width
* the width of the picking region in window coordinates
* @param height
* the height of the picking region in window coordinates
* @param viewport
* the viewport described by [x, y, width, height]
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4f pick(float x, float y, float width, float height, int[] viewport, Matrix4f dest);
/**
* Determine whether this matrix describes an affine transformation. This is the case iff its last row is equal to (0, 0, 0, 1).
*
* @return true iff this matrix is affine; false otherwise
*/
boolean isAffine();
/**
* 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)
*
* @param radius
* the arcball radius
* @param centerX
* the x coordinate of the center position of the arcball
* @param centerY
* the y coordinate of the center position of the arcball
* @param centerZ
* the z coordinate of the center position of the arcball
* @param angleX
* the rotation angle around the X axis in radians
* @param angleY
* the rotation angle around the Y axis in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4f arcball(float radius, float centerX, float centerY, float centerZ, float angleX, float angleY, Matrix4f 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)
*
* @param radius
* the arcball radius
* @param center
* the center position of the arcball
* @param angleX
* the rotation angle around the X axis in radians
* @param angleY
* the rotation angle around the Y axis in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4f arcball(float radius, Vector3fc center, float angleX, float angleY, Matrix4f dest);
/**
* Compute the axis-aligned bounding box of the frustum described by this matrix and store the minimum corner
* coordinates in the given min and the maximum corner coordinates in the given max vector.
*
* The matrix this is assumed to be the {@link #invert(Matrix4f) inverse} of the origial view-projection matrix
* for which to compute the axis-aligned bounding box in world-space.
*
* The axis-aligned bounding box of the unit frustum is (-1, -1, -1), (1, 1, 1).
*
* @param min
* will hold the minimum corner coordinates of the axis-aligned bounding box
* @param max
* will hold the maximum corner coordinates of the axis-aligned bounding box
* @return this
*/
Matrix4f frustumAabb(Vector3f min, Vector3f max);
/**
* 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.
*
* @param projector
* the projector view-projection transformation
* @param sLower
* the lower (smallest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid
* @param sUpper
* the upper (highest) Y-coordinate which any transformed vertex might have while still being visible on the projected grid
* @param dest
* will hold the resulting range matrix
* @return the computed range matrix; or null if the projected grid will not be visible
*/
Matrix4f projectedGridRange(Matrix4fc projector, float sLower, float sUpper, Matrix4f dest);
/**
* Change the near and far clip plane distances of this perspective frustum transformation matrix
* and store the result in dest.
*
* This method only works if this is a perspective projection frustum transformation, for example obtained
* via {@link #perspective(float, float, float, float, Matrix4f) perspective()} or {@link #frustum(float, float, float, float, float, float, Matrix4f) frustum()}.
*
* @see #perspective(float, float, float, float, Matrix4f)
* @see #frustum(float, float, float, float, float, float, Matrix4f)
*
* @param near
* the new near clip plane distance
* @param far
* the new far clip plane distance
* @param dest
* will hold the resulting matrix
* @return dest
*/
Matrix4f perspectiveFrustumSlice(float near, float far, Matrix4f 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 {@link #invert(Matrix4f) inverse} of a typical combined camera view-projection
* transformation, whose projection can be either orthographic or perspective.
*
* The view must be an {@link #isAffine() 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 {@link #lookAt(float, float, float, float, float, float, float, float, float, Matrix4f) lookAt()}.
*
* Reference: OpenGL SDK - Cascaded Shadow Maps
*
* @param view
* the view transformation to build a corresponding orthographic projection to fit the frustum of this
* @param dest
* will hold the crop projection transformation
* @return dest
*/
Matrix4f orthoCrop(Matrix4fc view, Matrix4f dest);
/**
* Transform the axis-aligned box given as the minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ)
* by this {@link #isAffine() 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
*
* @param minX
* the x coordinate of the minimum corner of the axis-aligned box
* @param minY
* the y coordinate of the minimum corner of the axis-aligned box
* @param minZ
* the z coordinate of the minimum corner of the axis-aligned box
* @param maxX
* the x coordinate of the maximum corner of the axis-aligned box
* @param maxY
* the y coordinate of the maximum corner of the axis-aligned box
* @param maxZ
* the y coordinate of the maximum corner of the axis-aligned box
* @param outMin
* will hold the minimum corner of the resulting axis-aligned box
* @param outMax
* will hold the maximum corner of the resulting axis-aligned box
* @return this
*/
Matrix4f transformAab(float minX, float minY, float minZ, float maxX, float maxY, float maxZ, Vector3f outMin, Vector3f outMax);
/**
* Transform the axis-aligned box given as the minimum corner min and maximum corner max
* by this {@link #isAffine() affine} matrix and compute the axis-aligned box of the result whose minimum corner is stored in outMin
* and maximum corner stored in outMax.
*
* @param min
* the minimum corner of the axis-aligned box
* @param max
* the maximum corner of the axis-aligned box
* @param outMin
* will hold the minimum corner of the resulting axis-aligned box
* @param outMax
* will hold the maximum corner of the resulting axis-aligned box
* @return this
*/
Matrix4f transformAab(Vector3fc min, Vector3fc max, Vector3f outMin, Vector3f outMax);
/**
* 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.
*
* @param other
* the other matrix
* @param t
* the interpolation factor between 0.0 and 1.0
* @param dest
* will hold the result
* @return dest
*/
Matrix4f lerp(Matrix4fc other, float t, Matrix4f 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 Matrix4f().lookAt(new Vector3f(), new Vector3f(dir).negate(), up).invertAffine(), dest)
*
* @see #rotateTowards(float, float, float, float, float, float, Matrix4f)
*
* @param dir
* the direction to rotate towards
* @param up
* the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateTowards(Vector3fc dir, Vector3fc up, Matrix4f dest);
/**
* Apply a model transformation to this matrix for a right-handed coordinate system,
* that aligns the local +Z axis with (dirX, dirY, dirZ)
* 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 Matrix4f().lookAt(0, 0, 0, -dirX, -dirY, -dirZ, upX, upY, upZ).invertAffine(), dest)
*
* @see #rotateTowards(Vector3fc, Vector3fc, Matrix4f)
*
* @param dirX
* the x-coordinate of the direction to rotate towards
* @param dirY
* the y-coordinate of the direction to rotate towards
* @param dirZ
* the z-coordinate of the direction to rotate towards
* @param upX
* the x-coordinate of the up vector
* @param upY
* the y-coordinate of the up vector
* @param upZ
* the z-coordinate of the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4f rotateTowards(float dirX, float dirY, float dirZ, float upX, float upY, float upZ, Matrix4f 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 {@link Matrix4fc#rotateZYX(float, float, float, Matrix4f)} 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).
*
* Matrix4f m = ...; // <- matrix only representing rotation
* Matrix4f n = new Matrix4f();
* n.rotateZYX(m.getEulerAnglesZYX(new Vector3f()));
*
*
* Reference: http://nghiaho.com/
*
* @param dest
* will hold the extracted Euler angles
* @return dest
*/
Vector3f getEulerAnglesZYX(Vector3f dest);
/**
* 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, {@link FrustumIntersection} should be used instead.
*
* Reference:
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
*
* @param x
* the x-coordinate of the point
* @param y
* the y-coordinate of the point
* @param z
* the z-coordinate of the point
* @return true if the given point is inside the frustum; false otherwise
*/
boolean testPoint(float x, float y, float z);
/**
* 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,
* {@link 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
*
* @param x
* the x-coordinate of the sphere's center
* @param y
* the y-coordinate of the sphere's center
* @param z
* the z-coordinate of the sphere's center
* @param r
* the sphere's radius
* @return true if the given sphere is partly or completely inside the frustum; false otherwise
*/
boolean testSphere(float x, float y, float z, float r);
/**
* 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,
* {@link 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
*
* @param minX
* the x-coordinate of the minimum corner
* @param minY
* the y-coordinate of the minimum corner
* @param minZ
* the z-coordinate of the minimum corner
* @param maxX
* the x-coordinate of the maximum corner
* @param maxY
* the y-coordinate of the maximum corner
* @param maxZ
* the z-coordinate of the maximum corner
* @return true if the axis-aligned box is completely or partly inside of the frustum; false otherwise
*/
boolean testAab(float minX, float minY, float minZ, float maxX, float maxY, float maxZ);
/**
* 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
*
*
* @param a
* the value for the z factor that applies to x
* @param b
* the value for the z factor that applies to y
* @param dest
* will hold the result
* @return dest
*/
Matrix4f obliqueZ(float a, float b, Matrix4f dest);
/**
* Apply a transformation to this matrix to ensure that the local Y axis (as obtained by {@link #positiveY(Vector3f)})
* will be coplanar to the plane spanned by the local Z axis (as obtained by {@link #positiveZ(Vector3f)}) and the
* given vector up, and store the result in dest.
*
* This effectively ensures that the resulting matrix will be equal to the one obtained from calling
* {@link Matrix4f#setLookAt(Vector3fc, Vector3fc, Vector3fc)} with the current
* local origin of this matrix (as obtained by {@link #originAffine(Vector3f)}), the sum of this position and the
* negated local Z axis as well as the given vector up.
*
* This method must only be called on {@link #isAffine()} matrices.
*
* @param up
* the up vector
* @param dest
* will hold the result
* @return this
*/
Matrix4f withLookAtUp(Vector3fc up, Matrix4f dest);
/**
* Apply a transformation to this matrix to ensure that the local Y axis (as obtained by {@link #positiveY(Vector3f)})
* will be coplanar to the plane spanned by the local Z axis (as obtained by {@link #positiveZ(Vector3f)}) and the
* given vector (upX, upY, upZ), and store the result in dest.
*
* This effectively ensures that the resulting matrix will be equal to the one obtained from calling
* {@link Matrix4f#setLookAt(float, float, float, float, float, float, float, float, float)} called with the current
* local origin of this matrix (as obtained by {@link #originAffine(Vector3f)}), the sum of this position and the
* negated local Z axis as well as the given vector (upX, upY, upZ).
*
* This method must only be called on {@link #isAffine()} matrices.
*
* @param upX
* the x coordinate of the up vector
* @param upY
* the y coordinate of the up vector
* @param upZ
* the z coordinate of the up vector
* @param dest
* will hold the result
* @return this
*/
Matrix4f withLookAtUp(float upX, float upY, float upZ, Matrix4f dest);
/**
* 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 {@link ArrayList} {@link HashSet} or {@link HashMap}
* and their operations, such as {@link ArrayList#contains(Object)} or {@link HashSet#remove(Object)}, since those
* data structures only use the {@link Object#equals(Object)} and {@link Object#hashCode()} methods.
*
* @param m
* the other matrix
* @param delta
* the allowed maximum difference
* @return true whether all of the matrix elements are equal; false otherwise
*/
boolean equals(Matrix4fc m, float delta);
/**
* Determine whether all matrix elements are finite floating-point values, that
* is, they are not {@link Float#isNaN() NaN} and not
* {@link Float#isInfinite() infinity}.
*
* @return {@code true} if all components are finite floating-point values;
* {@code false} otherwise
*/
boolean isFinite();
}