/*
* (C) Copyright 2016-2017 JOML
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/
package org.joml;
//#ifdef __HAS_NIO__
import java.nio.ByteBuffer;
import java.nio.DoubleBuffer;
import java.nio.FloatBuffer;
//#endif
/**
* Interface to an immutable 4x4 matrix of double-precision floats.
*
* @author Kai Burjack
*/
public interface Matrix4dc {
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>x=-1</tt> when using the identity matrix.
*/
int PLANE_NX = 0;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>x=1</tt> when using the identity matrix.
*/
int PLANE_PX = 1;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>y=-1</tt> when using the identity matrix.
*/
int PLANE_NY = 2;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>y=1</tt> when using the identity matrix.
*/
int PLANE_PY = 3;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>z=-1</tt> when using the identity matrix.
*/
int PLANE_NZ = 4;
/**
* Argument to the first parameter of {@link #frustumPlane(int, Vector4d)}
* identifying the plane with equation <tt>z=1</tt> when using the identity matrix.
*/
int PLANE_PZ = 5;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(-1, -1, -1)</tt> when using the identity matrix.
*/
int CORNER_NXNYNZ = 0;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(1, -1, -1)</tt> when using the identity matrix.
*/
int CORNER_PXNYNZ = 1;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(1, 1, -1)</tt> when using the identity matrix.
*/
int CORNER_PXPYNZ = 2;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(-1, 1, -1)</tt> when using the identity matrix.
*/
int CORNER_NXPYNZ = 3;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(1, -1, 1)</tt> when using the identity matrix.
*/
int CORNER_PXNYPZ = 4;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(-1, -1, 1)</tt> when using the identity matrix.
*/
int CORNER_NXNYPZ = 5;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(-1, 1, 1)</tt> when using the identity matrix.
*/
int CORNER_NXPYPZ = 6;
/**
* Argument to the first parameter of {@link #frustumCorner(int, Vector3d)}
* identifying the corner <tt>(1, 1, 1)</tt> 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;
/**
* @return the properties of the matrix
*/
byte properties();
/**
* Return the value of the matrix element at column 0 and row 0.
*
* @return the value of the matrix element
*/
double m00();
/**
* Return the value of the matrix element at column 0 and row 1.
*
* @return the value of the matrix element
*/
double m01();
/**
* Return the value of the matrix element at column 0 and row 2.
*
* @return the value of the matrix element
*/
double m02();
/**
* Return the value of the matrix element at column 0 and row 3.
*
* @return the value of the matrix element
*/
double m03();
/**
* Return the value of the matrix element at column 1 and row 0.
*
* @return the value of the matrix element
*/
double m10();
/**
* Return the value of the matrix element at column 1 and row 1.
*
* @return the value of the matrix element
*/
double m11();
/**
* Return the value of the matrix element at column 1 and row 2.
*
* @return the value of the matrix element
*/
double m12();
/**
* Return the value of the matrix element at column 1 and row 3.
*
* @return the value of the matrix element
*/
double m13();
/**
* Return the value of the matrix element at column 2 and row 0.
*
* @return the value of the matrix element
*/
double m20();
/**
* Return the value of the matrix element at column 2 and row 1.
*
* @return the value of the matrix element
*/
double m21();
/**
* Return the value of the matrix element at column 2 and row 2.
*
* @return the value of the matrix element
*/
double m22();
/**
* Return the value of the matrix element at column 2 and row 3.
*
* @return the value of the matrix element
*/
double m23();
/**
* Return the value of the matrix element at column 3 and row 0.
*
* @return the value of the matrix element
*/
double m30();
/**
* Return the value of the matrix element at column 3 and row 1.
*
* @return the value of the matrix element
*/
double m31();
/**
* Return the value of the matrix element at column 3 and row 2.
*
* @return the value of the matrix element
*/
double m32();
/**
* Return the value of the matrix element at column 3 and row 3.
*
* @return the value of the matrix element
*/
double m33();
/**
* Multiply this matrix by the supplied <code>right</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* transformation of the right matrix will be applied first!
*
* @param right
* the right operand of the multiplication
* @param dest
* will hold the result
* @return dest
*/
Matrix4d mul(Matrix4dc right, Matrix4d dest);
/**
* Pre-multiply this matrix by the supplied <code>left</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the <code>left</code> matrix,
* then the new matrix will be <code>L * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>L * M * v</code>, the
* transformation of <code>this</code> 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
*/
Matrix4d mulLocal(Matrix4dc left, Matrix4d dest);
/**
* Pre-multiply this matrix by the supplied <code>left</code> matrix, both of which are assumed to be {@link #isAffine() affine}, and store the result in <code>dest</code>.
* <p>
* This method assumes that <code>this</code> matrix and the given <code>left</code> matrix both represent an {@link #isAffine() affine} transformation
* (i.e. their last rows are equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* This method will not modify either the last row of <code>this</code> or the last row of <code>left</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the <code>left</code> matrix,
* then the new matrix will be <code>L * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>L * M * v</code>, the
* transformation of <code>this</code> matrix will be applied first!
*
* @param left
* the left operand of the matrix multiplication (the last row is assumed to be <tt>(0, 0, 0, 1)</tt>)
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulLocalAffine(Matrix4dc left, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d mul(Matrix3x2dc right, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d mul(Matrix3x2fc right, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix and store the result in <code>dest</code>.
* <p>
* The last row of the <code>right</code> matrix is assumed to be <tt>(0, 0, 0, 1)</tt>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d mul(Matrix4x3dc right, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix and store the result in <code>dest</code>.
* <p>
* The last row of the <code>right</code> matrix is assumed to be <tt>(0, 0, 0, 1)</tt>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d mul(Matrix4x3fc right, Matrix4d dest);
/**
* Multiply this matrix by the supplied parameter matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* transformation of the right matrix will be applied first!
*
* @param right
* the right operand of the multiplication
* @param dest
* will hold the result
* @return dest
*/
Matrix4d mul(Matrix4fc right, Matrix4d dest);
/**
* Multiply <code>this</code> symmetric perspective projection matrix by the supplied {@link #isAffine() affine} <code>view</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>P</code> is <code>this</code> matrix and <code>V</code> the <code>view</code> matrix,
* then the new matrix will be <code>P * V</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>P * V * v</code>, the
* transformation of the <code>view</code> matrix will be applied first!
*
* @param view
* the {@link #isAffine() affine} matrix to multiply <code>this</code> symmetric perspective projection matrix by
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulPerspectiveAffine(Matrix4dc view, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix, which is assumed to be {@link #isAffine() affine}, and store the result in <code>dest</code>.
* <p>
* This method assumes that the given <code>right</code> matrix represents an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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 <tt>(0, 0, 0, 1)</tt>)
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulAffineR(Matrix4dc right, Matrix4d dest);
/**
* Multiply this matrix by the supplied <code>right</code> matrix, both of which are assumed to be {@link #isAffine() affine}, and store the result in <code>dest</code>.
* <p>
* This method assumes that <code>this</code> matrix and the given <code>right</code> matrix both represent an {@link #isAffine() affine} transformation
* (i.e. their last rows are equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* This method will not modify either the last row of <code>this</code> or the last row of <code>right</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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 <tt>(0, 0, 0, 1)</tt>)
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulAffine(Matrix4dc right, Matrix4d dest);
/**
* Multiply this matrix, which is assumed to only contain a translation, by the supplied <code>right</code> matrix, which is assumed to be {@link #isAffine() affine}, and store the result in <code>dest</code>.
* <p>
* This method assumes that <code>this</code> matrix only contains a translation, and that the given <code>right</code> matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>).
* <p>
* This method will not modify either the last row of <code>this</code> or the last row of <code>right</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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 <tt>(0, 0, 0, 1)</tt>)
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulTranslationAffine(Matrix4dc right, Matrix4d dest);
/**
* Multiply <code>this</code> orthographic projection matrix by the supplied {@link #isAffine() affine} <code>view</code> matrix
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>V</code> the <code>view</code> matrix,
* then the new matrix will be <code>M * V</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * V * v</code>, the
* transformation of the <code>view</code> matrix will be applied first!
*
* @param view
* the affine matrix which to multiply <code>this</code> with
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d mulOrthoAffine(Matrix4dc view, Matrix4d dest);
/**
* Component-wise add the upper 4x3 submatrices of <code>this</code> and <code>other</code>
* by first multiplying each component of <code>other</code>'s 4x3 submatrix by <code>otherFactor</code>,
* adding that to <code>this</code> and storing the final result in <code>dest</code>.
* <p>
* The other components of <code>dest</code> will be set to the ones of <code>this</code>.
* <p>
* The matrices <code>this</code> and <code>other</code> 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
*/
Matrix4d fma4x3(Matrix4dc other, double otherFactor, Matrix4d dest);
/**
* Component-wise add <code>this</code> and <code>other</code> and store the result in <code>dest</code>.
*
* @param other
* the other addend
* @param dest
* will hold the result
* @return dest
*/
Matrix4d add(Matrix4dc other, Matrix4d dest);
/**
* Component-wise subtract <code>subtrahend</code> from <code>this</code> and store the result in <code>dest</code>.
*
* @param subtrahend
* the subtrahend
* @param dest
* will hold the result
* @return dest
*/
Matrix4d sub(Matrix4dc subtrahend, Matrix4d dest);
/**
* Component-wise multiply <code>this</code> by <code>other</code> and store the result in <code>dest</code>.
*
* @param other
* the other matrix
* @param dest
* will hold the result
* @return dest
*/
Matrix4d mulComponentWise(Matrix4dc other, Matrix4d dest);
/**
* Component-wise add the upper 4x3 submatrices of <code>this</code> and <code>other</code>
* and store the result in <code>dest</code>.
* <p>
* The other components of <code>dest</code> will be set to the ones of <code>this</code>.
*
* @param other
* the other addend
* @param dest
* will hold the result
* @return dest
*/
Matrix4d add4x3(Matrix4dc other, Matrix4d dest);
/**
* Component-wise add the upper 4x3 submatrices of <code>this</code> and <code>other</code>
* and store the result in <code>dest</code>.
* <p>
* The other components of <code>dest</code> will be set to the ones of <code>this</code>.
*
* @param other
* the other addend
* @param dest
* will hold the result
* @return dest
*/
Matrix4d add4x3(Matrix4fc other, Matrix4d dest);
/**
* Component-wise subtract the upper 4x3 submatrices of <code>subtrahend</code> from <code>this</code>
* and store the result in <code>dest</code>.
* <p>
* The other components of <code>dest</code> will be set to the ones of <code>this</code>.
*
* @param subtrahend
* the subtrahend
* @param dest
* will hold the result
* @return dest
*/
Matrix4d sub4x3(Matrix4dc subtrahend, Matrix4d dest);
/**
* Component-wise multiply the upper 4x3 submatrices of <code>this</code> by <code>other</code>
* and store the result in <code>dest</code>.
* <p>
* The other components of <code>dest</code> will be set to the ones of <code>this</code>.
*
* @param other
* the other matrix
* @param dest
* will hold the result
* @return dest
*/
Matrix4d mul4x3ComponentWise(Matrix4dc other, Matrix4d dest);
/**
* Return the determinant of this matrix.
* <p>
* If <code>this</code> matrix represents an {@link #isAffine() affine} transformation, such as translation, rotation, scaling and shearing,
* and thus its last row is equal to <tt>(0, 0, 0, 1)</tt>, then {@link #determinantAffine()} can be used instead of this method.
*
* @see #determinantAffine()
*
* @return the determinant
*/
double determinant();
/**
* Return the determinant of the upper left 3x3 submatrix of this matrix.
*
* @return the determinant
*/
double 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 <tt>(0, 0, 0, 1)</tt>.
*
* @return the determinant
*/
double determinantAffine();
/**
* Invert <code>this</code> matrix and store the result in <code>dest</code>.
* <p>
* If <code>this</code> matrix represents an {@link #isAffine() affine} transformation, such as translation, rotation, scaling and shearing,
* and thus its last row is equal to <tt>(0, 0, 0, 1)</tt>, then {@link #invertAffine(Matrix4d)} can be used instead of this method.
*
* @see #invertAffine(Matrix4d)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d invert(Matrix4d dest);
/**
* If <code>this</code> is a perspective projection matrix obtained via one of the {@link #perspective(double, double, double, double, Matrix4d) perspective()} methods,
* that is, if <code>this</code> is a symmetrical perspective frustum transformation,
* then this method builds the inverse of <code>this</code> and stores it into the given <code>dest</code>.
* <p>
* This method can be used to quickly obtain the inverse of a perspective projection matrix when being obtained via {@link #perspective(double, double, double, double, Matrix4d) perspective()}.
*
* @see #perspective(double, double, double, double, Matrix4d)
*
* @param dest
* will hold the inverse of <code>this</code>
* @return dest
*/
Matrix4d invertPerspective(Matrix4d dest);
/**
* If <code>this</code> is an arbitrary perspective projection matrix obtained via one of the {@link #frustum(double, double, double, double, double, double, Matrix4d) frustum()} methods,
* then this method builds the inverse of <code>this</code> and stores it into the given <code>dest</code>.
* <p>
* This method can be used to quickly obtain the inverse of a perspective projection matrix.
* <p>
* If this matrix represents a symmetric perspective frustum transformation, as obtained via {@link #perspective(double, double, double, double, Matrix4d) perspective()}, then
* {@link #invertPerspective(Matrix4d)} should be used instead.
*
* @see #frustum(double, double, double, double, double, double, Matrix4d)
* @see #invertPerspective(Matrix4d)
*
* @param dest
* will hold the inverse of <code>this</code>
* @return dest
*/
Matrix4d invertFrustum(Matrix4d dest);
/**
* Invert <code>this</code> orthographic projection matrix and store the result into the given <code>dest</code>.
* <p>
* This method can be used to quickly obtain the inverse of an orthographic projection matrix.
*
* @param dest
* will hold the inverse of <code>this</code>
* @return dest
*/
Matrix4d invertOrtho(Matrix4d dest);
/**
* If <code>this</code> is a perspective projection matrix obtained via one of the {@link #perspective(double, double, double, double, Matrix4d) perspective()} methods,
* that is, if <code>this</code> is a symmetrical perspective frustum transformation
* and the given <code>view</code> matrix is {@link #isAffine() affine} and has unit scaling (for example by being obtained via {@link #lookAt(double, double, double, double, double, double, double, double, double, Matrix4d) lookAt()}),
* then this method builds the inverse of <tt>this * view</tt> and stores it into the given <code>dest</code>.
* <p>
* 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(double, double, double, double, Matrix4d) perspective()} and {@link #lookAt(double, double, double, double, double, double, double, double, double, Matrix4d) lookAt()} or
* other methods, that build affine matrices, such as {@link #translate(double, double, double, Matrix4d) translate} and {@link #rotate(double, double, double, double, Matrix4d)}, except for {@link #scale(double, double, double, Matrix4d) scale()}.
* <p>
* For the special cases of the matrices <code>this</code> and <code>view</code> mentioned above this method, this method is equivalent to the following code:
* <pre>
* dest.set(this).mul(view).invert();
* </pre>
*
* @param view
* the view transformation (must be {@link #isAffine() affine} and have unit scaling)
* @param dest
* will hold the inverse of <tt>this * view</tt>
* @return dest
*/
Matrix4d invertPerspectiveView(Matrix4dc view, Matrix4d dest);
/**
* Invert this matrix by assuming that it is an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* and write the result into <code>dest</code>.
* <p>
* Note that if <code>this</code> matrix also has unit scaling, then the method {@link #invertAffineUnitScale(Matrix4d)} should be used instead.
*
* @see #invertAffineUnitScale(Matrix4d)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d invertAffine(Matrix4d dest);
/**
* Invert this matrix by assuming that it is an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* and has unit scaling (i.e. {@link #transformDirection(Vector3d) transformDirection} does not change the {@link Vector3dc#length() length} of the vector)
* and write the result into <code>dest</code>.
* <p>
* Reference: <a href="http://www.gamedev.net/topic/425118-inverse--matrix/">http://www.gamedev.net/</a>
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d invertAffineUnitScale(Matrix4d dest);
/**
* Invert this matrix by assuming that it is an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* and has unit scaling (i.e. {@link #transformDirection(Vector3d) transformDirection} does not change the {@link Vector3dc#length() length} of the vector),
* as is the case for matrices built via {@link #lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)} and their overloads, and write the result into <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #invertAffineUnitScale(Matrix4d)}
* <p>
* Reference: <a href="http://www.gamedev.net/topic/425118-inverse--matrix/">http://www.gamedev.net/</a>
*
* @see #invertAffineUnitScale(Matrix4d)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d invertLookAt(Matrix4d dest);
/**
* Transpose <code>this</code> matrix and store the result into <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d transpose(Matrix4d dest);
/**
* Transpose only the upper left 3x3 submatrix of this matrix and store the result in <code>dest</code>.
* <p>
* All other matrix elements are left unchanged.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d transpose3x3(Matrix4d dest);
/**
* Transpose only the upper left 3x3 submatrix of this matrix and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d transpose3x3(Matrix3d dest);
/**
* Get only the translation components <tt>(m30, m31, m32)</tt> of this matrix and store them in the given vector <code>xyz</code>.
*
* @param dest
* will hold the translation components of this matrix
* @return dest
*/
Vector3d getTranslation(Vector3d dest);
/**
* Get the scaling factors of <code>this</code> matrix for the three base axes.
*
* @param dest
* will hold the scaling factors for <tt>x</tt>, <tt>y</tt> and <tt>z</tt>
* @return dest
*/
Vector3d getScale(Vector3d dest);
/**
* Get the current values of <code>this</code> matrix and store them into
* <code>dest</code>.
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix4d get(Matrix4d dest);
/**
* Get the current values of the upper 4x3 submatrix of <code>this</code> matrix and store them into
* <code>dest</code>.
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix4x3d get4x3(Matrix4x3d dest);
/**
* Get the current values of the upper left 3x3 submatrix of <code>this</code> matrix and store them into
* <code>dest</code>.
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
Matrix3d get3x3(Matrix3d dest);
/**
* Get the current values of <code>this</code> matrix and store the represented rotation
* into the given {@link Quaternionf}.
* <p>
* 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(Matrix4dc)
*
* @param dest
* the destination {@link Quaternionf}
* @return the passed in destination
*/
Quaternionf getUnnormalizedRotation(Quaternionf dest);
/**
* Get the current values of <code>this</code> matrix and store the represented rotation
* into the given {@link Quaternionf}.
* <p>
* This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
*
* @see Quaternionf#setFromNormalized(Matrix4dc)
*
* @param dest
* the destination {@link Quaternionf}
* @return the passed in destination
*/
Quaternionf getNormalizedRotation(Quaternionf dest);
/**
* Get the current values of <code>this</code> matrix and store the represented rotation
* into the given {@link Quaterniond}.
* <p>
* 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(Matrix4dc)
*
* @param dest
* the destination {@link Quaterniond}
* @return the passed in destination
*/
Quaterniond getUnnormalizedRotation(Quaterniond dest);
/**
* Get the current values of <code>this</code> matrix and store the represented rotation
* into the given {@link Quaterniond}.
* <p>
* This method assumes that the first three column vectors of the upper left 3x3 submatrix are normalized.
*
* @see Quaterniond#setFromNormalized(Matrix4dc)
*
* @param dest
* the destination {@link Quaterniond}
* @return the passed in destination
*/
Quaterniond getNormalizedRotation(Quaterniond dest);
//#ifdef __HAS_NIO__
/**
* Store this matrix in column-major order into the supplied {@link DoubleBuffer} at the current
* buffer {@link DoubleBuffer#position() position}.
* <p>
* This method will not increment the position of the given DoubleBuffer.
* <p>
* In order to specify the offset into the DoubleBuffer at which
* the matrix is stored, use {@link #get(int, DoubleBuffer)}, taking
* the absolute position as parameter.
*
* @see #get(int, DoubleBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
DoubleBuffer get(DoubleBuffer buffer);
/**
* Store this matrix in column-major order into the supplied {@link DoubleBuffer} starting at the specified
* absolute buffer position/index.
* <p>
* This method will not increment the position of the given {@link DoubleBuffer}.
*
* @param index
* the absolute position into the {@link DoubleBuffer}
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
DoubleBuffer get(int index, DoubleBuffer buffer);
/**
* Store this matrix in column-major order into the supplied {@link FloatBuffer} at the current
* buffer {@link FloatBuffer#position() position}.
* <p>
* This method will not increment the position of the given
* FloatBuffer.
* <p>
* 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.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given FloatBuffer.
*
* @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.
* <p>
* This method will not increment the position of the given FloatBuffer.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given FloatBuffer.
*
* @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}.
* <p>
* This method will not increment the position of the given ByteBuffer.
* <p>
* 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.
* <p>
* 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 elements of this matrix as float values in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() position}.
* <p>
* This method will not increment the position of the given ByteBuffer.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given ByteBuffer.
* <p>
* In order to specify the offset into the ByteBuffer at which
* the matrix is stored, use {@link #getFloats(int, ByteBuffer)}, taking
* the absolute position as parameter.
*
* @see #getFloats(int, ByteBuffer)
*
* @param buffer
* will receive the elements of this matrix as float values in column-major order at its current position
* @return the passed in buffer
*/
ByteBuffer getFloats(ByteBuffer buffer);
/**
* Store the elements of this matrix as float values in column-major order into the supplied {@link ByteBuffer}
* starting at the specified absolute buffer position/index.
* <p>
* This method will not increment the position of the given ByteBuffer.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given ByteBuffer.
*
* @param index
* the absolute position into the ByteBuffer
* @param buffer
* will receive the elements of this matrix as float values in column-major order
* @return the passed in buffer
*/
ByteBuffer getFloats(int index, ByteBuffer buffer);
//#endif
/**
* Store this matrix into the supplied double 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
*/
double[] get(double[] arr, int offset);
/**
* Store this matrix into the supplied double array in column-major order.
* <p>
* In order to specify an explicit offset into the array, use the method {@link #get(double[], int)}.
*
* @see #get(double[], int)
*
* @param arr
* the array to write the matrix values into
* @return the passed in array
*/
double[] get(double[] arr);
/**
* Store the elements of this matrix as float values in column-major order into the supplied float array at the given offset.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given float array.
*
* @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 the elements of this matrix as float values in column-major order into the supplied float array.
* <p>
* Please note that due to this matrix storing double values those values will potentially
* lose precision when they are converted to float values before being put into the given float array.
* <p>
* 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);
//#ifdef __HAS_NIO__
/**
* Store the transpose of this matrix in column-major order into the supplied {@link DoubleBuffer} at the current
* buffer {@link DoubleBuffer#position() position}.
* <p>
* This method will not increment the position of the given DoubleBuffer.
* <p>
* In order to specify the offset into the DoubleBuffer at which
* the matrix is stored, use {@link #getTransposed(int, DoubleBuffer)}, taking
* the absolute position as parameter.
*
* @see #getTransposed(int, DoubleBuffer)
*
* @param buffer
* will receive the values of this matrix in column-major order at its current position
* @return the passed in buffer
*/
DoubleBuffer getTransposed(DoubleBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link DoubleBuffer} starting at the specified
* absolute buffer position/index.
* <p>
* This method will not increment the position of the given DoubleBuffer.
*
* @param index
* the absolute position into the DoubleBuffer
* @param buffer
* will receive the values of this matrix in column-major order
* @return the passed in buffer
*/
DoubleBuffer getTransposed(int index, DoubleBuffer buffer);
/**
* Store the transpose of this matrix in column-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() position}.
* <p>
* This method will not increment the position of the given ByteBuffer.
* <p>
* 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.
* <p>
* 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 <code>this</code> matrix in row-major order into the supplied {@link DoubleBuffer} at the current
* buffer {@link DoubleBuffer#position() position}.
* <p>
* This method will not increment the position of the given DoubleBuffer.
* <p>
* In order to specify the offset into the DoubleBuffer at which
* the matrix is stored, use {@link #get4x3Transposed(int, DoubleBuffer)}, taking
* the absolute position as parameter.
*
* @see #get4x3Transposed(int, DoubleBuffer)
*
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order at its current position
* @return the passed in buffer
*/
DoubleBuffer get4x3Transposed(DoubleBuffer buffer);
/**
* Store the upper 4x3 submatrix of <code>this</code> matrix in row-major order into the supplied {@link DoubleBuffer} starting at the specified
* absolute buffer position/index.
* <p>
* This method will not increment the position of the given DoubleBuffer.
*
* @param index
* the absolute position into the DoubleBuffer
* @param buffer
* will receive the values of the upper 4x3 submatrix in row-major order
* @return the passed in buffer
*/
DoubleBuffer get4x3Transposed(int index, DoubleBuffer buffer);
/**
* Store the upper 4x3 submatrix of <code>this</code> matrix in row-major order into the supplied {@link ByteBuffer} at the current
* buffer {@link ByteBuffer#position() position}.
* <p>
* This method will not increment the position of the given ByteBuffer.
* <p>
* 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 <code>this</code> matrix in row-major order into the supplied {@link ByteBuffer} starting at the specified
* absolute buffer position/index.
* <p>
* 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);
//#endif
/**
* Transform/multiply the given vector by this matrix and store the result in that vector.
*
* @see Vector4d#mul(Matrix4dc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4d transform(Vector4d v);
/**
* Transform/multiply the given vector by this matrix and store the result in <code>dest</code>.
*
* @see Vector4d#mul(Matrix4dc, Vector4d)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4d transform(Vector4dc v, Vector4d dest);
/**
* Transform/multiply the vector <tt>(x, y, z, w)</tt> by this matrix and store the result in <code>dest</code>.
*
* @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
*/
Vector4d transform(double x, double y, double z, double w, Vector4d dest);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
*
* @see Vector4d#mulProject(Matrix4dc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4d transformProject(Vector4d v);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in <code>dest</code>.
*
* @see Vector4d#mulProject(Matrix4dc, Vector4d)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector4d transformProject(Vector4dc v, Vector4d dest);
/**
* Transform/multiply the vector <tt>(x, y, z, w)</tt> by this matrix, perform perspective divide and store the result in <code>dest</code>.
*
* @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 contain the result
* @return dest
*/
Vector4d transformProject(double x, double y, double z, double w, Vector4d dest);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in that vector.
* <p>
* This method uses <tt>w=1.0</tt> as the fourth vector component.
*
* @see Vector3d#mulProject(Matrix4dc)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector3d transformProject(Vector3d v);
/**
* Transform/multiply the given vector by this matrix, perform perspective divide and store the result in <code>dest</code>.
* <p>
* This method uses <tt>w=1.0</tt> as the fourth vector component.
*
* @see Vector3d#mulProject(Matrix4dc, Vector3d)
*
* @param v
* the vector to transform
* @param dest
* will contain the result
* @return dest
*/
Vector3d transformProject(Vector3dc v, Vector3d dest);
/**
* Transform/multiply the vector <tt>(x, y, z)</tt> by this matrix, perform perspective divide and store the result in <code>dest</code>.
* <p>
* This method uses <tt>w=1.0</tt> 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
*/
Vector3d transformProject(double x, double y, double z, Vector3d dest);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by
* this matrix and store the result in that vector.
* <p>
* 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
* <tt>w</tt> component of the transformed vector.
* For perspective projection use {@link #transform(Vector4d)} or
* {@link #transformProject(Vector3d)} when perspective divide should be applied, too.
* <p>
* In order to store the result in another vector, use {@link #transformPosition(Vector3dc, Vector3d)}.
*
* @see #transformPosition(Vector3dc, Vector3d)
* @see #transform(Vector4d)
* @see #transformProject(Vector3d)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector3d transformPosition(Vector3d v);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=1, by
* this matrix and store the result in <code>dest</code>.
* <p>
* 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
* <tt>w</tt> component of the transformed vector.
* For perspective projection use {@link #transform(Vector4dc, Vector4d)} or
* {@link #transformProject(Vector3dc, Vector3d)} when perspective divide should be applied, too.
* <p>
* In order to store the result in the same vector, use {@link #transformPosition(Vector3d)}.
*
* @see #transformPosition(Vector3d)
* @see #transform(Vector4dc, Vector4d)
* @see #transformProject(Vector3dc, Vector3d)
*
* @param v
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3d transformPosition(Vector3dc v, Vector3d dest);
/**
* Transform/multiply the 3D-vector <tt>(x, y, z)</tt>, as if it was a 4D-vector with w=1, by
* this matrix and store the result in <code>dest</code>.
* <p>
* 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
* <tt>w</tt> component of the transformed vector.
* For perspective projection use {@link #transform(double, double, double, double, Vector4d)} or
* {@link #transformProject(double, double, double, Vector3d)} when perspective divide should be applied, too.
*
* @see #transform(double, double, double, double, Vector4d)
* @see #transformProject(double, double, double, Vector3d)
*
* @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
*/
Vector3d transformPosition(double x, double y, double z, Vector3d dest);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by
* this matrix and store the result in that vector.
* <p>
* The given 3D-vector is treated as a 4D-vector with its w-component being <tt>0.0</tt>, 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.
* <p>
* In order to store the result in another vector, use {@link #transformDirection(Vector3dc, Vector3d)}.
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector3d transformDirection(Vector3d v);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by
* this matrix and store the result in <code>dest</code>.
* <p>
* The given 3D-vector is treated as a 4D-vector with its w-component being <tt>0.0</tt>, 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.
* <p>
* In order to store the result in the same vector, use {@link #transformDirection(Vector3d)}.
*
* @param v
* the vector to transform and to hold the final result
* @param dest
* will hold the result
* @return dest
*/
Vector3d transformDirection(Vector3dc v, Vector3d dest);
/**
* Transform/multiply the given 3D-vector, as if it was a 4D-vector with w=0, by
* this matrix and store the result in that vector.
* <p>
* The given 3D-vector is treated as a 4D-vector with its w-component being <tt>0.0</tt>, 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.
* <p>
* In order to store the result in another vector, use {@link #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 <code>dest</code>.
* <p>
* The given 3D-vector is treated as a 4D-vector with its w-component being <tt>0.0</tt>, 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.
* <p>
* In order to store the result in the same vector, use {@link #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 3D-vector <tt>(x, y, z)</tt>, as if it was a 4D-vector with w=0, by
* this matrix and store the result in <code>dest</code>.
* <p>
* The given 3D-vector is treated as a 4D-vector with its w-component being <tt>0.0</tt>, 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
*/
Vector3d transformDirection(double x, double y, double z, Vector3d dest);
/**
* Transform/multiply the given 4D-vector by assuming that <code>this</code> matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>).
* <p>
* In order to store the result in another vector, use {@link #transformAffine(Vector4dc, Vector4d)}.
*
* @see #transformAffine(Vector4dc, Vector4d)
*
* @param v
* the vector to transform and to hold the final result
* @return v
*/
Vector4d transformAffine(Vector4d v);
/**
* Transform/multiply the given 4D-vector by assuming that <code>this</code> matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>) and store the result in <code>dest</code>.
* <p>
* In order to store the result in the same vector, use {@link #transformAffine(Vector4d)}.
*
* @see #transformAffine(Vector4d)
*
* @param v
* the vector to transform and to hold the final result
* @param dest
* will hold the result
* @return dest
*/
Vector4d transformAffine(Vector4dc v, Vector4d dest);
/**
* Transform/multiply the 4D-vector <tt>(x, y, z, w)</tt> by assuming that <code>this</code> matrix represents an {@link #isAffine() affine} transformation
* (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>) and store the result in <code>dest</code>.
*
* @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
*/
Vector4d transformAffine(double x, double y, double z, double w, Vector4d dest);
/**
* Apply scaling to <code>this</code> matrix by scaling the base axes by the given <tt>xyz.x</tt>,
* <tt>xyz.y</tt> and <tt>xyz.z</tt> factors, respectively and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>
* , 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
*/
Matrix4d scale(Vector3dc xyz, Matrix4d dest);
/**
* Apply scaling to <code>this</code> matrix by scaling the base axes by the given x,
* y and z factors and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>
* , 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
*/
Matrix4d scale(double x, double y, double z, Matrix4d dest);
/**
* Apply scaling to this matrix by uniformly scaling all base axes by the given xyz factor
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>
* , the scaling will be applied first!
*
* @see #scale(double, double, double, Matrix4d)
*
* @param xyz
* the factor for all components
* @param dest
* will hold the result
* @return dest
*/
Matrix4d scale(double xyz, Matrix4d dest);
/**
* Apply scaling to <code>this</code> matrix by scaling the base axes by the given sx,
* sy and sz factors while using <tt>(ox, oy, oz)</tt> as the scaling origin,
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>
* , the scaling will be applied first!
* <p>
* This method is equivalent to calling: <tt>translate(ox, oy, oz, dest).scale(sx, sy, sz).translate(-ox, -oy, -oz)</tt>
*
* @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
*/
Matrix4d scaleAround(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest);
/**
* Apply scaling to this matrix by scaling all three base axes by the given <code>factor</code>
* while using <tt>(ox, oy, oz)</tt> as the scaling origin,
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
* scaling will be applied first!
* <p>
* This method is equivalent to calling: <tt>translate(ox, oy, oz, dest).scale(factor).translate(-ox, -oy, -oz)</tt>
*
* @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
*/
Matrix4d scaleAround(double factor, double ox, double oy, double oz, Matrix4d dest);
/**
* Pre-multiply scaling to <code>this</code> matrix by scaling all base axes by the given <code>xyz</code> factor,
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>S * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>S * M * v</code>
* , 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
*/
Matrix4d scaleLocal(double xyz, Matrix4d dest);
/**
* Pre-multiply scaling to <code>this</code> matrix by scaling the base axes by the given x,
* y and z factors and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>S * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>S * M * v</code>
* , 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
*/
Matrix4d scaleLocal(double x, double y, double z, Matrix4d dest);
/**
* Pre-multiply scaling to <code>this</code> matrix by scaling the base axes by the given sx,
* sy and sz factors while using the given <tt>(ox, oy, oz)</tt> as the scaling origin,
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>S * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>S * M * v</code>
* , the scaling will be applied last!
* <p>
* This method is equivalent to calling: <tt>new Matrix4d().translate(ox, oy, oz).scale(sx, sy, sz).translate(-ox, -oy, -oz).mul(this, dest)</tt>
*
* @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
*/
Matrix4d scaleAroundLocal(double sx, double sy, double sz, double ox, double oy, double oz, Matrix4d dest);
/**
* Pre-multiply scaling to this matrix by scaling all three base axes by the given <code>factor</code>
* while using <tt>(ox, oy, oz)</tt> as the scaling origin,
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
* then the new matrix will be <code>S * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>S * M * v</code>, the
* scaling will be applied last!
* <p>
* This method is equivalent to calling: <tt>new Matrix4d().translate(ox, oy, oz).scale(factor).translate(-ox, -oy, -oz).mul(this, dest)</tt>
*
* @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
*/
Matrix4d scaleAroundLocal(double factor, double ox, double oy, double oz, Matrix4d dest);
/**
* Apply rotation to this matrix by rotating the given amount of radians
* about the given axis specified as x, y and z components and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>
* , the rotation will be applied first!
*
* @param ang
* the angle is 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
*/
Matrix4d rotate(double ang, double x, double y, double z, Matrix4d dest);
/**
* Apply rotation to this matrix, which is assumed to only contain a translation, by rotating the given amount of radians
* about the specified <tt>(x, y, z)</tt> axis and store the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to only contain a translation.
* <p>
* The axis described by the three components needs to be a unit vector.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @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
*/
Matrix4d rotateTranslation(double ang, double x, double y, double z, Matrix4d dest);
/**
* Apply rotation to this {@link #isAffine() affine} matrix by rotating the given amount of radians
* about the specified <tt>(x, y, z)</tt> axis and store the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to be {@link #isAffine() affine}.
* <p>
* The axis described by the three components needs to be a unit vector.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @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
*/
Matrix4d rotateAffine(double ang, double x, double y, double z, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix while using <tt>(ox, oy, oz)</tt> as the rotation origin,
* and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* This method is equivalent to calling: <tt>translate(ox, oy, oz, dest).rotate(quat).translate(-ox, -oy, -oz)</tt>
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @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
*/
Matrix4d rotateAround(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest);
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians
* about the specified <tt>(x, y, z)</tt> axis and store the result in <code>dest</code>.
* <p>
* The axis described by the three components needs to be a unit vector.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>R * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
* rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @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
*/
Matrix4d rotateLocal(double ang, double x, double y, double z, Matrix4d dest);
/**
* Pre-multiply a rotation around the X axis to this matrix by rotating the given amount of radians
* about the X axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>R * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
* rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians to rotate about the X axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateLocalX(double ang, Matrix4d dest);
/**
* Pre-multiply a rotation around the Y axis to this matrix by rotating the given amount of radians
* about the Y axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>R * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
* rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians to rotate about the Y axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateLocalY(double ang, Matrix4d dest);
/**
* Pre-multiply a rotation around the Z axis to this matrix by rotating the given amount of radians
* about the Z axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>R * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
* rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians to rotate about the Z axis
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateLocalZ(double ang, Matrix4d dest);
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix while using <tt>(ox, oy, oz)</tt>
* as the rotation origin, and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>Q * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>Q * M * v</code>,
* the quaternion rotation will be applied last!
* <p>
* This method is equivalent to calling: <tt>translateLocal(-ox, -oy, -oz, dest).rotateLocal(quat).translateLocal(ox, oy, oz)</tt>
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @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
*/
Matrix4d rotateAroundLocal(Quaterniondc quat, double ox, double oy, double oz, Matrix4d dest);
/**
* Apply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>M * T</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>M * T * v</code>, 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
*/
Matrix4d translate(Vector3dc offset, Matrix4d dest);
/**
* Apply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>M * T</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>M * T * v</code>, 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
*/
Matrix4d translate(Vector3fc offset, Matrix4d dest);
/**
* Apply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>M * T</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>M * T * v</code>, 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
*/
Matrix4d translate(double x, double y, double z, Matrix4d dest);
/**
* Pre-multiply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>T * M</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>T * M * v</code>, 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
*/
Matrix4d translateLocal(Vector3fc offset, Matrix4d dest);
/**
* Pre-multiply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>T * M</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>T * M * v</code>, 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
*/
Matrix4d translateLocal(Vector3dc offset, Matrix4d dest);
/**
* Pre-multiply a translation to this matrix by translating by the given number of
* units in x, y and z and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>T</code> the translation
* matrix, then the new matrix will be <code>T * M</code>. So when
* transforming a vector <code>v</code> with the new matrix by using
* <code>T * M * v</code>, 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
*/
Matrix4d translateLocal(double x, double y, double z, Matrix4d dest);
/**
* Apply rotation about the X axis to this matrix by rotating the given amount of radians
* and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateX(double ang, Matrix4d dest);
/**
* Apply rotation about the Y axis to this matrix by rotating the given amount of radians
* and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateY(double ang, Matrix4d dest);
/**
* Apply rotation about the Z axis to this matrix by rotating the given amount of radians
* and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateZ(double ang, Matrix4d dest);
/**
* Apply rotation about the Z axis to align the local <tt>+X</tt> towards <tt>(dirX, dirY)</tt> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* The vector <tt>(dirX, dirY)</tt> 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
*/
Matrix4d rotateTowardsXY(double dirX, double dirY, Matrix4d dest);
/**
* Apply rotation of <code>angleX</code> radians about the X axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
* followed by a rotation of <code>angleZ</code> radians about the Z axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* This method is equivalent to calling: <tt>rotateX(angleX, dest).rotateY(angleY).rotateZ(angleZ)</tt>
*
* @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
*/
Matrix4d rotateXYZ(double angleX, double angleY, double angleZ, Matrix4d dest);
/**
* Apply rotation of <code>angleX</code> radians about the X axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
* followed by a rotation of <code>angleZ</code> radians about the Z axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* This method assumes that <code>this</code> matrix represents an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d rotateAffineXYZ(double angleX, double angleY, double angleZ, Matrix4d dest);
/**
* Apply rotation of <code>angleZ</code> radians about the Z axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
* followed by a rotation of <code>angleX</code> radians about the X axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* This method is equivalent to calling: <tt>rotateZ(angleZ, dest).rotateY(angleY).rotateX(angleX)</tt>
*
* @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
*/
Matrix4d rotateZYX(double angleZ, double angleY, double angleX, Matrix4d dest);
/**
* Apply rotation of <code>angleZ</code> radians about the Z axis, followed by a rotation of <code>angleY</code> radians about the Y axis and
* followed by a rotation of <code>angleX</code> radians about the X axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* This method assumes that <code>this</code> matrix represents an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d rotateAffineZYX(double angleZ, double angleY, double angleX, Matrix4d dest);
/**
* Apply rotation of <code>angleY</code> radians about the Y axis, followed by a rotation of <code>angleX</code> radians about the X axis and
* followed by a rotation of <code>angleZ</code> radians about the Z axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* rotation will be applied first!
* <p>
* This method is equivalent to calling: <tt>rotateY(angleY, dest).rotateX(angleX).rotateZ(angleZ)</tt>
*
* @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
*/
Matrix4d rotateYXZ(double angleY, double angleX, double angleZ, Matrix4d dest);
/**
* Apply rotation of <code>angleY</code> radians about the Y axis, followed by a rotation of <code>angleX</code> radians about the X axis and
* followed by a rotation of <code>angleZ</code> radians about the Z axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* This method assumes that <code>this</code> matrix represents an {@link #isAffine() affine} transformation (i.e. its last row is equal to <tt>(0, 0, 0, 1)</tt>)
* 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).
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d rotateAffineYXZ(double angleY, double angleX, double angleZ, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix and store
* the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(Quaterniondc quat, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix and store
* the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(Quaternionfc quat, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this {@link #isAffine() affine} matrix and store
* the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to be {@link #isAffine() affine}.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateAffine(Quaterniondc quat, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix, which is assumed to only contain a translation, and store
* the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to only contain a translation.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateTranslation(Quaterniondc quat, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix, which is assumed to only contain a translation, and store
* the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to only contain a translation.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateTranslation(Quaternionfc quat, Matrix4d dest);
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix and store
* the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>Q * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>Q * M * v</code>,
* the quaternion rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateLocal(Quaterniondc quat, Matrix4d dest);
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this {@link #isAffine() affine} matrix and store
* the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to be {@link #isAffine() affine}.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>M * Q</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * Q * v</code>,
* the quaternion rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateAffine(Quaternionfc quat, Matrix4d dest);
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix and store
* the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>Q</code> the rotation matrix obtained from the given quaternion,
* then the new matrix will be <code>Q * M</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>Q * M * v</code>,
* the quaternion rotation will be applied last!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateLocal(Quaternionfc quat, Matrix4d dest);
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4f} and store the result in <code>dest</code>.
* <p>
* The axis described by the <code>axis</code> vector needs to be a unit vector.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given {@link AxisAngle4f},
* then the new matrix will be <code>M * A</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
* the {@link AxisAngle4f} rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(double, double, double, double, Matrix4d)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(AxisAngle4f axisAngle, Matrix4d dest);
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4d} and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given {@link AxisAngle4d},
* then the new matrix will be <code>M * A</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
* the {@link AxisAngle4d} rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(double, double, double, double, Matrix4d)
*
* @param axisAngle
* the {@link AxisAngle4d} (needs to be {@link AxisAngle4d#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(AxisAngle4d axisAngle, Matrix4d dest);
/**
* Apply a rotation transformation, rotating the given radians about the specified axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given angle and axis,
* then the new matrix will be <code>M * A</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
* the axis-angle rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(double, double, double, double, Matrix4d)
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis (needs to be {@link Vector3d#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(double angle, Vector3dc axis, Matrix4d dest);
/**
* Apply a rotation transformation, rotating the given radians about the specified axis and store the result in <code>dest</code>.
* <p>
* 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.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>A</code> the rotation matrix obtained from the given angle and axis,
* then the new matrix will be <code>M * A</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * A * v</code>,
* the axis-angle rotation will be applied first!
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(double, double, double, double, Matrix4d)
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis (needs to be {@link Vector3f#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotate(double angle, Vector3fc axis, Matrix4d dest);
/**
* Get the row at the given <code>row</code> index, starting with <code>0</code>.
*
* @param row
* the row index in <tt>[0..3]</tt>
* @param dest
* will hold the row components
* @return the passed in destination
* @throws IndexOutOfBoundsException if <code>row</code> is not in <tt>[0..3]</tt>
*/
Vector4d getRow(int row, Vector4d dest) throws IndexOutOfBoundsException;
/**
* Get the column at the given <code>column</code> index, starting with <code>0</code>.
*
* @param column
* the column index in <tt>[0..3]</tt>
* @param dest
* will hold the column components
* @return the passed in destination
* @throws IndexOutOfBoundsException if <code>column</code> is not in <tt>[0..3]</tt>
*/
Vector4d getColumn(int column, Vector4d dest) throws IndexOutOfBoundsException;
/**
* Compute a normal matrix from the upper left 3x3 submatrix of <code>this</code>
* and store it into the upper left 3x3 submatrix of <code>dest</code>.
* All other values of <code>dest</code> will be set to identity.
* <p>
* The normal matrix of <tt>m</tt> is the transpose of the inverse of <tt>m</tt>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d normal(Matrix4d dest);
/**
* Compute a normal matrix from the upper left 3x3 submatrix of <code>this</code>
* and store it into <code>dest</code>.
* <p>
* The normal matrix of <tt>m</tt> is the transpose of the inverse of <tt>m</tt>.
*
* @see #get3x3(Matrix3d)
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d normal(Matrix3d dest);
/**
* Normalize the upper left 3x3 submatrix of this matrix and store the result in <code>dest</code>.
* <p>
* 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 <i>skewing</i>).
*
* @param dest
* will hold the result
* @return dest
*/
Matrix4d normalize3x3(Matrix4d dest);
/**
* Normalize the upper left 3x3 submatrix of this matrix and store the result in <code>dest</code>.
* <p>
* 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 <i>skewing</i>).
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d normalize3x3(Matrix3d dest);
/**
* Unproject the given window coordinates <tt>(winX, winY, winZ)</tt> by <code>this</code> matrix using the specified viewport.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* The depth range of <tt>winZ</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInv(double, double, double, int[], Vector4d) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(double, double, double, int[], Vector4d)
* @see #invert(Matrix4d)
*
* @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 <tt>[0..1]</tt>
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4d unproject(double winX, double winY, double winZ, int[] viewport, Vector4d dest);
/**
* Unproject the given window coordinates <tt>(winX, winY, winZ)</tt> by <code>this</code> matrix using the specified viewport.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* The depth range of <tt>winZ</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInv(double, double, double, int[], Vector3d) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(double, double, double, int[], Vector3d)
* @see #invert(Matrix4d)
*
* @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 <tt>[0..1]</tt>
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3d unproject(double winX, double winY, double winZ, int[] viewport, Vector3d dest);
/**
* Unproject the given window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* The depth range of <tt>winCoords.z</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInv(double, double, double, int[], Vector4d) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(double, double, double, int[], Vector4d)
* @see #unproject(double, double, double, int[], Vector4d)
* @see #invert(Matrix4d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4d unproject(Vector3dc winCoords, int[] viewport, Vector4d dest);
/**
* Unproject the given window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* The depth range of <tt>winCoords.z</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInv(double, double, double, int[], Vector4d) unprojectInv()} can be invoked on it.
*
* @see #unprojectInv(double, double, double, int[], Vector4d)
* @see #unproject(double, double, double, int[], Vector4d)
* @see #invert(Matrix4d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3d unproject(Vector3dc winCoords, int[] viewport, Vector3d dest);
/**
* Unproject the given 2D window coordinates <tt>(winX, winY)</tt> by <code>this</code> matrix using the specified viewport
* and compute the origin and the direction of the resulting ray which starts at NDC <tt>z = -1.0</tt> and goes through NDC <tt>z = +1.0</tt>.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInvRay(double, double, int[], Vector3d, Vector3d) unprojectInvRay()} can be invoked on it.
*
* @see #unprojectInvRay(double, double, int[], Vector3d, Vector3d)
* @see #invert(Matrix4d)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4d unprojectRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest);
/**
* Unproject the given 2D window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport
* and compute the origin and the direction of the resulting ray which starts at NDC <tt>z = -1.0</tt> and goes through NDC <tt>z = +1.0</tt>.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by the inverse of <code>this</code> matrix.
* <p>
* As a necessary computation step for unprojecting, this method computes the inverse of <code>this</code> matrix.
* In order to avoid computing the matrix inverse with every invocation, the inverse of <code>this</code> matrix can be built
* once outside using {@link #invert(Matrix4d)} and then the method {@link #unprojectInvRay(double, double, int[], Vector3d, Vector3d) unprojectInvRay()} can be invoked on it.
*
* @see #unprojectInvRay(double, double, int[], Vector3d, Vector3d)
* @see #unprojectRay(double, double, int[], Vector3d, Vector3d)
* @see #invert(Matrix4d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4d unprojectRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest);
/**
* Unproject the given window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport.
* <p>
* This method differs from {@link #unproject(Vector3dc, int[], Vector4d) unproject()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by <code>this</code> matrix.
* <p>
* The depth range of <tt>winCoords.z</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #unproject(Vector3dc, int[], Vector4d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4d unprojectInv(Vector3dc winCoords, int[] viewport, Vector4d dest);
/**
* Unproject the given window coordinates <tt>(winX, winY, winZ)</tt> by <code>this</code> matrix using the specified viewport.
* <p>
* This method differs from {@link #unproject(double, double, double, int[], Vector4d) unproject()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by <code>this</code> matrix.
* <p>
* The depth range of <tt>winZ</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #unproject(double, double, double, int[], Vector4d)
*
* @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 <tt>[0..1]</tt>
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector4d unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector4d dest);
/**
* Unproject the given window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport.
* <p>
* This method differs from {@link #unproject(Vector3dc, int[], Vector3d) unproject()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by <code>this</code> matrix.
* <p>
* The depth range of <tt>winCoords.z</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #unproject(Vector3dc, int[], Vector3d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3d unprojectInv(Vector3dc winCoords, int[] viewport, Vector3d dest);
/**
* Unproject the given window coordinates <tt>(winX, winY, winZ)</tt> by <code>this</code> matrix using the specified viewport.
* <p>
* This method differs from {@link #unproject(double, double, double, int[], Vector3d) unproject()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
* <p>
* This method first converts the given window coordinates to normalized device coordinates in the range <tt>[-1..1]</tt>
* and then transforms those NDC coordinates by <code>this</code> matrix.
* <p>
* The depth range of <tt>winZ</tt> is assumed to be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #unproject(double, double, double, int[], Vector3d)
*
* @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 <tt>[0..1]</tt>
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param dest
* will hold the unprojected position
* @return dest
*/
Vector3d unprojectInv(double winX, double winY, double winZ, int[] viewport, Vector3d dest);
/**
* Unproject the given window coordinates <code>winCoords</code> by <code>this</code> matrix using the specified viewport
* and compute the origin and the direction of the resulting ray which starts at NDC <tt>z = -1.0</tt> and goes through NDC <tt>z = +1.0</tt>.
* <p>
* This method differs from {@link #unprojectRay(Vector2dc, int[], Vector3d, Vector3d) unprojectRay()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
*
* @see #unprojectRay(Vector2dc, int[], Vector3d, Vector3d)
*
* @param winCoords
* the window coordinates to unproject
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4d unprojectInvRay(Vector2dc winCoords, int[] viewport, Vector3d originDest, Vector3d dirDest);
/**
* Unproject the given 2D window coordinates <tt>(winX, winY)</tt> by <code>this</code> matrix using the specified viewport
* and compute the origin and the direction of the resulting ray which starts at NDC <tt>z = -1.0</tt> and goes through NDC <tt>z = +1.0</tt>.
* <p>
* This method differs from {@link #unprojectRay(double, double, int[], Vector3d, Vector3d) unprojectRay()}
* in that it assumes that <code>this</code> is already the inverse matrix of the original projection matrix.
* It exists to avoid recomputing the matrix inverse with every invocation.
*
* @see #unprojectRay(double, double, int[], Vector3d, Vector3d)
*
* @param winX
* the x-coordinate in window coordinates (pixels)
* @param winY
* the y-coordinate in window coordinates (pixels)
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param originDest
* will hold the ray origin
* @param dirDest
* will hold the (unnormalized) ray direction
* @return this
*/
Matrix4d unprojectInvRay(double winX, double winY, int[] viewport, Vector3d originDest, Vector3d dirDest);
/**
* Project the given <tt>(x, y, z)</tt> position via <code>this</code> matrix using the specified viewport
* and store the resulting window coordinates in <code>winCoordsDest</code>.
* <p>
* This method transforms the given coordinates by <code>this</code> matrix including perspective division to
* obtain normalized device coordinates, and then translates these into window coordinates by using the
* given <code>viewport</code> settings <tt>[x, y, width, height]</tt>.
* <p>
* The depth range of the returned <code>winCoordsDest.z</code> will be <tt>[0..1]</tt>, 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 <tt>[x, y, width, height]</tt>
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector4d project(double x, double y, double z, int[] viewport, Vector4d winCoordsDest);
/**
* Project the given <tt>(x, y, z)</tt> position via <code>this</code> matrix using the specified viewport
* and store the resulting window coordinates in <code>winCoordsDest</code>.
* <p>
* This method transforms the given coordinates by <code>this</code> matrix including perspective division to
* obtain normalized device coordinates, and then translates these into window coordinates by using the
* given <code>viewport</code> settings <tt>[x, y, width, height]</tt>.
* <p>
* The depth range of the returned <code>winCoordsDest.z</code> will be <tt>[0..1]</tt>, 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 <tt>[x, y, width, height]</tt>
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector3d project(double x, double y, double z, int[] viewport, Vector3d winCoordsDest);
/**
* Project the given <code>position</code> via <code>this</code> matrix using the specified viewport
* and store the resulting window coordinates in <code>winCoordsDest</code>.
* <p>
* This method transforms the given coordinates by <code>this</code> matrix including perspective division to
* obtain normalized device coordinates, and then translates these into window coordinates by using the
* given <code>viewport</code> settings <tt>[x, y, width, height]</tt>.
* <p>
* The depth range of the returned <code>winCoordsDest.z</code> will be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #project(double, double, double, int[], Vector4d)
*
* @param position
* the position to project into window coordinates
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector4d project(Vector3dc position, int[] viewport, Vector4d winCoordsDest);
/**
* Project the given <code>position</code> via <code>this</code> matrix using the specified viewport
* and store the resulting window coordinates in <code>winCoordsDest</code>.
* <p>
* This method transforms the given coordinates by <code>this</code> matrix including perspective division to
* obtain normalized device coordinates, and then translates these into window coordinates by using the
* given <code>viewport</code> settings <tt>[x, y, width, height]</tt>.
* <p>
* The depth range of the returned <code>winCoordsDest.z</code> will be <tt>[0..1]</tt>, which is also the OpenGL default.
*
* @see #project(double, double, double, int[], Vector4d)
*
* @param position
* the position to project into window coordinates
* @param viewport
* the viewport described by <tt>[x, y, width, height]</tt>
* @param winCoordsDest
* will hold the projected window coordinates
* @return winCoordsDest
*/
Vector3d project(Vector3dc position, int[] viewport, Vector3d winCoordsDest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects about the given plane
* specified via the equation <tt>x*a + y*b + z*c + d = 0</tt> and store the result in <code>dest</code>.
* <p>
* The vector <tt>(a, b, c)</tt> must be a unit vector.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the reflection matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* reflection will be applied first!
* <p>
* Reference: <a href="https://msdn.microsoft.com/en-us/library/windows/desktop/bb281733(v=vs.85).aspx">msdn.microsoft.com</a>
*
* @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
*/
Matrix4d reflect(double a, double b, double c, double d, Matrix4d dest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects about the given plane
* specified via the plane normal and a point on the plane, and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the reflection matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d reflect(double nx, double ny, double nz, double px, double py, double pz, Matrix4d dest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects about a plane
* specified via the plane orientation and a point on the plane, and store the result in <code>dest</code>.
* <p>
* 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 <tt>(0, 0, 1)</tt>. So, if the given {@link Quaterniondc} is
* the identity (does not apply any additional rotation), the reflection plane will be <tt>z=0</tt>, offset by the given <code>point</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the reflection matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
* reflection will be applied first!
*
* @param orientation
* the plane orientation
* @param point
* a point on the plane
* @param dest
* will hold the result
* @return dest
*/
Matrix4d reflect(Quaterniondc orientation, Vector3dc point, Matrix4d dest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects about the given plane
* specified via the plane normal and a point on the plane, and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>R</code> the reflection matrix,
* then the new matrix will be <code>M * R</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * R * v</code>, 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
*/
Matrix4d reflect(Vector3dc normal, Vector3dc point, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a right-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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 <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @param dest
* will hold the result
* @return dest
*/
Matrix4d ortho(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a right-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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
*/
Matrix4d ortho(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a left-handed coordiante system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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 <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @param dest
* will hold the result
* @return dest
*/
Matrix4d orthoLH(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a left-handed coordiante system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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
*/
Matrix4d orthoLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest);
/**
* Apply a symmetric orthographic projection transformation for a right-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #ortho(double, double, double, double, double, double, boolean, Matrix4d) ortho()} with
* <code>left=-width/2</code>, <code>right=+width/2</code>, <code>bottom=-height/2</code> and <code>top=+height/2</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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 <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @return dest
*/
Matrix4d orthoSymmetric(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply a symmetric orthographic projection transformation for a right-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #ortho(double, double, double, double, double, double, Matrix4d) ortho()} with
* <code>left=-width/2</code>, <code>right=+width/2</code>, <code>bottom=-height/2</code> and <code>top=+height/2</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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
*/
Matrix4d orthoSymmetric(double width, double height, double zNear, double zFar, Matrix4d dest);
/**
* Apply a symmetric orthographic projection transformation for a left-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #orthoLH(double, double, double, double, double, double, boolean, Matrix4d) orthoLH()} with
* <code>left=-width/2</code>, <code>right=+width/2</code>, <code>bottom=-height/2</code> and <code>top=+height/2</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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 <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @return dest
*/
Matrix4d orthoSymmetricLH(double width, double height, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply a symmetric orthographic projection transformation for a left-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #orthoLH(double, double, double, double, double, double, Matrix4d) orthoLH()} with
* <code>left=-width/2</code>, <code>right=+width/2</code>, <code>bottom=-height/2</code> and <code>top=+height/2</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @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
*/
Matrix4d orthoSymmetricLH(double width, double height, double zNear, double zFar, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a right-handed coordinate system
* to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #ortho(double, double, double, double, double, double, Matrix4d) ortho()} with
* <code>zNear=-1</code> and <code>zFar=+1</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @see #ortho(double, double, double, double, double, double, Matrix4d)
*
* @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
*/
Matrix4d ortho2D(double left, double right, double bottom, double top, Matrix4d dest);
/**
* Apply an orthographic projection transformation for a left-handed coordinate system to this matrix and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling {@link #orthoLH(double, double, double, double, double, double, Matrix4d) orthoLH()} with
* <code>zNear=-1</code> and <code>zFar=+1</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the orthographic projection matrix,
* then the new matrix will be <code>M * O</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * O * v</code>, the
* orthographic projection transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#ortho">http://www.songho.ca</a>
*
* @see #orthoLH(double, double, double, double, double, double, Matrix4d)
*
* @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
*/
Matrix4d ortho2DLH(double left, double right, double bottom, double top, Matrix4d dest);
/**
* Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
* lookalong rotation transformation will be applied first!
* <p>
* This is equivalent to calling
* {@link #lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d) lookAt}
* with <code>eye = (0, 0, 0)</code> and <code>center = dir</code>.
*
* @see #lookAlong(double, double, double, double, double, double, Matrix4d)
* @see #lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
Matrix4d lookAlong(Vector3dc dir, Vector3dc up, Matrix4d dest);
/**
* Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</code>
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookalong rotation matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>, the
* lookalong rotation transformation will be applied first!
* <p>
* This is equivalent to calling
* {@link #lookAt(double, double, double, double, double, double, double, double, double, Matrix4d) lookAt()}
* with <code>eye = (0, 0, 0)</code> and <code>center = dir</code>.
*
* @see #lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)
*
* @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
*/
Matrix4d lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a right-handed coordinate system,
* that aligns <code>-z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
*
* @see #lookAt(double, double, double, double, double, double, double, double, double, Matrix4d)
*
* @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
*/
Matrix4d lookAt(Vector3dc eye, Vector3dc center, Vector3dc up, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a right-handed coordinate system,
* that aligns <code>-z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
*
* @see #lookAt(Vector3dc, Vector3dc, Vector3dc, Matrix4d)
*
* @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
*/
Matrix4d lookAt(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a right-handed coordinate system,
* that aligns <code>-z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to be a perspective transformation, obtained via
* {@link #frustum(double, double, double, double, double, double, Matrix4d) frustum()} or {@link #perspective(double, double, double, double, Matrix4d) perspective()} or
* one of their overloads.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* 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
*/
Matrix4d lookAtPerspective(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a left-handed coordinate system,
* that aligns <code>+z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
*
* @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
*/
Matrix4d lookAtLH(Vector3dc eye, Vector3dc center, Vector3dc up, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a left-handed coordinate system,
* that aligns <code>+z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
*
* @see #lookAtLH(Vector3dc, Vector3dc, Vector3dc, Matrix4d)
*
* @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
*/
Matrix4d lookAtLH(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Apply a "lookat" transformation to this matrix for a left-handed coordinate system,
* that aligns <code>+z</code> with <code>center - eye</code> and store the result in <code>dest</code>.
* <p>
* This method assumes <code>this</code> to be a perspective transformation, obtained via
* {@link #frustumLH(double, double, double, double, double, double, Matrix4d) frustumLH()} or {@link #perspectiveLH(double, double, double, double, Matrix4d) perspectiveLH()} or
* one of their overloads.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* 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
*/
Matrix4d lookAtPerspectiveLH(double eyeX, double eyeY, double eyeZ, double centerX, double centerY, double centerZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>P</code> the perspective projection matrix,
* then the new matrix will be <code>M * P</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * P * v</code>,
* 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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @param zZeroToOne
* whether to use Vulkan's and Direct3D's NDC z range of <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @return dest
*/
Matrix4d perspective(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply a symmetric perspective projection frustum transformation for a right-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>P</code> the perspective projection matrix,
* then the new matrix will be <code>M * P</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * P * v</code>,
* 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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4d perspective(double fovy, double aspect, double zNear, double zFar, Matrix4d dest);
/**
* Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>P</code> the perspective projection matrix,
* then the new matrix will be <code>M * P</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * P * v</code>,
* 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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zZeroToOne
* whether to use Vulkan's and Direct3D's NDC z range of <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @param dest
* will hold the result
* @return dest
*/
Matrix4d perspectiveLH(double fovy, double aspect, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply a symmetric perspective projection frustum transformation for a left-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>P</code> the perspective projection matrix,
* then the new matrix will be <code>M * P</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * P * v</code>,
* 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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4d perspectiveLH(double fovy, double aspect, double zNear, double zFar, Matrix4d dest);
/**
* Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>F</code> the frustum matrix,
* then the new matrix will be <code>M * F</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * F * v</code>,
* the frustum transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#perspective">http://www.songho.ca</a>
*
* @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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zZeroToOne
* whether to use Vulkan's and Direct3D's NDC z range of <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @param dest
* will hold the result
* @return dest
*/
Matrix4d frustum(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply an arbitrary perspective projection frustum transformation for a right-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>F</code> the frustum matrix,
* then the new matrix will be <code>M * F</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * F * v</code>,
* the frustum transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#perspective">http://www.songho.ca</a>
*
* @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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4d frustum(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest);
/**
* Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system
* using the given NDC z range to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>F</code> the frustum matrix,
* then the new matrix will be <code>M * F</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * F * v</code>,
* the frustum transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#perspective">http://www.songho.ca</a>
*
* @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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zZeroToOne
* whether to use Vulkan's and Direct3D's NDC z range of <tt>[0..+1]</tt> when <code>true</code>
* or whether to use OpenGL's NDC z range of <tt>[-1..+1]</tt> when <code>false</code>
* @param dest
* will hold the result
* @return dest
*/
Matrix4d frustumLH(double left, double right, double bottom, double top, double zNear, double zFar, boolean zZeroToOne, Matrix4d dest);
/**
* Apply an arbitrary perspective projection frustum transformation for a left-handed coordinate system
* using OpenGL's NDC z range of <tt>[-1..+1]</tt> to this matrix and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>F</code> the frustum matrix,
* then the new matrix will be <code>M * F</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * F * v</code>,
* the frustum transformation will be applied first!
* <p>
* Reference: <a href="http://www.songho.ca/opengl/gl_projectionmatrix.html#perspective">http://www.songho.ca</a>
*
* @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 Double#POSITIVE_INFINITY} is used, the near clipping plane will be at positive infinity.
* In that case, <code>zFar</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param zFar
* far clipping plane distance. If the special value {@link Double#POSITIVE_INFINITY} is used, the far clipping plane will be at positive infinity.
* In that case, <code>zNear</code> may not also be {@link Double#POSITIVE_INFINITY}.
* @param dest
* will hold the result
* @return dest
*/
Matrix4d frustumLH(double left, double right, double bottom, double top, double zNear, double zFar, Matrix4d dest);
/**
* Calculate a frustum plane of <code>this</code> matrix, which
* can be a projection matrix or a combined modelview-projection matrix, and store the result
* in the given <code>planeEquation</code>.
* <p>
* Generally, this method computes the frustum plane in the local frame of
* any coordinate system that existed before <code>this</code>
* transformation was applied to it in order to yield homogeneous clipping space.
* <p>
* The frustum plane will be given in the form of a general plane equation:
* <tt>a*x + b*y + c*z + d = 0</tt>, where the given {@link Vector4d} components will
* hold the <tt>(a, b, c, d)</tt> values of the equation.
* <p>
* The plane normal, which is <tt>(a, b, c)</tt>, is directed "inwards" of the frustum.
* Any plane/point test using <tt>a*x + b*y + c*z + d</tt> therefore will yield a result greater than zero
* if the point is within the frustum (i.e. at the <i>positive</i> side of the frustum plane).
* <p>
* 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.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @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 <tt>(a, b, c)</tt> will be a unit vector
* @return planeEquation
*/
Vector4d frustumPlane(int plane, Vector4d planeEquation);
/**
* Compute the corner coordinates of the frustum defined by <code>this</code> matrix, which
* can be a projection matrix or a combined modelview-projection matrix, and store the result
* in the given <code>point</code>.
* <p>
* Generally, this method computes the frustum corners in the local frame of
* any coordinate system that existed before <code>this</code>
* transformation was applied to it in order to yield homogeneous clipping space.
* <p>
* Reference: <a href="http://geomalgorithms.com/a05-_intersect-1.html">http://geomalgorithms.com</a>
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @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
*/
Vector3d frustumCorner(int corner, Vector3d point);
/**
* Compute the eye/origin of the perspective frustum transformation defined by <code>this</code> matrix,
* which can be a projection matrix or a combined modelview-projection matrix, and store the result
* in the given <code>origin</code>.
* <p>
* Note that this method will only work using perspective projections obtained via one of the
* perspective methods, such as {@link #perspective(double, double, double, double, Matrix4d) perspective()}
* or {@link #frustum(double, double, double, double, double, double, Matrix4d) frustum()}.
* <p>
* Generally, this method computes the origin in the local frame of
* any coordinate system that existed before <code>this</code>
* transformation was applied to it in order to yield homogeneous clipping space.
* <p>
* Reference: <a href="http://geomalgorithms.com/a05-_intersect-1.html">http://geomalgorithms.com</a>
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @param origin
* will hold the origin of the coordinate system before applying <code>this</code>
* perspective projection transformation
* @return origin
*/
Vector3d perspectiveOrigin(Vector3d origin);
/**
* Return the vertical field-of-view angle in radians of this perspective transformation matrix.
* <p>
* Note that this method will only work using perspective projections obtained via one of the
* perspective methods, such as {@link #perspective(double, double, double, double, Matrix4d) perspective()}
* or {@link #frustum(double, double, double, double, double, double, Matrix4d) frustum()}.
* <p>
* For orthogonal transformations this method will return <tt>0.0</tt>.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @return the vertical field-of-view angle in radians
*/
double perspectiveFov();
/**
* Extract the near clip plane distance from <code>this</code> perspective projection matrix.
* <p>
* This method only works if <code>this</code> is a perspective projection matrix, for example obtained via {@link #perspective(double, double, double, double, Matrix4d)}.
*
* @return the near clip plane distance
*/
double perspectiveNear();
/**
* Extract the far clip plane distance from <code>this</code> perspective projection matrix.
* <p>
* This method only works if <code>this</code> is a perspective projection matrix, for example obtained via {@link #perspective(double, double, double, double, Matrix4d)}.
*
* @return the far clip plane distance
*/
double perspectiveFar();
/**
* Obtain the direction of a ray starting at the center of the coordinate system and going
* through the near frustum plane.
* <p>
* This method computes the <code>dir</code> vector in the local frame of
* any coordinate system that existed before <code>this</code>
* transformation was applied to it in order to yield homogeneous clipping space.
* <p>
* The parameters <code>x</code> and <code>y</code> are used to interpolate the generated ray direction
* from the bottom-left to the top-right frustum corners.
* <p>
* 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
* <tt>(0, 0)</tt>, <tt>(1, 0)</tt>, <tt>(0, 1)</tt> and <tt>(1, 1)</tt>
* and then bilinearly interpolating between them; or to use the {@link FrustumRayBuilder}.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @param x
* the interpolation factor along the left-to-right frustum planes, within <tt>[0..1]</tt>
* @param y
* the interpolation factor along the bottom-to-top frustum planes, within <tt>[0..1]</tt>
* @param dir
* will hold the normalized ray direction in the local frame of the coordinate system before
* transforming to homogeneous clipping space using <code>this</code> matrix
* @return dir
*/
Vector3d frustumRayDir(double x, double y, Vector3d dir);
/**
* Obtain the direction of <tt>+Z</tt> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+Z</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).invert();
* inv.transformDirection(dir.set(0, 0, 1)).normalize();
* </pre>
* If <code>this</code> is already an orthogonal matrix, then consider using {@link #normalizedPositiveZ(Vector3d)} instead.
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+Z</tt>
* @return dir
*/
Vector3d positiveZ(Vector3d dir);
/**
* Obtain the direction of <tt>+Z</tt> before the transformation represented by <code>this</code> <i>orthogonal</i> matrix is applied.
* This method only produces correct results if <code>this</code> is an <i>orthogonal</i> matrix.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+Z</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).transpose();
* inv.transformDirection(dir.set(0, 0, 1));
* </pre>
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+Z</tt>
* @return dir
*/
Vector3d normalizedPositiveZ(Vector3d dir);
/**
* Obtain the direction of <tt>+X</tt> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+X</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).invert();
* inv.transformDirection(dir.set(1, 0, 0)).normalize();
* </pre>
* If <code>this</code> is already an orthogonal matrix, then consider using {@link #normalizedPositiveX(Vector3d)} instead.
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+X</tt>
* @return dir
*/
Vector3d positiveX(Vector3d dir);
/**
* Obtain the direction of <tt>+X</tt> before the transformation represented by <code>this</code> <i>orthogonal</i> matrix is applied.
* This method only produces correct results if <code>this</code> is an <i>orthogonal</i> matrix.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+X</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).transpose();
* inv.transformDirection(dir.set(1, 0, 0));
* </pre>
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+X</tt>
* @return dir
*/
Vector3d normalizedPositiveX(Vector3d dir);
/**
* Obtain the direction of <tt>+Y</tt> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+Y</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).invert();
* inv.transformDirection(dir.set(0, 1, 0)).normalize();
* </pre>
* If <code>this</code> is already an orthogonal matrix, then consider using {@link #normalizedPositiveY(Vector3d)} instead.
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+Y</tt>
* @return dir
*/
Vector3d positiveY(Vector3d dir);
/**
* Obtain the direction of <tt>+Y</tt> before the transformation represented by <code>this</code> <i>orthogonal</i> matrix is applied.
* This method only produces correct results if <code>this</code> is an <i>orthogonal</i> matrix.
* <p>
* This method uses the rotation component of the upper left 3x3 submatrix to obtain the direction
* that is transformed to <tt>+Y</tt> by <code>this</code> matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4d inv = new Matrix4d(this).transpose();
* inv.transformDirection(dir.set(0, 1, 0));
* </pre>
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/threeD/">http://www.euclideanspace.com</a>
*
* @param dir
* will hold the direction of <tt>+Y</tt>
* @return dir
*/
Vector3d normalizedPositiveY(Vector3d dir);
/**
* Obtain the position that gets transformed to the origin by <code>this</code> {@link #isAffine() affine} matrix.
* This can be used to get the position of the "camera" from a given <i>view</i> transformation matrix.
* <p>
* This method only works with {@link #isAffine() affine} matrices.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4f inv = new Matrix4f(this).invertAffine();
* inv.transformPosition(origin.set(0, 0, 0));
* </pre>
*
* @param origin
* will hold the position transformed to the origin
* @return origin
*/
Vector3d originAffine(Vector3d origin);
/**
* Obtain the position that gets transformed to the origin by <code>this</code> matrix.
* This can be used to get the position of the "camera" from a given <i>view/projection</i> transformation matrix.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix4f inv = new Matrix4f(this).invert();
* inv.transformPosition(origin.set(0, 0, 0));
* </pre>
*
* @param origin
* will hold the position transformed to the origin
* @return origin
*/
Vector3d origin(Vector3d origin);
/**
* Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation
* <tt>x*a + y*b + z*c + d = 0</tt> as if casting a shadow from a given light position/direction <code>light</code>
* and store the result in <code>dest</code>.
* <p>
* If <tt>light.w</tt> is <tt>0.0</tt> the light is being treated as a directional light; if it is <tt>1.0</tt> it is a point light.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the shadow matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
* reflection will be applied first!
* <p>
* Reference: <a href="ftp://ftp.sgi.com/opengl/contrib/blythe/advanced99/notes/node192.html">ftp.sgi.com</a>
*
* @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
*/
Matrix4d shadow(Vector4dc light, double a, double b, double c, double d, Matrix4d dest);
/**
* Apply a projection transformation to this matrix that projects onto the plane specified via the general plane equation
* <tt>x*a + y*b + z*c + d = 0</tt> as if casting a shadow from a given light position/direction <tt>(lightX, lightY, lightZ, lightW)</tt>
* and store the result in <code>dest</code>.
* <p>
* If <code>lightW</code> is <tt>0.0</tt> the light is being treated as a directional light; if it is <tt>1.0</tt> it is a point light.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the shadow matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
* reflection will be applied first!
* <p>
* Reference: <a href="ftp://ftp.sgi.com/opengl/contrib/blythe/advanced99/notes/node192.html">ftp.sgi.com</a>
*
* @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
*/
Matrix4d shadow(double lightX, double lightY, double lightZ, double lightW, double a, double b, double c, double d, Matrix4d dest);
/**
* Apply a projection transformation to this matrix that projects onto the plane with the general plane equation
* <tt>y = 0</tt> as if casting a shadow from a given light position/direction <code>light</code>
* and store the result in <code>dest</code>.
* <p>
* Before the shadow projection is applied, the plane is transformed via the specified <code>planeTransformation</code>.
* <p>
* If <tt>light.w</tt> is <tt>0.0</tt> the light is being treated as a directional light; if it is <tt>1.0</tt> it is a point light.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the shadow matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
* reflection will be applied first!
*
* @param light
* the light's vector
* @param planeTransform
* the transformation to transform the implied plane <tt>y = 0</tt> before applying the projection
* @param dest
* will hold the result
* @return dest
*/
Matrix4d shadow(Vector4dc light, Matrix4dc planeTransform, Matrix4d dest);
/**
* Apply a projection transformation to this matrix that projects onto the plane with the general plane equation
* <tt>y = 0</tt> as if casting a shadow from a given light position/direction <tt>(lightX, lightY, lightZ, lightW)</tt>
* and store the result in <code>dest</code>.
* <p>
* Before the shadow projection is applied, the plane is transformed via the specified <code>planeTransformation</code>.
* <p>
* If <code>lightW</code> is <tt>0.0</tt> the light is being treated as a directional light; if it is <tt>1.0</tt> it is a point light.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>S</code> the shadow matrix,
* then the new matrix will be <code>M * S</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * S * v</code>, 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 <tt>y = 0</tt> before applying the projection
* @param dest
* will hold the result
* @return dest
*/
Matrix4d shadow(double lightX, double lightY, double lightZ, double lightW, Matrix4dc planeTransform, Matrix4d dest);
/**
* Apply a picking transformation to this matrix using the given window coordinates <tt>(x, y)</tt> as the pick center
* and the given <tt>(width, height)</tt> as the size of the picking region in window coordinates, and store the result
* in <code>dest</code>.
*
* @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 <tt>[x, y, width, height]</tt>
* @param dest
* the destination matrix, which will hold the result
* @return dest
*/
Matrix4d pick(double x, double y, double width, double height, int[] viewport, Matrix4d dest);
/**
* Determine whether this matrix describes an affine transformation. This is the case iff its last row is equal to <tt>(0, 0, 0, 1)</tt>.
*
* @return <code>true</code> iff this matrix is affine; <code>false</code> otherwise
*/
boolean isAffine();
/**
* Apply an arcball view transformation to this matrix with the given <code>radius</code> and center <tt>(centerX, centerY, centerZ)</tt>
* position of the arcball and the specified X and Y rotation angles, and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling: <tt>translate(0, 0, -radius).rotateX(angleX).rotateY(angleY).translate(-centerX, -centerY, -centerZ)</tt>
*
* @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
*/
Matrix4d arcball(double radius, double centerX, double centerY, double centerZ, double angleX, double angleY, Matrix4d dest);
/**
* Apply an arcball view transformation to this matrix with the given <code>radius</code> and <code>center</code>
* position of the arcball and the specified X and Y rotation angles, and store the result in <code>dest</code>.
* <p>
* This method is equivalent to calling: <tt>translate(0, 0, -radius).rotateX(angleX).rotateY(angleY).translate(-center.x, -center.y, -center.z)</tt>
*
* @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
*/
Matrix4d arcball(double radius, Vector3dc center, double angleX, double angleY, Matrix4d dest);
/**
* Compute the <i>range matrix</i> for the Projected Grid transformation as described in chapter "2.4.2 Creating the range conversion matrix"
* of the paper <a href="http://fileadmin.cs.lth.se/graphics/theses/projects/projgrid/projgrid-lq.pdf">Real-time water rendering - Introducing the projected grid concept</a>
* based on the <i>inverse</i> of the view-projection matrix which is assumed to be <code>this</code>, and store that range matrix into <code>dest</code>.
* <p>
* If the projected grid will not be visible then this method returns <code>null</code>.
* <p>
* This method uses the <tt>y = 0</tt> 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 <code>null</code> if the projected grid will not be visible
*/
Matrix4d projectedGridRange(Matrix4dc projector, double sLower, double sUpper, Matrix4d dest);
/**
* Change the near and far clip plane distances of <code>this</code> perspective frustum transformation matrix
* and store the result in <code>dest</code>.
* <p>
* This method only works if <code>this</code> is a perspective projection frustum transformation, for example obtained
* via {@link #perspective(double, double, double, double, Matrix4d) perspective()} or {@link #frustum(double, double, double, double, double, double, Matrix4d) frustum()}.
*
* @see #perspective(double, double, double, double, Matrix4d)
* @see #frustum(double, double, double, double, double, double, Matrix4d)
*
* @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
*/
Matrix4d perspectiveFrustumSlice(double near, double far, Matrix4d dest);
/**
* Build an ortographic projection transformation that fits the view-projection transformation represented by <code>this</code>
* into the given affine <code>view</code> transformation.
* <p>
* The transformation represented by <code>this</code> must be given as the {@link #invert(Matrix4d) inverse} of a typical combined camera view-projection
* transformation, whose projection can be either orthographic or perspective.
* <p>
* The <code>view</code> 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(double, double, double, double, double, double, double, double, double, Matrix4d) lookAt()}.
* <p>
* Reference: <a href="http://developer.download.nvidia.com/SDK/10.5/opengl/screenshots/samples/cascaded_shadow_maps.html">OpenGL SDK - Cascaded Shadow Maps</a>
*
* @param view
* the view transformation to build a corresponding orthographic projection to fit the frustum of <code>this</code>
* @param dest
* will hold the crop projection transformation
* @return dest
*/
Matrix4d orthoCrop(Matrix4dc view, Matrix4d dest);
/**
* Transform the axis-aligned box given as the minimum corner <tt>(minX, minY, minZ)</tt> and maximum corner <tt>(maxX, maxY, maxZ)</tt>
* by <code>this</code> {@link #isAffine() affine} matrix and compute the axis-aligned box of the result whose minimum corner is stored in <code>outMin</code>
* and maximum corner stored in <code>outMax</code>.
* <p>
* Reference: <a href="http://dev.theomader.com/transform-bounding-boxes/">http://dev.theomader.com</a>
*
* @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
*/
Matrix4d transformAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ, Vector3d outMin, Vector3d outMax);
/**
* Transform the axis-aligned box given as the minimum corner <code>min</code> and maximum corner <code>max</code>
* by <code>this</code> {@link #isAffine() affine} matrix and compute the axis-aligned box of the result whose minimum corner is stored in <code>outMin</code>
* and maximum corner stored in <code>outMax</code>.
*
* @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
*/
Matrix4d transformAab(Vector3dc min, Vector3dc max, Vector3d outMin, Vector3d outMax);
/**
* Linearly interpolate <code>this</code> and <code>other</code> using the given interpolation factor <code>t</code>
* and store the result in <code>dest</code>.
* <p>
* If <code>t</code> is <tt>0.0</tt> then the result is <code>this</code>. If the interpolation factor is <code>1.0</code>
* then the result is <code>other</code>.
*
* @param other
* the other matrix
* @param t
* the interpolation factor between 0.0 and 1.0
* @param dest
* will hold the result
* @return dest
*/
Matrix4d lerp(Matrix4dc other, double t, Matrix4d dest);
/**
* Apply a model transformation to this matrix for a right-handed coordinate system,
* that aligns the local <code>+Z</code> axis with <code>direction</code>
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
* <p>
* This method is equivalent to calling: <tt>mulAffine(new Matrix4d().lookAt(new Vector3d(), new Vector3d(dir).negate(), up).invertAffine(), dest)</tt>
*
* @see #rotateTowards(double, double, double, double, double, double, Matrix4d)
*
* @param direction
* the direction to rotate towards
* @param up
* the up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix4d rotateTowards(Vector3dc direction, Vector3dc up, Matrix4d dest);
/**
* Apply a model transformation to this matrix for a right-handed coordinate system,
* that aligns the local <code>+Z</code> axis with <code>dir</code>
* and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>L</code> the lookat matrix,
* then the new matrix will be <code>M * L</code>. So when transforming a
* vector <code>v</code> with the new matrix by using <code>M * L * v</code>,
* the lookat transformation will be applied first!
* <p>
* This method is equivalent to calling: <tt>mulAffine(new Matrix4d().lookAt(0, 0, 0, -dirX, -dirY, -dirZ, upX, upY, upZ).invertAffine(), dest)</tt>
*
* @see #rotateTowards(Vector3dc, Vector3dc, Matrix4d)
*
* @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
*/
Matrix4d rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix4d dest);
/**
* Extract the Euler angles from the rotation represented by the upper left 3x3 submatrix of <code>this</code>
* and store the extracted Euler angles in <code>dest</code>.
* <p>
* This method assumes that the upper left of <code>this</code> only represents a rotation without scaling.
* <p>
* Note that the returned Euler angles must be applied in the order <tt>Z * Y * X</tt> to obtain the identical matrix.
* This means that calling {@link Matrix4dc#rotateZYX(double, double, double, Matrix4d)} using the obtained Euler angles will yield
* the same rotation as the original matrix from which the Euler angles were obtained, so in the below code the matrix
* <tt>m2</tt> should be identical to <tt>m</tt> (disregarding possible floating-point inaccuracies).
* <pre>
* Matrix4d m = ...; // <- matrix only representing rotation
* Matrix4d n = new Matrix4d();
* n.rotateZYX(m.getEulerAnglesZYX(new Vector3d()));
* </pre>
* <p>
* Reference: <a href="http://nghiaho.com/?page_id=846">http://nghiaho.com/</a>
*
* @param dest
* will hold the extracted Euler angles
* @return dest
*/
Vector3d getEulerAnglesZYX(Vector3d dest);
/**
* Test whether the given point <tt>(x, y, z)</tt> is within the frustum defined by <code>this</code> matrix.
* <p>
* This method assumes <code>this</code> matrix to be a transformation from any arbitrary coordinate system/space <tt>M</tt>
* into standard OpenGL clip space and tests whether the given point with the coordinates <tt>(x, y, z)</tt> given
* in space <tt>M</tt> is within the clip space.
* <p>
* When testing multiple points using the same transformation matrix, {@link FrustumIntersection} should be used instead.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @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 <code>true</code> if the given point is inside the frustum; <code>false</code> otherwise
*/
boolean testPoint(double x, double y, double z);
/**
* Test whether the given sphere is partly or completely within or outside of the frustum defined by <code>this</code> matrix.
* <p>
* This method assumes <code>this</code> matrix to be a transformation from any arbitrary coordinate system/space <tt>M</tt>
* into standard OpenGL clip space and tests whether the given sphere with the coordinates <tt>(x, y, z)</tt> given
* in space <tt>M</tt> is within the clip space.
* <p>
* When testing multiple spheres using the same transformation matrix, or more sophisticated/optimized intersection algorithms are required,
* {@link FrustumIntersection} should be used instead.
* <p>
* The algorithm implemented by this method is conservative. This means that in certain circumstances a <i>false positive</i>
* can occur, when the method returns <tt>true</tt> for spheres that are actually not visible.
* See <a href="http://iquilezles.org/www/articles/frustumcorrect/frustumcorrect.htm">iquilezles.org</a> for an examination of this problem.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @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 <code>true</code> if the given sphere is partly or completely inside the frustum; <code>false</code> otherwise
*/
boolean testSphere(double x, double y, double z, double r);
/**
* Test whether the given axis-aligned box is partly or completely within or outside of the frustum defined by <code>this</code> matrix.
* The box is specified via its min and max corner coordinates.
* <p>
* This method assumes <code>this</code> matrix to be a transformation from any arbitrary coordinate system/space <tt>M</tt>
* into standard OpenGL clip space and tests whether the given axis-aligned box with its minimum corner coordinates <tt>(minX, minY, minZ)</tt>
* and maximum corner coordinates <tt>(maxX, maxY, maxZ)</tt> given in space <tt>M</tt> is within the clip space.
* <p>
* 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.
* <p>
* The algorithm implemented by this method is conservative. This means that in certain circumstances a <i>false positive</i>
* can occur, when the method returns <tt>-1</tt> for boxes that are actually not visible/do not intersect the frustum.
* See <a href="http://iquilezles.org/www/articles/frustumcorrect/frustumcorrect.htm">iquilezles.org</a> for an examination of this problem.
* <p>
* Reference: <a href="http://www.cescg.org/CESCG-2002/DSykoraJJelinek/">Efficient View Frustum Culling</a>
* <br>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
*
* @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 <code>true</code> if the axis-aligned box is completely or partly inside of the frustum; <code>false</code> otherwise
*/
boolean testAab(double minX, double minY, double minZ, double maxX, double maxY, double maxZ);
}