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Flywheel/joml/Matrix3dc.java
PepperCode1 dd18300b70 Scheme-a-version 
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/*
* The MIT License
*
* Copyright (c) 2016-2021 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 com.jozufozu.flywheel.repack.joml;
import java.nio.ByteBuffer;
import java.nio.DoubleBuffer;
import java.nio.FloatBuffer;
import java.util.*;
/**
* Interface to a read-only view of a 3x3 matrix of double-precision floats.
*
* @author Kai Burjack
*/
public interface Matrix3dc {
/**
* 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 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 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();
/**
* Multiply this matrix by the supplied matrix and store the result in <code>dest</code>.
* This matrix will be the left one.
* <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
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mul(Matrix3dc right, Matrix3d 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
*/
Matrix3d mulLocal(Matrix3dc left, Matrix3d dest);
/**
* Multiply this matrix by the supplied matrix and store the result in <code>dest</code>.
* This matrix will be the left one.
* <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
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mul(Matrix3fc right, Matrix3d dest);
/**
* Return the determinant of this matrix.
*
* @return the determinant
*/
double determinant();
/**
* Invert <code>this</code> matrix and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d invert(Matrix3d dest);
/**
* Transpose <code>this</code> matrix and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d transpose(Matrix3d 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
*/
Matrix3d get(Matrix3d dest);
/**
* Get the current values of <code>this</code> matrix and store the represented rotation
* into the given {@link AxisAngle4f}.
*
* @see AxisAngle4f#set(Matrix3dc)
*
* @param dest
* the destination {@link AxisAngle4f}
* @return the passed in destination
*/
AxisAngle4f getRotation(AxisAngle4f 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 three column vectors of this matrix are not normalized and
* thus allows to ignore any additional scaling factor that is applied to the matrix.
*
* @see Quaternionf#setFromUnnormalized(Matrix3dc)
*
* @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 three column vectors of this matrix are normalized.
*
* @see Quaternionf#setFromNormalized(Matrix3dc)
*
* @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 three column vectors of this matrix are not normalized and
* thus allows to ignore any additional scaling factor that is applied to the matrix.
*
* @see Quaterniond#setFromUnnormalized(Matrix3dc)
*
* @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 three column vectors of this matrix are normalized.
*
* @see Quaterniond#setFromNormalized(Matrix3dc)
*
* @param dest
* the destination {@link Quaterniond}
* @return the passed in destination
*/
Quaterniond getNormalizedRotation(Quaterniond dest);
/**
* Store this matrix into the supplied {@link DoubleBuffer} at the current
* buffer {@link DoubleBuffer#position() position} using column-major order.
* <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 into the supplied {@link DoubleBuffer} starting at the specified
* absolute buffer position/index using column-major order.
* <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);
/**
* Store this matrix in column-major order at the given off-heap address.
* <p>
* This method will throw an {@link UnsupportedOperationException} when JOML is used with `-Djoml.nounsafe`.
* <p>
* <em>This method is unsafe as it can result in a crash of the JVM process when the specified address range does not belong to this process.</em>
*
* @param address
* the off-heap address where to store this matrix
* @return this
*/
Matrix3dc getToAddress(long address);
/**
* 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);
/**
* Apply scaling to <code>this</code> matrix by scaling the base axes by the given <code>xyz.x</code>,
* <code>xyz.y</code> and <code>xyz.z</code> 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
*/
Matrix3d scale(Vector3dc xyz, Matrix3d dest);
/**
* Apply scaling to this 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
*/
Matrix3d scale(double x, double y, double z, Matrix3d dest);
/**
* Apply scaling to this matrix by uniformly 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>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, Matrix3d)
*
* @param xyz
* the factor for all components
* @param dest
* will hold the result
* @return dest
*/
Matrix3d scale(double xyz, Matrix3d 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
*/
Matrix3d scaleLocal(double x, double y, double z, Matrix3d dest);
/**
* Transform the given vector by this matrix.
*
* @param v
* the vector to transform
* @return v
*/
Vector3d transform(Vector3d v);
/**
* Transform the given vector by this matrix and store the result in <code>dest</code>.
*
* @param v
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3d transform(Vector3dc v, Vector3d dest);
/**
* Transform the given vector by this matrix.
*
* @param v
* the vector to transform
* @return v
*/
Vector3f transform(Vector3f v);
/**
* Transform the given vector by this matrix and store the result in <code>dest</code>.
*
* @param v
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3f transform(Vector3fc v, Vector3f dest);
/**
* Transform the vector <code>(x, y, z)</code> 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 dest
* will hold the result
* @return dest
*/
Vector3d transform(double x, double y, double z, Vector3d dest);
/**
* Transform the given vector by the transpose of this matrix.
*
* @param v
* the vector to transform
* @return v
*/
Vector3d transformTranspose(Vector3d v);
/**
* Transform the given vector by the transpose of this matrix and store the result in <code>dest</code>.
*
* @param v
* the vector to transform
* @param dest
* will hold the result
* @return dest
*/
Vector3d transformTranspose(Vector3dc v, Vector3d dest);
/**
* Transform the vector <code>(x, y, z)</code> by the transpose of 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 dest
* will hold the result
* @return dest
*/
Vector3d transformTranspose(double x, double y, double z, Vector3d 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
*/
Matrix3d rotateX(double ang, Matrix3d 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
*/
Matrix3d rotateY(double ang, Matrix3d 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
*/
Matrix3d rotateZ(double ang, Matrix3d 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: <code>rotateX(angleX, dest).rotateY(angleY).rotateZ(angleZ)</code>
*
* @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
*/
Matrix3d rotateXYZ(double angleX, double angleY, double angleZ, Matrix3d 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: <code>rotateZ(angleZ, dest).rotateY(angleY).rotateX(angleX)</code>
*
* @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
*/
Matrix3d rotateZYX(double angleZ, double angleY, double angleX, Matrix3d 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: <code>rotateY(angleY, dest).rotateX(angleX).rotateZ(angleZ)</code>
*
* @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
*/
Matrix3d rotateYXZ(double angleY, double angleX, double angleZ, Matrix3d 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>
* 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
*/
Matrix3d rotate(double ang, double x, double y, double z, Matrix3d dest);
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians
* about the specified <code>(x, y, z)</code> 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
*/
Matrix3d rotateLocal(double ang, double x, double y, double z, Matrix3d 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
*/
Matrix3d rotateLocalX(double ang, Matrix3d 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
*/
Matrix3d rotateLocalY(double ang, Matrix3d 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
*/
Matrix3d rotateLocalZ(double ang, Matrix3d 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
*/
Matrix3d rotateLocal(Quaterniondc quat, Matrix3d 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
*/
Matrix3d rotateLocal(Quaternionfc quat, Matrix3d 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
*/
Matrix3d rotate(Quaterniondc quat, Matrix3d 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
*/
Matrix3d rotate(Quaternionfc quat, Matrix3d dest);
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4f} 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 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, Matrix3d)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix3d rotate(AxisAngle4f axisAngle, Matrix3d 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, Matrix3d)
*
* @param axisAngle
* the {@link AxisAngle4d} (needs to be {@link AxisAngle4d#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
Matrix3d rotate(AxisAngle4d axisAngle, Matrix3d dest);
/**
* Apply a rotation transformation, rotating the given radians about the specified axis 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 axis and angle,
* 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, Matrix3d)
*
* @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
*/
Matrix3d rotate(double angle, Vector3dc axis, Matrix3d dest);
/**
* Apply a rotation transformation, rotating the given radians about the specified axis 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 axis and angle,
* 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, Matrix3d)
*
* @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
*/
Matrix3d rotate(double angle, Vector3fc axis, Matrix3d dest);
/**
* Get the row at the given <code>row</code> index, starting with <code>0</code>.
*
* @param row
* the row index in <code>[0..2]</code>
* @param dest
* will hold the row components
* @return the passed in destination
* @throws IndexOutOfBoundsException if <code>row</code> is not in <code>[0..2]</code>
*/
Vector3d getRow(int row, Vector3d dest) throws IndexOutOfBoundsException;
/**
* Get the column at the given <code>column</code> index, starting with <code>0</code>.
*
* @param column
* the column index in <code>[0..2]</code>
* @param dest
* will hold the column components
* @return the passed in destination
* @throws IndexOutOfBoundsException if <code>column</code> is not in <code>[0..2]</code>
*/
Vector3d getColumn(int column, Vector3d dest) throws IndexOutOfBoundsException;
/**
* Get the matrix element value at the given column and row.
*
* @param column
* the colum index in <code>[0..2]</code>
* @param row
* the row index in <code>[0..2]</code>
* @return the element value
*/
double get(int column, int row);
/**
* Get the matrix element value at the given row and column.
*
* @param row
* the row index in <code>[0..2]</code>
* @param column
* the colum index in <code>[0..2]</code>
* @return the element value
*/
double getRowColumn(int row, int column);
/**
* Compute a normal matrix from <code>this</code> matrix and store it into <code>dest</code>.
* <p>
* The normal matrix of <code>m</code> is the transpose of the inverse of <code>m</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d normal(Matrix3d dest);
/**
* Compute the cofactor matrix of <code>this</code> and store it into <code>dest</code>.
* <p>
* The cofactor matrix can be used instead of {@link #normal(Matrix3d)} to transform normals
* when the orientation of the normals with respect to the surface should be preserved.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d cofactor(Matrix3d 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!
*
* @see #lookAlong(double, double, double, double, double, double, Matrix3d)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
Matrix3d lookAlong(Vector3dc dir, Vector3dc up, Matrix3d 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!
*
* @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
*/
Matrix3d lookAlong(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix3d dest);
/**
* Get the scaling factors of <code>this</code> matrix for the three base axes.
*
* @param dest
* will hold the scaling factors for <code>x</code>, <code>y</code> and <code>z</code>
* @return dest
*/
Vector3d getScale(Vector3d dest);
/**
* Obtain the direction of <code>+Z</code> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).invert();
* inv.transform(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 <code>+Z</code>
* @return dir
*/
Vector3d positiveZ(Vector3d dir);
/**
* Obtain the direction of <code>+Z</code> 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 is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).transpose();
* inv.transform(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 <code>+Z</code>
* @return dir
*/
Vector3d normalizedPositiveZ(Vector3d dir);
/**
* Obtain the direction of <code>+X</code> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).invert();
* inv.transform(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 <code>+X</code>
* @return dir
*/
Vector3d positiveX(Vector3d dir);
/**
* Obtain the direction of <code>+X</code> 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 is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).transpose();
* inv.transform(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 <code>+X</code>
* @return dir
*/
Vector3d normalizedPositiveX(Vector3d dir);
/**
* Obtain the direction of <code>+Y</code> before the transformation represented by <code>this</code> matrix is applied.
* <p>
* This method is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).invert();
* inv.transform(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 <code>+Y</code>
* @return dir
*/
Vector3d positiveY(Vector3d dir);
/**
* Obtain the direction of <code>+Y</code> 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 is equivalent to the following code:
* <pre>
* Matrix3d inv = new Matrix3d(this).transpose();
* inv.transform(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 <code>+Y</code>
* @return dir
*/
Vector3d normalizedPositiveY(Vector3d dir);
/**
* 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
*/
Matrix3d add(Matrix3dc other, Matrix3d 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
*/
Matrix3d sub(Matrix3dc subtrahend, Matrix3d 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
*/
Matrix3d mulComponentWise(Matrix3dc other, Matrix3d dest);
/**
* 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 <code>0.0</code> 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
*/
Matrix3d lerp(Matrix3dc other, double t, Matrix3d 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: <code>mul(new Matrix3d().lookAlong(new Vector3d(dir).negate(), up).invert(), dest)</code>
*
* @see #rotateTowards(double, double, double, double, double, double, Matrix3d)
*
* @param direction
* the direction to rotate towards
* @param up
* the model's up vector
* @param dest
* will hold the result
* @return dest
*/
Matrix3d rotateTowards(Vector3dc direction, Vector3dc up, Matrix3d 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: <code>mul(new Matrix3d().lookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert(), dest)</code>
*
* @see #rotateTowards(Vector3dc, Vector3dc, Matrix3d)
*
* @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
*/
Matrix3d rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix3d dest);
/**
* Extract the Euler angles from the rotation represented by <code>this</code> matrix and store the extracted Euler angles in <code>dest</code>.
* <p>
* This method assumes that <code>this</code> matrix only represents a rotation without scaling.
* <p>
* The Euler angles are always returned as the angle around X in the {@link Vector3d#x} field, the angle around Y in the {@link Vector3d#y}
* field and the angle around Z in the {@link Vector3d#z} field of the supplied {@link Vector3d} instance.
* <p>
* Note that the returned Euler angles must be applied in the order <code>X * Y * Z</code> to obtain the identical matrix.
* This means that calling {@link Matrix3dc#rotateXYZ(double, double, double, Matrix3d)} 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
* <code>m2</code> should be identical to <code>m</code> (disregarding possible floating-point inaccuracies).
* <pre>
* Matrix3d m = ...; // &lt;- matrix only representing rotation
* Matrix3d n = new Matrix3d();
* n.rotateXYZ(m.getEulerAnglesXYZ(new Vector3d()));
* </pre>
* <p>
* Reference: <a href="https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix">http://en.wikipedia.org/</a>
*
* @param dest
* will hold the extracted Euler angles
* @return dest
*/
Vector3d getEulerAnglesXYZ(Vector3d dest);
/**
* Extract the Euler angles from the rotation represented by <code>this</code> matrix and store the extracted Euler angles in <code>dest</code>.
* <p>
* This method assumes that <code>this</code> matrix only represents a rotation without scaling.
* <p>
* The Euler angles are always returned as the angle around X in the {@link Vector3d#x} field, the angle around Y in the {@link Vector3d#y}
* field and the angle around Z in the {@link Vector3d#z} field of the supplied {@link Vector3d} instance.
* <p>
* Note that the returned Euler angles must be applied in the order <code>Z * Y * X</code> to obtain the identical matrix.
* This means that calling {@link Matrix3dc#rotateZYX(double, double, double, Matrix3d)} 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
* <code>m2</code> should be identical to <code>m</code> (disregarding possible floating-point inaccuracies).
* <pre>
* Matrix3d m = ...; // &lt;- matrix only representing rotation
* Matrix3d n = new Matrix3d();
* n.rotateZYX(m.getEulerAnglesZYX(new Vector3d()));
* </pre>
* <p>
* Reference: <a href="https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix">http://en.wikipedia.org/</a>
*
* @param dest
* will hold the extracted Euler angles
* @return dest
*/
Vector3d getEulerAnglesZYX(Vector3d dest);
/**
* Apply an oblique projection transformation to this matrix with the given values for <code>a</code> and
* <code>b</code> and store the result in <code>dest</code>.
* <p>
* If <code>M</code> is <code>this</code> matrix and <code>O</code> the oblique transformation 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
* oblique transformation will be applied first!
* <p>
* The oblique transformation is defined as:
* <pre>
* x' = x + a*z
* y' = y + a*z
* z' = z
* </pre>
* or in matrix form:
* <pre>
* 1 0 a
* 0 1 b
* 0 0 1
* </pre>
*
* @param a
* the value for the z factor that applies to x
* @param b
* the value for the z factor that applies to y
* @param dest
* will hold the result
* @return dest
*/
Matrix3d obliqueZ(double a, double b, Matrix3d dest);
/**
* Compare the matrix elements of <code>this</code> matrix with the given matrix using the given <code>delta</code>
* and return whether all of them are equal within a maximum difference of <code>delta</code>.
* <p>
* Please note that this method is not used by any data structure such as {@link ArrayList} {@link HashSet} or {@link HashMap}
* and their operations, such as {@link ArrayList#contains(Object)} or {@link HashSet#remove(Object)}, since those
* data structures only use the {@link Object#equals(Object)} and {@link Object#hashCode()} methods.
*
* @param m
* the other matrix
* @param delta
* the allowed maximum difference
* @return <code>true</code> whether all of the matrix elements are equal; <code>false</code> otherwise
*/
boolean equals(Matrix3dc m, double delta);
/**
* Apply a mirror/reflection transformation to this matrix that reflects through the given plane
* specified via the plane normal <code>(nx, ny, nz)</code>, 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 dest
* will hold the result
* @return this
*/
Matrix3d reflect(double nx, double ny, double nz, Matrix3d dest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects through a plane
* specified via the plane orientation, 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 <code>(0, 0, 1)</code>. So, if the given {@link Quaterniondc} is
* the identity (does not apply any additional rotation), the reflection plane will be <code>z=0</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 dest
* will hold the result
* @return this
*/
Matrix3d reflect(Quaterniondc orientation, Matrix3d dest);
/**
* Apply a mirror/reflection transformation to this matrix that reflects through the given plane
* specified via the plane normal, 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 dest
* will hold the result
* @return this
*/
Matrix3d reflect(Vector3dc normal, Matrix3d dest);
/**
* Determine whether all matrix elements are finite floating-point values, that
* is, they are not {@link Double#isNaN() NaN} and not
* {@link Double#isInfinite() infinity}.
*
* @return {@code true} if all components are finite floating-point values;
* {@code false} otherwise
*/
boolean isFinite();
/**
* Compute <code>(x, y, z)^T * this * (x, y, z)</code>.
*
* @param x
* the x coordinate of the vector to multiply
* @param y
* the y coordinate of the vector to multiply
* @param z
* the z coordinate of the vector to multiply
* @return the result
*/
double quadraticFormProduct(double x, double y, double z);
/**
* Compute <code>v^T * this * v</code>.
*
* @param v
* the vector to multiply
* @return the result
*/
double quadraticFormProduct(Vector3dc v);
/**
* Compute <code>v^T * this * v</code>.
*
* @param v
* the vector to multiply
* @return the result
*/
double quadraticFormProduct(Vector3fc v);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 0 1
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapXZY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 0 -1
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapXZnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 -1 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapXnYnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 0 1
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapXnZY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 0 -1
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapXnZnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 1 0 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYXZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 1 0 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYXnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 1 0 0
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYZX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 1 0 0
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYZnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 1 0 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYnXZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 1 0 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYnXnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 1 0 0
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYnZX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 1 0 0
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapYnZnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 0 0 1
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZXY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 0 0 -1
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZXnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 0 1 0
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZYX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 0 1 0
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZYnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 0 0 1
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZnXY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 0 0 -1
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZnXnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 0 -1 0
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZnYX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 0 -1 0
* 1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapZnYnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 1 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXYnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 0 1
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXZY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 0 -1
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXZnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 -1 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXnYZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 -1 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXnYnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 0 1
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXnZY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 0 -1
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnXnZnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* -1 0 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYXZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* -1 0 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYXnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* -1 0 0
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYZX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* -1 0 0
* 0 1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYZnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* -1 0 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYnXZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* -1 0 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYnXnZ(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* -1 0 0
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYnZX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* -1 0 0
* 0 -1 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnYnZnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 0 0 1
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZXY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 1 0
* 0 0 -1
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZXnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 0 1 0
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZYX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 0 1 0
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZYnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 0 0 1
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZnXY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 -1 0
* 0 0 -1
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZnXnY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 1
* 0 -1 0
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZnYX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 0 0 -1
* 0 -1 0
* -1 0 0
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d mapnZnYnX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* -1 0 0
* 0 1 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d negateX(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 -1 0
* 0 0 1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d negateY(Matrix3d dest);
/**
* Multiply <code>this</code> by the matrix
* <pre>
* 1 0 0
* 0 1 0
* 0 0 -1
* </pre>
* and store the result in <code>dest</code>.
*
* @param dest
* will hold the result
* @return dest
*/
Matrix3d negateZ(Matrix3d dest);
}
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