/*
* The MIT License
*
* Copyright (c) 2015-2020 Richard Greenlees
*
* 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;
import java.io.Externalizable;
import java.io.IOException;
import java.io.ObjectInput;
import java.io.ObjectOutput;
//#ifdef __HAS_NIO__
import java.nio.ByteBuffer;
import java.nio.DoubleBuffer;
import java.nio.FloatBuffer;
//#endif
import java.text.DecimalFormat;
import java.text.NumberFormat;
/**
* Contains the definition of a 3x3 matrix of doubles, and associated functions to transform
* it. The matrix is column-major to match OpenGL's interpretation, and it looks like this:
* <p>
* m00 m10 m20<br>
* m01 m11 m21<br>
* m02 m12 m22<br>
*
* @author Richard Greenlees
* @author Kai Burjack
*/
public class Matrix3d implements Externalizable, Matrix3dc {
private static final long serialVersionUID = 1L;
public double m00, m01, m02;
public double m10, m11, m12;
public double m20, m21, m22;
/**
* Create a new {@link Matrix3d} and initialize it to {@link #identity() identity}.
*/
public Matrix3d() {
m00 = 1.0;
m11 = 1.0;
m22 = 1.0;
}
/**
* Create a new {@link Matrix3d} by setting its uppper left 2x2 submatrix to the values of the given {@link Matrix2dc}
* and the rest to identity.
*
* @param mat
* the {@link Matrix2dc}
*/
public Matrix3d(Matrix2dc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} by setting its uppper left 2x2 submatrix to the values of the given {@link Matrix2fc}
* and the rest to identity.
*
* @param mat
* the {@link Matrix2fc}
*/
public Matrix3d(Matrix2fc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} and initialize it with the values from the given matrix.
*
* @param mat
* the matrix to initialize this matrix with
*/
public Matrix3d(Matrix3dc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} and initialize it with the values from the given matrix.
*
* @param mat
* the matrix to initialize this matrix with
*/
public Matrix3d(Matrix3fc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} and make it a copy of the upper left 3x3 of the given {@link Matrix4fc}.
*
* @param mat
* the {@link Matrix4fc} to copy the values from
*/
public Matrix3d(Matrix4fc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} and make it a copy of the upper left 3x3 of the given {@link Matrix4dc}.
*
* @param mat
* the {@link Matrix4dc} to copy the values from
*/
public Matrix3d(Matrix4dc mat) {
set(mat);
}
/**
* Create a new {@link Matrix3d} and initialize its elements with the given values.
*
* @param m00
* the value of m00
* @param m01
* the value of m01
* @param m02
* the value of m02
* @param m10
* the value of m10
* @param m11
* the value of m11
* @param m12
* the value of m12
* @param m20
* the value of m20
* @param m21
* the value of m21
* @param m22
* the value of m22
*/
public Matrix3d(double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22) {
this.m00 = m00;
this.m01 = m01;
this.m02 = m02;
this.m10 = m10;
this.m11 = m11;
this.m12 = m12;
this.m20 = m20;
this.m21 = m21;
this.m22 = m22;
}
//#ifdef __HAS_NIO__
/**
* Create a new {@link Matrix3d} by reading its 9 double components from the given {@link DoubleBuffer}
* at the buffer's current position.
* <p>
* That DoubleBuffer is expected to hold the values in column-major order.
* <p>
* The buffer's position will not be changed by this method.
*
* @param buffer
* the {@link DoubleBuffer} to read the matrix values from
*/
public Matrix3d(DoubleBuffer buffer) {
MemUtil.INSTANCE.get(this, buffer.position(), buffer);
}
//#endif
/**
* Create a new {@link Matrix3d} and initialize its three columns using the supplied vectors.
*
* @param col0
* the first column
* @param col1
* the second column
* @param col2
* the third column
*/
public Matrix3d(Vector3dc col0, Vector3dc col1, Vector3dc col2) {
set(col0, col1, col2);
}
public double m00() {
return m00;
}
public double m01() {
return m01;
}
public double m02() {
return m02;
}
public double m10() {
return m10;
}
public double m11() {
return m11;
}
public double m12() {
return m12;
}
public double m20() {
return m20;
}
public double m21() {
return m21;
}
public double m22() {
return m22;
}
/**
* Set the value of the matrix element at column 0 and row 0.
*
* @param m00
* the new value
* @return this
*/
public Matrix3d m00(double m00) {
this.m00 = m00;
return this;
}
/**
* Set the value of the matrix element at column 0 and row 1.
*
* @param m01
* the new value
* @return this
*/
public Matrix3d m01(double m01) {
this.m01 = m01;
return this;
}
/**
* Set the value of the matrix element at column 0 and row 2.
*
* @param m02
* the new value
* @return this
*/
public Matrix3d m02(double m02) {
this.m02 = m02;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 0.
*
* @param m10
* the new value
* @return this
*/
public Matrix3d m10(double m10) {
this.m10 = m10;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 1.
*
* @param m11
* the new value
* @return this
*/
public Matrix3d m11(double m11) {
this.m11 = m11;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 2.
*
* @param m12
* the new value
* @return this
*/
public Matrix3d m12(double m12) {
this.m12 = m12;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 0.
*
* @param m20
* the new value
* @return this
*/
public Matrix3d m20(double m20) {
this.m20 = m20;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 1.
*
* @param m21
* the new value
* @return this
*/
public Matrix3d m21(double m21) {
this.m21 = m21;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 2.
*
* @param m22
* the new value
* @return this
*/
public Matrix3d m22(double m22) {
this.m22 = m22;
return this;
}
/**
* Set the value of the matrix element at column 0 and row 0.
*
* @param m00
* the new value
* @return this
*/
Matrix3d _m00(double m00) {
this.m00 = m00;
return this;
}
/**
* Set the value of the matrix element at column 0 and row 1.
*
* @param m01
* the new value
* @return this
*/
Matrix3d _m01(double m01) {
this.m01 = m01;
return this;
}
/**
* Set the value of the matrix element at column 0 and row 2.
*
* @param m02
* the new value
* @return this
*/
Matrix3d _m02(double m02) {
this.m02 = m02;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 0.
*
* @param m10
* the new value
* @return this
*/
Matrix3d _m10(double m10) {
this.m10 = m10;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 1.
*
* @param m11
* the new value
* @return this
*/
Matrix3d _m11(double m11) {
this.m11 = m11;
return this;
}
/**
* Set the value of the matrix element at column 1 and row 2.
*
* @param m12
* the new value
* @return this
*/
Matrix3d _m12(double m12) {
this.m12 = m12;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 0.
*
* @param m20
* the new value
* @return this
*/
Matrix3d _m20(double m20) {
this.m20 = m20;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 1.
*
* @param m21
* the new value
* @return this
*/
Matrix3d _m21(double m21) {
this.m21 = m21;
return this;
}
/**
* Set the value of the matrix element at column 2 and row 2.
*
* @param m22
* the new value
* @return this
*/
Matrix3d _m22(double m22) {
this.m22 = m22;
return this;
}
/**
* Set the values in this matrix to the ones in m.
*
* @param m
* the matrix whose values will be copied
* @return this
*/
public Matrix3d set(Matrix3dc m) {
m00 = m.m00();
m01 = m.m01();
m02 = m.m02();
m10 = m.m10();
m11 = m.m11();
m12 = m.m12();
m20 = m.m20();
m21 = m.m21();
m22 = m.m22();
return this;
}
/**
* Store the values of the transpose of the given matrix <code>m</code> into <code>this</code> matrix.
*
* @param m
* the matrix to copy the transposed values from
* @return this
*/
public Matrix3d setTransposed(Matrix3dc m) {
double nm10 = m.m01(), nm12 = m.m21();
double nm20 = m.m02(), nm21 = m.m12();
return this
._m00(m.m00())._m01(m.m10())._m02(m.m20())
._m10(nm10)._m11(m.m11())._m12(nm12)
._m20(nm20)._m21(nm21)._m22(m.m22());
}
/**
* Set the values in this matrix to the ones in m.
*
* @param m
* the matrix whose values will be copied
* @return this
*/
public Matrix3d set(Matrix3fc m) {
m00 = m.m00();
m01 = m.m01();
m02 = m.m02();
m10 = m.m10();
m11 = m.m11();
m12 = m.m12();
m20 = m.m20();
m21 = m.m21();
m22 = m.m22();
return this;
}
/**
* Store the values of the transpose of the given matrix <code>m</code> into <code>this</code> matrix.
*
* @param m
* the matrix to copy the transposed values from
* @return this
*/
public Matrix3d setTransposed(Matrix3fc m) {
float nm10 = m.m01(), nm12 = m.m21();
float nm20 = m.m02(), nm21 = m.m12();
return this
._m00(m.m00())._m01(m.m10())._m02(m.m20())
._m10(nm10)._m11(m.m11())._m12(nm12)
._m20(nm20)._m21(nm21)._m22(m.m22());
}
/**
* Set the elements of this matrix to the left 3x3 submatrix of <code>m</code>.
*
* @param m
* the matrix to copy the elements from
* @return this
*/
public Matrix3d set(Matrix4x3dc m) {
m00 = m.m00();
m01 = m.m01();
m02 = m.m02();
m10 = m.m10();
m11 = m.m11();
m12 = m.m12();
m20 = m.m20();
m21 = m.m21();
m22 = m.m22();
return this;
}
/**
* Set the elements of this matrix to the upper left 3x3 of the given {@link Matrix4fc}.
*
* @param mat
* the {@link Matrix4fc} to copy the values from
* @return this
*/
public Matrix3d set(Matrix4fc mat) {
m00 = mat.m00();
m01 = mat.m01();
m02 = mat.m02();
m10 = mat.m10();
m11 = mat.m11();
m12 = mat.m12();
m20 = mat.m20();
m21 = mat.m21();
m22 = mat.m22();
return this;
}
/**
* Set the elements of this matrix to the upper left 3x3 of the given {@link Matrix4dc}.
*
* @param mat
* the {@link Matrix4dc} to copy the values from
* @return this
*/
public Matrix3d set(Matrix4dc mat) {
m00 = mat.m00();
m01 = mat.m01();
m02 = mat.m02();
m10 = mat.m10();
m11 = mat.m11();
m12 = mat.m12();
m20 = mat.m20();
m21 = mat.m21();
m22 = mat.m22();
return this;
}
/**
* Set the upper left 2x2 submatrix of this {@link Matrix3d} to the given {@link Matrix2fc}
* and the rest to identity.
*
* @see #Matrix3d(Matrix2fc)
*
* @param mat
* the {@link Matrix2fc}
* @return this
*/
public Matrix3d set(Matrix2fc mat) {
m00 = mat.m00();
m01 = mat.m01();
m02 = 0.0;
m10 = mat.m10();
m11 = mat.m11();
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = 1.0;
return this;
}
/**
* Set the upper left 2x2 submatrix of this {@link Matrix3d} to the given {@link Matrix2dc}
* and the rest to identity.
*
* @see #Matrix3d(Matrix2dc)
*
* @param mat
* the {@link Matrix2dc}
* @return this
*/
public Matrix3d set(Matrix2dc mat) {
m00 = mat.m00();
m01 = mat.m01();
m02 = 0.0;
m10 = mat.m10();
m11 = mat.m11();
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = 1.0;
return this;
}
/**
* Set this matrix to be equivalent to the rotation specified by the given {@link AxisAngle4f}.
*
* @param axisAngle
* the {@link AxisAngle4f}
* @return this
*/
public Matrix3d set(AxisAngle4f axisAngle) {
double x = axisAngle.x;
double y = axisAngle.y;
double z = axisAngle.z;
double angle = axisAngle.angle;
double invLength = Math.invsqrt(x*x + y*y + z*z);
x *= invLength;
y *= invLength;
z *= invLength;
double s = Math.sin(angle);
double c = Math.cosFromSin(s, angle);
double omc = 1.0 - c;
m00 = c + x*x*omc;
m11 = c + y*y*omc;
m22 = c + z*z*omc;
double tmp1 = x*y*omc;
double tmp2 = z*s;
m10 = tmp1 - tmp2;
m01 = tmp1 + tmp2;
tmp1 = x*z*omc;
tmp2 = y*s;
m20 = tmp1 + tmp2;
m02 = tmp1 - tmp2;
tmp1 = y*z*omc;
tmp2 = x*s;
m21 = tmp1 - tmp2;
m12 = tmp1 + tmp2;
return this;
}
/**
* Set this matrix to be equivalent to the rotation specified by the given {@link AxisAngle4d}.
*
* @param axisAngle
* the {@link AxisAngle4d}
* @return this
*/
public Matrix3d set(AxisAngle4d axisAngle) {
double x = axisAngle.x;
double y = axisAngle.y;
double z = axisAngle.z;
double angle = axisAngle.angle;
double invLength = Math.invsqrt(x*x + y*y + z*z);
x *= invLength;
y *= invLength;
z *= invLength;
double s = Math.sin(angle);
double c = Math.cosFromSin(s, angle);
double omc = 1.0 - c;
m00 = c + x*x*omc;
m11 = c + y*y*omc;
m22 = c + z*z*omc;
double tmp1 = x*y*omc;
double tmp2 = z*s;
m10 = tmp1 - tmp2;
m01 = tmp1 + tmp2;
tmp1 = x*z*omc;
tmp2 = y*s;
m20 = tmp1 + tmp2;
m02 = tmp1 - tmp2;
tmp1 = y*z*omc;
tmp2 = x*s;
m21 = tmp1 - tmp2;
m12 = tmp1 + tmp2;
return this;
}
/**
* Set this matrix to a rotation - and possibly scaling - equivalent to the given quaternion.
* <p>
* This method is equivalent to calling: <code>rotation(q)</code>
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/">http://www.euclideanspace.com/</a>
*
* @see #rotation(Quaternionfc)
*
* @param q
* the quaternion
* @return this
*/
public Matrix3d set(Quaternionfc q) {
return rotation(q);
}
/**
* Set this matrix to a rotation - and possibly scaling - equivalent to the given quaternion.
* <p>
* This method is equivalent to calling: <code>rotation(q)</code>
* <p>
* Reference: <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/">http://www.euclideanspace.com/</a>
*
* @see #rotation(Quaterniondc)
*
* @param q
* the quaternion
* @return this
*/
public Matrix3d set(Quaterniondc q) {
return rotation(q);
}
/**
* Multiply this matrix by the supplied matrix.
* 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
* @return this
*/
public Matrix3d mul(Matrix3dc right) {
return mul(right, this);
}
public Matrix3d mul(Matrix3dc right, Matrix3d dest) {
double nm00 = Math.fma(m00, right.m00(), Math.fma(m10, right.m01(), m20 * right.m02()));
double nm01 = Math.fma(m01, right.m00(), Math.fma(m11, right.m01(), m21 * right.m02()));
double nm02 = Math.fma(m02, right.m00(), Math.fma(m12, right.m01(), m22 * right.m02()));
double nm10 = Math.fma(m00, right.m10(), Math.fma(m10, right.m11(), m20 * right.m12()));
double nm11 = Math.fma(m01, right.m10(), Math.fma(m11, right.m11(), m21 * right.m12()));
double nm12 = Math.fma(m02, right.m10(), Math.fma(m12, right.m11(), m22 * right.m12()));
double nm20 = Math.fma(m00, right.m20(), Math.fma(m10, right.m21(), m20 * right.m22()));
double nm21 = Math.fma(m01, right.m20(), Math.fma(m11, right.m21(), m21 * right.m22()));
double nm22 = Math.fma(m02, right.m20(), Math.fma(m12, right.m21(), m22 * right.m22()));
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply this matrix by the supplied <code>left</code> matrix and store the result in <code>this</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
* @return this
*/
public Matrix3d mulLocal(Matrix3dc left) {
return mulLocal(left, this);
}
public Matrix3d mulLocal(Matrix3dc left, Matrix3d dest) {
double nm00 = left.m00() * m00 + left.m10() * m01 + left.m20() * m02;
double nm01 = left.m01() * m00 + left.m11() * m01 + left.m21() * m02;
double nm02 = left.m02() * m00 + left.m12() * m01 + left.m22() * m02;
double nm10 = left.m00() * m10 + left.m10() * m11 + left.m20() * m12;
double nm11 = left.m01() * m10 + left.m11() * m11 + left.m21() * m12;
double nm12 = left.m02() * m10 + left.m12() * m11 + left.m22() * m12;
double nm20 = left.m00() * m20 + left.m10() * m21 + left.m20() * m22;
double nm21 = left.m01() * m20 + left.m11() * m21 + left.m21() * m22;
double nm22 = left.m02() * m20 + left.m12() * m21 + left.m22() * m22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Multiply this matrix by the supplied matrix.
* 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
* @return this
*/
public Matrix3d mul(Matrix3fc right) {
return mul(right, this);
}
public Matrix3d mul(Matrix3fc right, Matrix3d dest) {
double nm00 = Math.fma(m00, right.m00(), Math.fma(m10, right.m01(), m20 * right.m02()));
double nm01 = Math.fma(m01, right.m00(), Math.fma(m11, right.m01(), m21 * right.m02()));
double nm02 = Math.fma(m02, right.m00(), Math.fma(m12, right.m01(), m22 * right.m02()));
double nm10 = Math.fma(m00, right.m10(), Math.fma(m10, right.m11(), m20 * right.m12()));
double nm11 = Math.fma(m01, right.m10(), Math.fma(m11, right.m11(), m21 * right.m12()));
double nm12 = Math.fma(m02, right.m10(), Math.fma(m12, right.m11(), m22 * right.m12()));
double nm20 = Math.fma(m00, right.m20(), Math.fma(m10, right.m21(), m20 * right.m22()));
double nm21 = Math.fma(m01, right.m20(), Math.fma(m11, right.m21(), m21 * right.m22()));
double nm22 = Math.fma(m02, right.m20(), Math.fma(m12, right.m21(), m22 * right.m22()));
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Set the values within this matrix to the supplied double values. The result looks like this:
* <p>
* m00, m10, m20<br>
* m01, m11, m21<br>
* m02, m12, m22<br>
*
* @param m00
* the new value of m00
* @param m01
* the new value of m01
* @param m02
* the new value of m02
* @param m10
* the new value of m10
* @param m11
* the new value of m11
* @param m12
* the new value of m12
* @param m20
* the new value of m20
* @param m21
* the new value of m21
* @param m22
* the new value of m22
* @return this
*/
public Matrix3d set(double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22) {
this.m00 = m00;
this.m01 = m01;
this.m02 = m02;
this.m10 = m10;
this.m11 = m11;
this.m12 = m12;
this.m20 = m20;
this.m21 = m21;
this.m22 = m22;
return this;
}
/**
* Set the values in this matrix based on the supplied double array. The result looks like this:
* <p>
* 0, 3, 6<br>
* 1, 4, 7<br>
* 2, 5, 8<br>
* <p>
* Only uses the first 9 values, all others are ignored.
*
* @param m
* the array to read the matrix values from
* @return this
*/
public Matrix3d set(double m[]) {
m00 = m[0];
m01 = m[1];
m02 = m[2];
m10 = m[3];
m11 = m[4];
m12 = m[5];
m20 = m[6];
m21 = m[7];
m22 = m[8];
return this;
}
/**
* Set the values in this matrix based on the supplied double array. The result looks like this:
* <p>
* 0, 3, 6<br>
* 1, 4, 7<br>
* 2, 5, 8<br>
* <p>
* Only uses the first 9 values, all others are ignored
*
* @param m
* the array to read the matrix values from
* @return this
*/
public Matrix3d set(float m[]) {
m00 = m[0];
m01 = m[1];
m02 = m[2];
m10 = m[3];
m11 = m[4];
m12 = m[5];
m20 = m[6];
m21 = m[7];
m22 = m[8];
return this;
}
public double determinant() {
return (m00 * m11 - m01 * m10) * m22
+ (m02 * m10 - m00 * m12) * m21
+ (m01 * m12 - m02 * m11) * m20;
}
/**
* Invert this matrix.
*
* @return this
*/
public Matrix3d invert() {
return invert(this);
}
public Matrix3d invert(Matrix3d dest) {
double a = Math.fma(m00, m11, -m01 * m10);
double b = Math.fma(m02, m10, -m00 * m12);
double c = Math.fma(m01, m12, -m02 * m11);
double d = Math.fma(a, m22, Math.fma(b, m21, c * m20));
double s = 1.0 / d;
double nm00 = Math.fma(m11, m22, -m21 * m12) * s;
double nm01 = Math.fma(m21, m02, -m01 * m22) * s;
double nm02 = c * s;
double nm10 = Math.fma(m20, m12, -m10 * m22) * s;
double nm11 = Math.fma(m00, m22, -m20 * m02) * s;
double nm12 = b * s;
double nm20 = Math.fma(m10, m21, -m20 * m11) * s;
double nm21 = Math.fma(m20, m01, -m00 * m21) * s;
double nm22 = a * s;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Transpose this matrix.
*
* @return this
*/
public Matrix3d transpose() {
return transpose(this);
}
public Matrix3d transpose(Matrix3d dest) {
dest.set(m00, m10, m20,
m01, m11, m21,
m02, m12, m22);
return dest;
}
/**
* Return a string representation of this matrix.
* <p>
* This method creates a new {@link DecimalFormat} on every invocation with the format string "<code>0.000E0;-</code>".
*
* @return the string representation
*/
public String toString() {
DecimalFormat formatter = new DecimalFormat(" 0.000E0;-");
String str = toString(formatter);
StringBuffer res = new StringBuffer();
int eIndex = Integer.MIN_VALUE;
for (int i = 0; i < str.length(); i++) {
char c = str.charAt(i);
if (c == 'E') {
eIndex = i;
} else if (c == ' ' && eIndex == i - 1) {
// workaround Java 1.4 DecimalFormat bug
res.append('+');
continue;
} else if (Character.isDigit(c) && eIndex == i - 1) {
res.append('+');
}
res.append(c);
}
return res.toString();
}
/**
* Return a string representation of this matrix by formatting the matrix elements with the given {@link NumberFormat}.
*
* @param formatter
* the {@link NumberFormat} used to format the matrix values with
* @return the string representation
*/
public String toString(NumberFormat formatter) {
return Runtime.format(m00, formatter) + " " + Runtime.format(m10, formatter) + " " + Runtime.format(m20, formatter) + "\n"
+ Runtime.format(m01, formatter) + " " + Runtime.format(m11, formatter) + " " + Runtime.format(m21, formatter) + "\n"
+ Runtime.format(m02, formatter) + " " + Runtime.format(m12, formatter) + " " + Runtime.format(m22, formatter) + "\n";
}
/**
* Get the current values of <code>this</code> matrix and store them into
* <code>dest</code>.
* <p>
* This is the reverse method of {@link #set(Matrix3dc)} and allows to obtain
* intermediate calculation results when chaining multiple transformations.
*
* @see #set(Matrix3dc)
*
* @param dest
* the destination matrix
* @return the passed in destination
*/
public Matrix3d get(Matrix3d dest) {
return dest.set(this);
}
public AxisAngle4f getRotation(AxisAngle4f dest) {
return dest.set(this);
}
public Quaternionf getUnnormalizedRotation(Quaternionf dest) {
return dest.setFromUnnormalized(this);
}
public Quaternionf getNormalizedRotation(Quaternionf dest) {
return dest.setFromNormalized(this);
}
public Quaterniond getUnnormalizedRotation(Quaterniond dest) {
return dest.setFromUnnormalized(this);
}
public Quaterniond getNormalizedRotation(Quaterniond dest) {
return dest.setFromNormalized(this);
}
//#ifdef __HAS_NIO__
public DoubleBuffer get(DoubleBuffer buffer) {
return get(buffer.position(), buffer);
}
public DoubleBuffer get(int index, DoubleBuffer buffer) {
MemUtil.INSTANCE.put(this, index, buffer);
return buffer;
}
public FloatBuffer get(FloatBuffer buffer) {
return get(buffer.position(), buffer);
}
public FloatBuffer get(int index, FloatBuffer buffer) {
MemUtil.INSTANCE.putf(this, index, buffer);
return buffer;
}
public ByteBuffer get(ByteBuffer buffer) {
return get(buffer.position(), buffer);
}
public ByteBuffer get(int index, ByteBuffer buffer) {
MemUtil.INSTANCE.put(this, index, buffer);
return buffer;
}
public ByteBuffer getFloats(ByteBuffer buffer) {
return getFloats(buffer.position(), buffer);
}
public ByteBuffer getFloats(int index, ByteBuffer buffer) {
MemUtil.INSTANCE.putf(this, index, buffer);
return buffer;
}
//#endif
//#ifdef __HAS_UNSAFE__
public Matrix3dc getToAddress(long address) {
if (Options.NO_UNSAFE)
throw new UnsupportedOperationException("Not supported when using joml.nounsafe");
MemUtil.MemUtilUnsafe.put(this, address);
return this;
}
//#endif
public double[] get(double[] arr, int offset) {
arr[offset+0] = m00;
arr[offset+1] = m01;
arr[offset+2] = m02;
arr[offset+3] = m10;
arr[offset+4] = m11;
arr[offset+5] = m12;
arr[offset+6] = m20;
arr[offset+7] = m21;
arr[offset+8] = m22;
return arr;
}
public double[] get(double[] arr) {
return get(arr, 0);
}
public float[] get(float[] arr, int offset) {
arr[offset+0] = (float)m00;
arr[offset+1] = (float)m01;
arr[offset+2] = (float)m02;
arr[offset+3] = (float)m10;
arr[offset+4] = (float)m11;
arr[offset+5] = (float)m12;
arr[offset+6] = (float)m20;
arr[offset+7] = (float)m21;
arr[offset+8] = (float)m22;
return arr;
}
public float[] get(float[] arr) {
return get(arr, 0);
}
//#ifdef __HAS_NIO__
/**
* Set the values of this matrix by reading 9 double values from the given {@link DoubleBuffer} in column-major order,
* starting at its current position.
* <p>
* The DoubleBuffer is expected to contain the values in column-major order.
* <p>
* The position of the DoubleBuffer will not be changed by this method.
*
* @param buffer
* the DoubleBuffer to read the matrix values from in column-major order
* @return this
*/
public Matrix3d set(DoubleBuffer buffer) {
MemUtil.INSTANCE.get(this, buffer.position(), buffer);
return this;
}
/**
* Set the values of this matrix by reading 9 float values from the given {@link FloatBuffer} in column-major order,
* starting at its current position.
* <p>
* The FloatBuffer is expected to contain the values in column-major order.
* <p>
* The position of the FloatBuffer will not be changed by this method.
*
* @param buffer
* the FloatBuffer to read the matrix values from in column-major order
* @return this
*/
public Matrix3d set(FloatBuffer buffer) {
MemUtil.INSTANCE.getf(this, buffer.position(), buffer);
return this;
}
/**
* Set the values of this matrix by reading 9 double values from the given {@link ByteBuffer} in column-major order,
* starting at its current position.
* <p>
* The ByteBuffer is expected to contain the values in column-major order.
* <p>
* The position of the ByteBuffer will not be changed by this method.
*
* @param buffer
* the ByteBuffer to read the matrix values from in column-major order
* @return this
*/
public Matrix3d set(ByteBuffer buffer) {
MemUtil.INSTANCE.get(this, buffer.position(), buffer);
return this;
}
/**
* Set the values of this matrix by reading 9 float values from the given {@link ByteBuffer} in column-major order,
* starting at its current position.
* <p>
* The ByteBuffer is expected to contain the values in column-major order.
* <p>
* The position of the ByteBuffer will not be changed by this method.
*
* @param buffer
* the ByteBuffer to read the matrix values from in column-major order
* @return this
*/
public Matrix3d setFloats(ByteBuffer buffer) {
MemUtil.INSTANCE.getf(this, buffer.position(), buffer);
return this;
}
//#endif
//#ifdef __HAS_UNSAFE__
/**
* Set the values of this matrix by reading 9 double values from off-heap memory in column-major order,
* starting at the given 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 memory address to read the matrix values from in column-major order
* @return this
*/
public Matrix3d setFromAddress(long address) {
if (Options.NO_UNSAFE)
throw new UnsupportedOperationException("Not supported when using joml.nounsafe");
MemUtil.MemUtilUnsafe.get(this, address);
return this;
}
//#endif
/**
* Set the three columns of this matrix to the supplied vectors, respectively.
*
* @param col0
* the first column
* @param col1
* the second column
* @param col2
* the third column
* @return this
*/
public Matrix3d set(Vector3dc col0,
Vector3dc col1,
Vector3dc col2) {
this.m00 = col0.x();
this.m01 = col0.y();
this.m02 = col0.z();
this.m10 = col1.x();
this.m11 = col1.y();
this.m12 = col1.z();
this.m20 = col2.x();
this.m21 = col2.y();
this.m22 = col2.z();
return this;
}
/**
* Set all the values within this matrix to 0.
*
* @return this
*/
public Matrix3d zero() {
m00 = 0.0;
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = 0.0;
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = 0.0;
return this;
}
/**
* Set this matrix to the identity.
*
* @return this
*/
public Matrix3d identity() {
m00 = 1.0;
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = 1.0;
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = 1.0;
return this;
}
/**
* Set this matrix to be a simple scale matrix, which scales all axes uniformly by the given factor.
* <p>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional scaling.
* <p>
* In order to post-multiply a scaling transformation directly to a
* matrix, use {@link #scale(double) scale()} instead.
*
* @see #scale(double)
*
* @param factor
* the scale factor in x, y and z
* @return this
*/
public Matrix3d scaling(double factor) {
m00 = factor;
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = factor;
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = factor;
return this;
}
/**
* Set this matrix to be a simple scale matrix.
*
* @param x
* the scale in x
* @param y
* the scale in y
* @param z
* the scale in z
* @return this
*/
public Matrix3d scaling(double x, double y, double z) {
m00 = x;
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = y;
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = z;
return this;
}
/**
* Set this matrix to be a simple scale matrix which scales the base axes by <code>xyz.x</code>, <code>xyz.y</code> and <code>xyz.z</code> respectively.
* <p>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional scaling.
* <p>
* In order to post-multiply a scaling transformation directly to a
* matrix use {@link #scale(Vector3dc) scale()} instead.
*
* @see #scale(Vector3dc)
*
* @param xyz
* the scale in x, y and z respectively
* @return this
*/
public Matrix3d scaling(Vector3dc xyz) {
m00 = xyz.x();
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = xyz.y();
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = xyz.z();
return this;
}
public Matrix3d scale(Vector3dc xyz, Matrix3d dest) {
return scale(xyz.x(), xyz.y(), xyz.z(), dest);
}
/**
* Apply scaling to this matrix by scaling the base axes by the given <code>xyz.x</code>,
* <code>xyz.y</code> and <code>xyz.z</code> factors, respectively.
* <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
* @return this
*/
public Matrix3d scale(Vector3dc xyz) {
return scale(xyz.x(), xyz.y(), xyz.z(), this);
}
public Matrix3d scale(double x, double y, double z, Matrix3d dest) {
// scale matrix elements:
// m00 = x, m11 = y, m22 = z
// all others = 0
dest.m00 = m00 * x;
dest.m01 = m01 * x;
dest.m02 = m02 * x;
dest.m10 = m10 * y;
dest.m11 = m11 * y;
dest.m12 = m12 * y;
dest.m20 = m20 * z;
dest.m21 = m21 * z;
dest.m22 = m22 * z;
return dest;
}
/**
* Apply scaling to this matrix by scaling the base axes by the given x,
* y and z factors.
* <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
* @return this
*/
public Matrix3d scale(double x, double y, double z) {
return scale(x, y, z, this);
}
public Matrix3d scale(double xyz, Matrix3d dest) {
return scale(xyz, xyz, xyz, dest);
}
/**
* Apply scaling to this matrix by uniformly scaling all base axes by the given <code>xyz</code> factor.
* <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)
*
* @param xyz
* the factor for all components
* @return this
*/
public Matrix3d scale(double xyz) {
return scale(xyz, xyz, xyz);
}
public Matrix3d scaleLocal(double x, double y, double z, Matrix3d dest) {
double nm00 = x * m00;
double nm01 = y * m01;
double nm02 = z * m02;
double nm10 = x * m10;
double nm11 = y * m11;
double nm12 = z * m12;
double nm20 = x * m20;
double nm21 = y * m21;
double nm22 = z * m22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply scaling to this matrix by scaling the base axes by the given x,
* y and z factors.
* <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
* @return this
*/
public Matrix3d scaleLocal(double x, double y, double z) {
return scaleLocal(x, y, z, this);
}
/**
* Set this matrix to a rotation matrix which rotates the given radians about a given axis.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to post-multiply a rotation transformation directly to a
* matrix, use {@link #rotate(double, Vector3dc) rotate()} instead.
*
* @see #rotate(double, Vector3dc)
*
* @param angle
* the angle in radians
* @param axis
* the axis to rotate about (needs to be {@link Vector3d#normalize() normalized})
* @return this
*/
public Matrix3d rotation(double angle, Vector3dc axis) {
return rotation(angle, axis.x(), axis.y(), axis.z());
}
/**
* Set this matrix to a rotation matrix which rotates the given radians about a given axis.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to post-multiply a rotation transformation directly to a
* matrix, use {@link #rotate(double, Vector3fc) rotate()} instead.
*
* @see #rotate(double, Vector3fc)
*
* @param angle
* the angle in radians
* @param axis
* the axis to rotate about (needs to be {@link Vector3f#normalize() normalized})
* @return this
*/
public Matrix3d rotation(double angle, Vector3fc axis) {
return rotation(angle, axis.x(), axis.y(), axis.z());
}
/**
* Set this matrix to a rotation transformation using the given {@link AxisAngle4f}.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to apply the rotation transformation to an existing transformation,
* use {@link #rotate(AxisAngle4f) rotate()} instead.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(AxisAngle4f)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @return this
*/
public Matrix3d rotation(AxisAngle4f axisAngle) {
return rotation(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* Set this matrix to a rotation transformation using the given {@link AxisAngle4d}.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to apply the rotation transformation to an existing transformation,
* use {@link #rotate(AxisAngle4d) rotate()} instead.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(AxisAngle4d)
*
* @param axisAngle
* the {@link AxisAngle4d} (needs to be {@link AxisAngle4d#normalize() normalized})
* @return this
*/
public Matrix3d rotation(AxisAngle4d axisAngle) {
return rotation(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* Set this matrix to a rotation matrix which rotates the given radians about a given axis.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to apply the rotation transformation to an existing transformation,
* use {@link #rotate(double, double, double, double) rotate()} instead.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotate(double, double, double, double)
*
* @param angle
* the angle in radians
* @param x
* the x-component of the rotation axis
* @param y
* the y-component of the rotation axis
* @param z
* the z-component of the rotation axis
* @return this
*/
public Matrix3d rotation(double angle, double x, double y, double z) {
double sin = Math.sin(angle);
double cos = Math.cosFromSin(sin, angle);
double C = 1.0 - cos;
double xy = x * y, xz = x * z, yz = y * z;
m00 = cos + x * x * C;
m10 = xy * C - z * sin;
m20 = xz * C + y * sin;
m01 = xy * C + z * sin;
m11 = cos + y * y * C;
m21 = yz * C - x * sin;
m02 = xz * C - y * sin;
m12 = yz * C + x * sin;
m22 = cos + z * z * C;
return this;
}
/**
* Set this matrix to a rotation transformation about the X axis.
* <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>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @return this
*/
public Matrix3d rotationX(double ang) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
m00 = 1.0;
m01 = 0.0;
m02 = 0.0;
m10 = 0.0;
m11 = cos;
m12 = sin;
m20 = 0.0;
m21 = -sin;
m22 = cos;
return this;
}
/**
* Set this matrix to a rotation transformation about the Y axis.
* <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>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @return this
*/
public Matrix3d rotationY(double ang) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
m00 = cos;
m01 = 0.0;
m02 = -sin;
m10 = 0.0;
m11 = 1.0;
m12 = 0.0;
m20 = sin;
m21 = 0.0;
m22 = cos;
return this;
}
/**
* Set this matrix to a rotation transformation about the Z axis.
* <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>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations">http://en.wikipedia.org</a>
*
* @param ang
* the angle in radians
* @return this
*/
public Matrix3d rotationZ(double ang) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
m00 = cos;
m01 = sin;
m02 = 0.0;
m10 = -sin;
m11 = cos;
m12 = 0.0;
m20 = 0.0;
m21 = 0.0;
m22 = 1.0;
return this;
}
/**
* Set this matrix to a 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.
* <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 is equivalent to calling: <code>rotationX(angleX).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
* @return this
*/
public Matrix3d rotationXYZ(double angleX, double angleY, double angleZ) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinX = -sinX;
double m_sinY = -sinY;
double m_sinZ = -sinZ;
// rotateX
double nm11 = cosX;
double nm12 = sinX;
double nm21 = m_sinX;
double nm22 = cosX;
// rotateY
double nm00 = cosY;
double nm01 = nm21 * m_sinY;
double nm02 = nm22 * m_sinY;
m20 = sinY;
m21 = nm21 * cosY;
m22 = nm22 * cosY;
// rotateZ
m00 = nm00 * cosZ;
m01 = nm01 * cosZ + nm11 * sinZ;
m02 = nm02 * cosZ + nm12 * sinZ;
m10 = nm00 * m_sinZ;
m11 = nm01 * m_sinZ + nm11 * cosZ;
m12 = nm02 * m_sinZ + nm12 * cosZ;
return this;
}
/**
* Set this matrix to a 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.
* <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 is equivalent to calling: <code>rotationZ(angleZ).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
* @return this
*/
public Matrix3d rotationZYX(double angleZ, double angleY, double angleX) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinZ = -sinZ;
double m_sinY = -sinY;
double m_sinX = -sinX;
// rotateZ
double nm00 = cosZ;
double nm01 = sinZ;
double nm10 = m_sinZ;
double nm11 = cosZ;
// rotateY
double nm20 = nm00 * sinY;
double nm21 = nm01 * sinY;
double nm22 = cosY;
m00 = nm00 * cosY;
m01 = nm01 * cosY;
m02 = m_sinY;
// rotateX
m10 = nm10 * cosX + nm20 * sinX;
m11 = nm11 * cosX + nm21 * sinX;
m12 = nm22 * sinX;
m20 = nm10 * m_sinX + nm20 * cosX;
m21 = nm11 * m_sinX + nm21 * cosX;
m22 = nm22 * cosX;
return this;
}
/**
* Set this matrix to a 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.
* <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 is equivalent to calling: <code>rotationY(angleY).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
* @return this
*/
public Matrix3d rotationYXZ(double angleY, double angleX, double angleZ) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinY = -sinY;
double m_sinX = -sinX;
double m_sinZ = -sinZ;
// rotateY
double nm00 = cosY;
double nm02 = m_sinY;
double nm20 = sinY;
double nm22 = cosY;
// rotateX
double nm10 = nm20 * sinX;
double nm11 = cosX;
double nm12 = nm22 * sinX;
m20 = nm20 * cosX;
m21 = m_sinX;
m22 = nm22 * cosX;
// rotateZ
m00 = nm00 * cosZ + nm10 * sinZ;
m01 = nm11 * sinZ;
m02 = nm02 * cosZ + nm12 * sinZ;
m10 = nm00 * m_sinZ + nm10 * cosZ;
m11 = nm11 * cosZ;
m12 = nm02 * m_sinZ + nm12 * cosZ;
return this;
}
/**
* Set this matrix to the rotation - and possibly scaling - transformation of the given {@link Quaterniondc}.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to apply the rotation transformation to an existing transformation,
* use {@link #rotate(Quaterniondc) rotate()} instead.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotate(Quaterniondc)
*
* @param quat
* the {@link Quaterniondc}
* @return this
*/
public Matrix3d rotation(Quaterniondc quat) {
double w2 = quat.w() * quat.w();
double x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y();
double z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw;
double xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz;
double yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz;
double xw = quat.x() * quat.w(), dxw = xw + xw;
m00 = w2 + x2 - z2 - y2;
m01 = dxy + dzw;
m02 = dxz - dyw;
m10 = -dzw + dxy;
m11 = y2 - z2 + w2 - x2;
m12 = dyz + dxw;
m20 = dyw + dxz;
m21 = dyz - dxw;
m22 = z2 - y2 - x2 + w2;
return this;
}
/**
* Set this matrix to the rotation - and possibly scaling - transformation of the given {@link Quaternionfc}.
* <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>
* The resulting matrix can be multiplied against another transformation
* matrix to obtain an additional rotation.
* <p>
* In order to apply the rotation transformation to an existing transformation,
* use {@link #rotate(Quaternionfc) rotate()} instead.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotate(Quaternionfc)
*
* @param quat
* the {@link Quaternionfc}
* @return this
*/
public Matrix3d rotation(Quaternionfc quat) {
double w2 = quat.w() * quat.w();
double x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y();
double z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw;
double xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz;
double yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz;
double xw = quat.x() * quat.w(), dxw = xw + xw;
m00 = w2 + x2 - z2 - y2;
m01 = dxy + dzw;
m02 = dxz - dyw;
m10 = -dzw + dxy;
m11 = y2 - z2 + w2 - x2;
m12 = dyz + dxw;
m20 = dyw + dxz;
m21 = dyz - dxw;
m22 = z2 - y2 - x2 + w2;
return this;
}
public Vector3d transform(Vector3d v) {
return v.mul(this);
}
public Vector3d transform(Vector3dc v, Vector3d dest) {
v.mul(this, dest);
return dest;
}
public Vector3f transform(Vector3f v) {
return v.mul(this);
}
public Vector3f transform(Vector3fc v, Vector3f dest) {
return v.mul(this, dest);
}
public Vector3d transform(double x, double y, double z, Vector3d dest) {
return dest.set(Math.fma(m00, x, Math.fma(m10, y, m20 * z)),
Math.fma(m01, x, Math.fma(m11, y, m21 * z)),
Math.fma(m02, x, Math.fma(m12, y, m22 * z)));
}
public Vector3d transformTranspose(Vector3d v) {
return v.mulTranspose(this);
}
public Vector3d transformTranspose(Vector3dc v, Vector3d dest) {
return v.mulTranspose(this, dest);
}
public Vector3d transformTranspose(double x, double y, double z, Vector3d dest) {
return dest.set(Math.fma(m00, x, Math.fma(m01, y, m02 * z)),
Math.fma(m10, x, Math.fma(m11, y, m12 * z)),
Math.fma(m20, x, Math.fma(m21, y, m22 * z)));
}
public void writeExternal(ObjectOutput out) throws IOException {
out.writeDouble(m00);
out.writeDouble(m01);
out.writeDouble(m02);
out.writeDouble(m10);
out.writeDouble(m11);
out.writeDouble(m12);
out.writeDouble(m20);
out.writeDouble(m21);
out.writeDouble(m22);
}
public void readExternal(ObjectInput in) throws IOException {
m00 = in.readDouble();
m01 = in.readDouble();
m02 = in.readDouble();
m10 = in.readDouble();
m11 = in.readDouble();
m12 = in.readDouble();
m20 = in.readDouble();
m21 = in.readDouble();
m22 = in.readDouble();
}
public Matrix3d rotateX(double ang, Matrix3d dest) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
double rm11 = cos;
double rm21 = -sin;
double rm12 = sin;
double rm22 = cos;
// add temporaries for dependent values
double nm10 = m10 * rm11 + m20 * rm12;
double nm11 = m11 * rm11 + m21 * rm12;
double nm12 = m12 * rm11 + m22 * rm12;
// set non-dependent values directly
dest.m20 = m10 * rm21 + m20 * rm22;
dest.m21 = m11 * rm21 + m21 * rm22;
dest.m22 = m12 * rm21 + m22 * rm22;
// set other values
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m00 = m00;
dest.m01 = m01;
dest.m02 = m02;
return dest;
}
/**
* Apply rotation about the X axis to this matrix by rotating the given amount of radians.
* <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
* @return this
*/
public Matrix3d rotateX(double ang) {
return rotateX(ang, this);
}
public Matrix3d rotateY(double ang, Matrix3d dest) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
double rm00 = cos;
double rm20 = sin;
double rm02 = -sin;
double rm22 = cos;
// add temporaries for dependent values
double nm00 = m00 * rm00 + m20 * rm02;
double nm01 = m01 * rm00 + m21 * rm02;
double nm02 = m02 * rm00 + m22 * rm02;
// set non-dependent values directly
dest.m20 = m00 * rm20 + m20 * rm22;
dest.m21 = m01 * rm20 + m21 * rm22;
dest.m22 = m02 * rm20 + m22 * rm22;
// set other values
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = m10;
dest.m11 = m11;
dest.m12 = m12;
return dest;
}
/**
* Apply rotation about the Y axis to this matrix by rotating the given amount of radians.
* <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
* @return this
*/
public Matrix3d rotateY(double ang) {
return rotateY(ang, this);
}
public Matrix3d rotateZ(double ang, Matrix3d dest) {
double sin, cos;
sin = Math.sin(ang);
cos = Math.cosFromSin(sin, ang);
double rm00 = cos;
double rm10 = -sin;
double rm01 = sin;
double rm11 = cos;
// add temporaries for dependent values
double nm00 = m00 * rm00 + m10 * rm01;
double nm01 = m01 * rm00 + m11 * rm01;
double nm02 = m02 * rm00 + m12 * rm01;
// set non-dependent values directly
dest.m10 = m00 * rm10 + m10 * rm11;
dest.m11 = m01 * rm10 + m11 * rm11;
dest.m12 = m02 * rm10 + m12 * rm11;
// set other values
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m20 = m20;
dest.m21 = m21;
dest.m22 = m22;
return dest;
}
/**
* Apply rotation about the Z axis to this matrix by rotating the given amount of radians.
* <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
* @return this
*/
public Matrix3d rotateZ(double ang) {
return rotateZ(ang, this);
}
/**
* 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.
* <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).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
* @return this
*/
public Matrix3d rotateXYZ(double angleX, double angleY, double angleZ) {
return rotateXYZ(angleX, angleY, angleZ, this);
}
public Matrix3d rotateXYZ(double angleX, double angleY, double angleZ, Matrix3d dest) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinX = -sinX;
double m_sinY = -sinY;
double m_sinZ = -sinZ;
// rotateX
double nm10 = m10 * cosX + m20 * sinX;
double nm11 = m11 * cosX + m21 * sinX;
double nm12 = m12 * cosX + m22 * sinX;
double nm20 = m10 * m_sinX + m20 * cosX;
double nm21 = m11 * m_sinX + m21 * cosX;
double nm22 = m12 * m_sinX + m22 * cosX;
// rotateY
double nm00 = m00 * cosY + nm20 * m_sinY;
double nm01 = m01 * cosY + nm21 * m_sinY;
double nm02 = m02 * cosY + nm22 * m_sinY;
dest.m20 = m00 * sinY + nm20 * cosY;
dest.m21 = m01 * sinY + nm21 * cosY;
dest.m22 = m02 * sinY + nm22 * cosY;
// rotateZ
dest.m00 = nm00 * cosZ + nm10 * sinZ;
dest.m01 = nm01 * cosZ + nm11 * sinZ;
dest.m02 = nm02 * cosZ + nm12 * sinZ;
dest.m10 = nm00 * m_sinZ + nm10 * cosZ;
dest.m11 = nm01 * m_sinZ + nm11 * cosZ;
dest.m12 = nm02 * m_sinZ + nm12 * cosZ;
return 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.
* <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).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
* @return this
*/
public Matrix3d rotateZYX(double angleZ, double angleY, double angleX) {
return rotateZYX(angleZ, angleY, angleX, this);
}
public Matrix3d rotateZYX(double angleZ, double angleY, double angleX, Matrix3d dest) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinZ = -sinZ;
double m_sinY = -sinY;
double m_sinX = -sinX;
// rotateZ
double nm00 = m00 * cosZ + m10 * sinZ;
double nm01 = m01 * cosZ + m11 * sinZ;
double nm02 = m02 * cosZ + m12 * sinZ;
double nm10 = m00 * m_sinZ + m10 * cosZ;
double nm11 = m01 * m_sinZ + m11 * cosZ;
double nm12 = m02 * m_sinZ + m12 * cosZ;
// rotateY
double nm20 = nm00 * sinY + m20 * cosY;
double nm21 = nm01 * sinY + m21 * cosY;
double nm22 = nm02 * sinY + m22 * cosY;
dest.m00 = nm00 * cosY + m20 * m_sinY;
dest.m01 = nm01 * cosY + m21 * m_sinY;
dest.m02 = nm02 * cosY + m22 * m_sinY;
// rotateX
dest.m10 = nm10 * cosX + nm20 * sinX;
dest.m11 = nm11 * cosX + nm21 * sinX;
dest.m12 = nm12 * cosX + nm22 * sinX;
dest.m20 = nm10 * m_sinX + nm20 * cosX;
dest.m21 = nm11 * m_sinX + nm21 * cosX;
dest.m22 = nm12 * m_sinX + nm22 * cosX;
return dest;
}
/**
* Apply rotation of <code>angles.y</code> radians about the Y axis, followed by a rotation of <code>angles.x</code> radians about the X axis and
* followed by a rotation of <code>angles.z</code> radians about the Z axis.
* <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(angles.y).rotateX(angles.x).rotateZ(angles.z)</code>
*
* @param angles
* the Euler angles
* @return this
*/
public Matrix3d rotateYXZ(Vector3d angles) {
return rotateYXZ(angles.y, angles.x, angles.z);
}
/**
* 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.
* <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).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
* @return this
*/
public Matrix3d rotateYXZ(double angleY, double angleX, double angleZ) {
return rotateYXZ(angleY, angleX, angleZ, this);
}
public Matrix3d rotateYXZ(double angleY, double angleX, double angleZ, Matrix3d dest) {
double sinX = Math.sin(angleX);
double cosX = Math.cosFromSin(sinX, angleX);
double sinY = Math.sin(angleY);
double cosY = Math.cosFromSin(sinY, angleY);
double sinZ = Math.sin(angleZ);
double cosZ = Math.cosFromSin(sinZ, angleZ);
double m_sinY = -sinY;
double m_sinX = -sinX;
double m_sinZ = -sinZ;
// rotateY
double nm20 = m00 * sinY + m20 * cosY;
double nm21 = m01 * sinY + m21 * cosY;
double nm22 = m02 * sinY + m22 * cosY;
double nm00 = m00 * cosY + m20 * m_sinY;
double nm01 = m01 * cosY + m21 * m_sinY;
double nm02 = m02 * cosY + m22 * m_sinY;
// rotateX
double nm10 = m10 * cosX + nm20 * sinX;
double nm11 = m11 * cosX + nm21 * sinX;
double nm12 = m12 * cosX + nm22 * sinX;
dest.m20 = m10 * m_sinX + nm20 * cosX;
dest.m21 = m11 * m_sinX + nm21 * cosX;
dest.m22 = m12 * m_sinX + nm22 * cosX;
// rotateZ
dest.m00 = nm00 * cosZ + nm10 * sinZ;
dest.m01 = nm01 * cosZ + nm11 * sinZ;
dest.m02 = nm02 * cosZ + nm12 * sinZ;
dest.m10 = nm00 * m_sinZ + nm10 * cosZ;
dest.m11 = nm01 * m_sinZ + nm11 * cosZ;
dest.m12 = nm02 * m_sinZ + nm12 * cosZ;
return dest;
}
/**
* Apply rotation to this matrix by rotating the given amount of radians
* about the given axis specified as x, y and z components.
* <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
* @return this
*/
public Matrix3d rotate(double ang, double x, double y, double z) {
return rotate(ang, x, y, z, this);
}
public Matrix3d rotate(double ang, double x, double y, double z, Matrix3d dest) {
double s = Math.sin(ang);
double c = Math.cosFromSin(s, ang);
double C = 1.0 - c;
// rotation matrix elements:
// m30, m31, m32, m03, m13, m23 = 0
double xx = x * x, xy = x * y, xz = x * z;
double yy = y * y, yz = y * z;
double zz = z * z;
double rm00 = xx * C + c;
double rm01 = xy * C + z * s;
double rm02 = xz * C - y * s;
double rm10 = xy * C - z * s;
double rm11 = yy * C + c;
double rm12 = yz * C + x * s;
double rm20 = xz * C + y * s;
double rm21 = yz * C - x * s;
double rm22 = zz * C + c;
// add temporaries for dependent values
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
// set non-dependent values directly
dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
// set other values
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
return 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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotation(double, double, double, double) rotation()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotation(double, double, double, double)
*
* @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
*/
public Matrix3d rotateLocal(double ang, double x, double y, double z, Matrix3d dest) {
double s = Math.sin(ang);
double c = Math.cosFromSin(s, ang);
double C = 1.0 - c;
double xx = x * x, xy = x * y, xz = x * z;
double yy = y * y, yz = y * z;
double zz = z * z;
double lm00 = xx * C + c;
double lm01 = xy * C + z * s;
double lm02 = xz * C - y * s;
double lm10 = xy * C - z * s;
double lm11 = yy * C + c;
double lm12 = yz * C + x * s;
double lm20 = xz * C + y * s;
double lm21 = yz * C - x * s;
double lm22 = zz * C + c;
double nm00 = lm00 * m00 + lm10 * m01 + lm20 * m02;
double nm01 = lm01 * m00 + lm11 * m01 + lm21 * m02;
double nm02 = lm02 * m00 + lm12 * m01 + lm22 * m02;
double nm10 = lm00 * m10 + lm10 * m11 + lm20 * m12;
double nm11 = lm01 * m10 + lm11 * m11 + lm21 * m12;
double nm12 = lm02 * m10 + lm12 * m11 + lm22 * m12;
double nm20 = lm00 * m20 + lm10 * m21 + lm20 * m22;
double nm21 = lm01 * m20 + lm11 * m21 + lm21 * m22;
double nm22 = lm02 * m20 + lm12 * m21 + lm22 * m22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians
* about the specified <code>(x, y, z)</code> axis.
* <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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotation(double, double, double, double) rotation()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotation(double, double, double, double)
*
* @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
* @return this
*/
public Matrix3d rotateLocal(double ang, double x, double y, double z) {
return rotateLocal(ang, x, y, z, this);
}
/**
* 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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationX(double) rotationX()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationX(double)
*
* @param ang
* the angle in radians to rotate about the X axis
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateLocalX(double ang, Matrix3d dest) {
double sin = Math.sin(ang);
double cos = Math.cosFromSin(sin, ang);
double nm01 = cos * m01 - sin * m02;
double nm02 = sin * m01 + cos * m02;
double nm11 = cos * m11 - sin * m12;
double nm12 = sin * m11 + cos * m12;
double nm21 = cos * m21 - sin * m22;
double nm22 = sin * m21 + cos * m22;
dest.m00 = m00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = m10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = m20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians about the X axis.
* <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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationX(double) rotationX()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationX(double)
*
* @param ang
* the angle in radians to rotate about the X axis
* @return this
*/
public Matrix3d rotateLocalX(double ang) {
return rotateLocalX(ang, this);
}
/**
* 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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationY(double) rotationY()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationY(double)
*
* @param ang
* the angle in radians to rotate about the Y axis
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateLocalY(double ang, Matrix3d dest) {
double sin = Math.sin(ang);
double cos = Math.cosFromSin(sin, ang);
double nm00 = cos * m00 + sin * m02;
double nm02 = -sin * m00 + cos * m02;
double nm10 = cos * m10 + sin * m12;
double nm12 = -sin * m10 + cos * m12;
double nm20 = cos * m20 + sin * m22;
double nm22 = -sin * m20 + cos * m22;
dest.m00 = nm00;
dest.m01 = m01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = m11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = m21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians about the Y axis.
* <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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationY(double) rotationY()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationY(double)
*
* @param ang
* the angle in radians to rotate about the Y axis
* @return this
*/
public Matrix3d rotateLocalY(double ang) {
return rotateLocalY(ang, this);
}
/**
* 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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationZ(double) rotationZ()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationZ(double)
*
* @param ang
* the angle in radians to rotate about the Z axis
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateLocalZ(double ang, Matrix3d dest) {
double sin = Math.sin(ang);
double cos = Math.cosFromSin(sin, ang);
double nm00 = cos * m00 - sin * m01;
double nm01 = sin * m00 + cos * m01;
double nm10 = cos * m10 - sin * m11;
double nm11 = sin * m10 + cos * m11;
double nm20 = cos * m20 - sin * m21;
double nm21 = sin * m20 + cos * m21;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = m02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = m12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = m22;
return dest;
}
/**
* Pre-multiply a rotation to this matrix by rotating the given amount of radians about the Z axis.
* <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>
* In order to set the matrix to a rotation matrix without pre-multiplying the rotation
* transformation, use {@link #rotationZ(double) rotationY()}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle">http://en.wikipedia.org</a>
*
* @see #rotationY(double)
*
* @param ang
* the angle in radians to rotate about the Z axis
* @return this
*/
public Matrix3d rotateLocalZ(double ang) {
return rotateLocalZ(ang, this);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without pre-multiplying,
* use {@link #rotation(Quaterniondc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaterniondc)
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateLocal(Quaterniondc quat, Matrix3d dest) {
double w2 = quat.w() * quat.w(), x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y(), z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw, xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz, yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz, xw = quat.x() * quat.w(), dxw = xw + xw;
double lm00 = w2 + x2 - z2 - y2;
double lm01 = dxy + dzw;
double lm02 = dxz - dyw;
double lm10 = dxy - dzw;
double lm11 = y2 - z2 + w2 - x2;
double lm12 = dyz + dxw;
double lm20 = dyw + dxz;
double lm21 = dyz - dxw;
double lm22 = z2 - y2 - x2 + w2;
double nm00 = lm00 * m00 + lm10 * m01 + lm20 * m02;
double nm01 = lm01 * m00 + lm11 * m01 + lm21 * m02;
double nm02 = lm02 * m00 + lm12 * m01 + lm22 * m02;
double nm10 = lm00 * m10 + lm10 * m11 + lm20 * m12;
double nm11 = lm01 * m10 + lm11 * m11 + lm21 * m12;
double nm12 = lm02 * m10 + lm12 * m11 + lm22 * m12;
double nm20 = lm00 * m20 + lm10 * m21 + lm20 * m22;
double nm21 = lm01 * m20 + lm11 * m21 + lm21 * m22;
double nm22 = lm02 * m20 + lm12 * m21 + lm22 * m22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without pre-multiplying,
* use {@link #rotation(Quaterniondc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaterniondc)
*
* @param quat
* the {@link Quaterniondc}
* @return this
*/
public Matrix3d rotateLocal(Quaterniondc quat) {
return rotateLocal(quat, this);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without pre-multiplying,
* use {@link #rotation(Quaternionfc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaternionfc)
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateLocal(Quaternionfc quat, Matrix3d dest) {
double w2 = quat.w() * quat.w(), x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y(), z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw, xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz, yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz, xw = quat.x() * quat.w(), dxw = xw + xw;
double lm00 = w2 + x2 - z2 - y2;
double lm01 = dxy + dzw;
double lm02 = dxz - dyw;
double lm10 = dxy - dzw;
double lm11 = y2 - z2 + w2 - x2;
double lm12 = dyz + dxw;
double lm20 = dyw + dxz;
double lm21 = dyz - dxw;
double lm22 = z2 - y2 - x2 + w2;
double nm00 = lm00 * m00 + lm10 * m01 + lm20 * m02;
double nm01 = lm01 * m00 + lm11 * m01 + lm21 * m02;
double nm02 = lm02 * m00 + lm12 * m01 + lm22 * m02;
double nm10 = lm00 * m10 + lm10 * m11 + lm20 * m12;
double nm11 = lm01 * m10 + lm11 * m11 + lm21 * m12;
double nm12 = lm02 * m10 + lm12 * m11 + lm22 * m12;
double nm20 = lm00 * m20 + lm10 * m21 + lm20 * m22;
double nm21 = lm01 * m20 + lm11 * m21 + lm21 * m22;
double nm22 = lm02 * m20 + lm12 * m21 + lm22 * m22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Pre-multiply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without pre-multiplying,
* use {@link #rotation(Quaternionfc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaternionfc)
*
* @param quat
* the {@link Quaternionfc}
* @return this
*/
public Matrix3d rotateLocal(Quaternionfc quat) {
return rotateLocal(quat, this);
}
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaterniondc} to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(Quaterniondc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaterniondc)
*
* @param quat
* the {@link Quaterniondc}
* @return this
*/
public Matrix3d rotate(Quaterniondc quat) {
return rotate(quat, this);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(Quaterniondc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaterniondc)
*
* @param quat
* the {@link Quaterniondc}
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotate(Quaterniondc quat, Matrix3d dest) {
double w2 = quat.w() * quat.w(), x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y(), z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw, xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz, yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz, xw = quat.x() * quat.w(), dxw = xw + xw;
double rm00 = w2 + x2 - z2 - y2;
double rm01 = dxy + dzw;
double rm02 = dxz - dyw;
double rm10 = dxy - dzw;
double rm11 = y2 - z2 + w2 - x2;
double rm12 = dyz + dxw;
double rm20 = dyw + dxz;
double rm21 = dyz - dxw;
double rm22 = z2 - y2 - x2 + w2;
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
return dest;
}
/**
* Apply the rotation - and possibly scaling - transformation of the given {@link Quaternionfc} to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(Quaternionfc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaternionfc)
*
* @param quat
* the {@link Quaternionfc}
* @return this
*/
public Matrix3d rotate(Quaternionfc quat) {
return rotate(quat, this);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(Quaternionfc)}.
* <p>
* Reference: <a href="http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion">http://en.wikipedia.org</a>
*
* @see #rotation(Quaternionfc)
*
* @param quat
* the {@link Quaternionfc}
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotate(Quaternionfc quat, Matrix3d dest) {
double w2 = quat.w() * quat.w(), x2 = quat.x() * quat.x();
double y2 = quat.y() * quat.y(), z2 = quat.z() * quat.z();
double zw = quat.z() * quat.w(), dzw = zw + zw, xy = quat.x() * quat.y(), dxy = xy + xy;
double xz = quat.x() * quat.z(), dxz = xz + xz, yw = quat.y() * quat.w(), dyw = yw + yw;
double yz = quat.y() * quat.z(), dyz = yz + yz, xw = quat.x() * quat.w(), dxw = xw + xw;
double rm00 = w2 + x2 - z2 - y2;
double rm01 = dxy + dzw;
double rm02 = dxz - dyw;
double rm10 = dxy - dzw;
double rm11 = y2 - z2 + w2 - x2;
double rm12 = dyz + dxw;
double rm20 = dyw + dxz;
double rm21 = dyz - dxw;
double rm22 = z2 - y2 - x2 + w2;
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
return dest;
}
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4f}, to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(AxisAngle4f)}.
* <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)
* @see #rotation(AxisAngle4f)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @return this
*/
public Matrix3d rotate(AxisAngle4f axisAngle) {
return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(AxisAngle4f)}.
* <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)
* @see #rotation(AxisAngle4f)
*
* @param axisAngle
* the {@link AxisAngle4f} (needs to be {@link AxisAngle4f#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotate(AxisAngle4f axisAngle, Matrix3d dest) {
return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z, dest);
}
/**
* Apply a rotation transformation, rotating about the given {@link AxisAngle4d}, to this matrix.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(AxisAngle4d)}.
* <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)
* @see #rotation(AxisAngle4d)
*
* @param axisAngle
* the {@link AxisAngle4d} (needs to be {@link AxisAngle4d#normalize() normalized})
* @return this
*/
public Matrix3d rotate(AxisAngle4d axisAngle) {
return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(AxisAngle4d)}.
* <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)
* @see #rotation(AxisAngle4d)
*
* @param axisAngle
* the {@link AxisAngle4d} (needs to be {@link AxisAngle4d#normalize() normalized})
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotate(AxisAngle4d axisAngle, Matrix3d dest) {
return rotate(axisAngle.angle, axisAngle.x, axisAngle.y, axisAngle.z, dest);
}
/**
* Apply a rotation transformation, rotating the given radians about the specified axis, to this matrix.
* <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 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(double, Vector3dc)}.
* <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)
* @see #rotation(double, Vector3dc)
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis (needs to be {@link Vector3d#normalize() normalized})
* @return this
*/
public Matrix3d rotate(double angle, Vector3dc axis) {
return rotate(angle, axis.x(), axis.y(), axis.z());
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(double, Vector3dc)}.
* <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)
* @see #rotation(double, Vector3dc)
*
* @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
*/
public Matrix3d rotate(double angle, Vector3dc axis, Matrix3d dest) {
return rotate(angle, axis.x(), axis.y(), axis.z(), dest);
}
/**
* Apply a rotation transformation, rotating the given radians about the specified axis, to this matrix.
* <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 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(double, Vector3fc)}.
* <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)
* @see #rotation(double, Vector3fc)
*
* @param angle
* the angle in radians
* @param axis
* the rotation axis (needs to be {@link Vector3f#normalize() normalized})
* @return this
*/
public Matrix3d rotate(double angle, Vector3fc axis) {
return rotate(angle, axis.x(), axis.y(), axis.z());
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying,
* use {@link #rotation(double, Vector3fc)}.
* <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)
* @see #rotation(double, Vector3fc)
*
* @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
*/
public Matrix3d rotate(double angle, Vector3fc axis, Matrix3d dest) {
return rotate(angle, axis.x(), axis.y(), axis.z(), dest);
}
public Vector3d getRow(int row, Vector3d dest) throws IndexOutOfBoundsException {
switch (row) {
case 0:
return dest.set(m00, m10, m20);
case 1:
return dest.set(m01, m11, m21);
case 2:
return dest.set(m02, m12, m22);
default:
throw new IndexOutOfBoundsException();
}
}
/**
* Set 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 src
* the row components to set
* @return this
* @throws IndexOutOfBoundsException if <code>row</code> is not in <code>[0..2]</code>
*/
public Matrix3d setRow(int row, Vector3dc src) throws IndexOutOfBoundsException {
return setRow(row, src.x(), src.y(), src.z());
}
/**
* Set the row at the given <code>row</code> index, starting with <code>0</code>.
*
* @param row
* the column index in <code>[0..2]</code>
* @param x
* the first element in the row
* @param y
* the second element in the row
* @param z
* the third element in the row
* @return this
* @throws IndexOutOfBoundsException if <code>row</code> is not in <code>[0..2]</code>
*/
public Matrix3d setRow(int row, double x, double y, double z) throws IndexOutOfBoundsException {
switch (row) {
case 0:
this.m00 = x;
this.m10 = y;
this.m20 = z;
break;
case 1:
this.m01 = x;
this.m11 = y;
this.m21 = z;
break;
case 2:
this.m02 = x;
this.m12 = y;
this.m22 = z;
break;
default:
throw new IndexOutOfBoundsException();
}
return this;
}
public Vector3d getColumn(int column, Vector3d dest) throws IndexOutOfBoundsException {
switch (column) {
case 0:
return dest.set(m00, m01, m02);
case 1:
return dest.set(m10, m11, m12);
case 2:
return dest.set(m20, m21, m22);
default:
throw new IndexOutOfBoundsException();
}
}
/**
* Set 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 src
* the column components to set
* @return this
* @throws IndexOutOfBoundsException if <code>column</code> is not in <code>[0..2]</code>
*/
public Matrix3d setColumn(int column, Vector3dc src) throws IndexOutOfBoundsException {
return setColumn(column, src.x(), src.y(), src.z());
}
/**
* Set 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 x
* the first element in the column
* @param y
* the second element in the column
* @param z
* the third element in the column
* @return this
* @throws IndexOutOfBoundsException if <code>column</code> is not in <code>[0..2]</code>
*/
public Matrix3d setColumn(int column, double x, double y, double z) throws IndexOutOfBoundsException {
switch (column) {
case 0:
this.m00 = x;
this.m01 = y;
this.m02 = z;
break;
case 1:
this.m10 = x;
this.m11 = y;
this.m12 = z;
break;
case 2:
this.m20 = x;
this.m21 = y;
this.m22 = z;
break;
default:
throw new IndexOutOfBoundsException();
}
return this;
}
public double get(int column, int row) {
return MemUtil.INSTANCE.get(this, column, row);
}
/**
* Set the matrix element at the given column and row to the specified value.
*
* @param column
* the colum index in <code>[0..2]</code>
* @param row
* the row index in <code>[0..2]</code>
* @param value
* the value
* @return this
*/
public Matrix3d set(int column, int row, double value) {
return MemUtil.INSTANCE.set(this, column, row, value);
}
public double getRowColumn(int row, int column) {
return MemUtil.INSTANCE.get(this, column, row);
}
/**
* Set the matrix element at the given row and column to the specified value.
*
* @param row
* the row index in <code>[0..2]</code>
* @param column
* the colum index in <code>[0..2]</code>
* @param value
* the value
* @return this
*/
public Matrix3d setRowColumn(int row, int column, double value) {
return MemUtil.INSTANCE.set(this, column, row, value);
}
/**
* Set <code>this</code> matrix to its own normal matrix.
* <p>
* The normal matrix of <code>m</code> is the transpose of the inverse of <code>m</code>.
* <p>
* Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors,
* then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
* In this case, use {@link #set(Matrix3dc)} to set a given Matrix3f to this matrix.
*
* @see #set(Matrix3dc)
*
* @return this
*/
public Matrix3d normal() {
return normal(this);
}
/**
* 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>.
* <p>
* Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors,
* then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
* In this case, use {@link #set(Matrix3dc)} to set a given Matrix3d to this matrix.
*
* @see #set(Matrix3dc)
*
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d normal(Matrix3d dest) {
double m00m11 = m00 * m11;
double m01m10 = m01 * m10;
double m02m10 = m02 * m10;
double m00m12 = m00 * m12;
double m01m12 = m01 * m12;
double m02m11 = m02 * m11;
double det = (m00m11 - m01m10) * m22 + (m02m10 - m00m12) * m21 + (m01m12 - m02m11) * m20;
double s = 1.0 / det;
/* Invert and transpose in one go */
double nm00 = (m11 * m22 - m21 * m12) * s;
double nm01 = (m20 * m12 - m10 * m22) * s;
double nm02 = (m10 * m21 - m20 * m11) * s;
double nm10 = (m21 * m02 - m01 * m22) * s;
double nm11 = (m00 * m22 - m20 * m02) * s;
double nm12 = (m20 * m01 - m00 * m21) * s;
double nm20 = (m01m12 - m02m11) * s;
double nm21 = (m02m10 - m00m12) * s;
double nm22 = (m00m11 - m01m10) * s;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Compute the cofactor matrix of <code>this</code>.
* <p>
* The cofactor matrix can be used instead of {@link #normal()} to transform normals
* when the orientation of the normals with respect to the surface should be preserved.
*
* @return this
*/
public Matrix3d cofactor() {
return cofactor(this);
}
/**
* 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
*/
public Matrix3d cofactor(Matrix3d dest) {
double nm00 = m11 * m22 - m21 * m12;
double nm01 = m20 * m12 - m10 * m22;
double nm02 = m10 * m21 - m20 * m11;
double nm10 = m21 * m02 - m01 * m22;
double nm11 = m00 * m22 - m20 * m02;
double nm12 = m20 * m01 - m00 * m21;
double nm20 = m01 * m12 - m11 * m02;
double nm21 = m02 * m10 - m12 * m00;
double nm22 = m00 * m11 - m10 * m01;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
dest.m20 = nm20;
dest.m21 = nm21;
dest.m22 = nm22;
return dest;
}
/**
* Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</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>
* In order to set the matrix to a lookalong transformation without post-multiplying it,
* use {@link #setLookAlong(Vector3dc, Vector3dc) setLookAlong()}.
*
* @see #lookAlong(double, double, double, double, double, double)
* @see #setLookAlong(Vector3dc, Vector3dc)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @return this
*/
public Matrix3d lookAlong(Vector3dc dir, Vector3dc up) {
return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), this);
}
/**
* 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>
* In order to set the matrix to a lookalong transformation without post-multiplying it,
* use {@link #setLookAlong(Vector3dc, Vector3dc) setLookAlong()}.
*
* @see #lookAlong(double, double, double, double, double, double)
* @see #setLookAlong(Vector3dc, Vector3dc)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d lookAlong(Vector3dc dir, Vector3dc up, Matrix3d dest) {
return lookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z(), 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>
* In order to set the matrix to a lookalong transformation without post-multiplying it,
* use {@link #setLookAlong(double, double, double, double, double, double) setLookAlong()}
*
* @see #setLookAlong(double, double, double, double, double, double)
*
* @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
*/
public Matrix3d lookAlong(double dirX, double dirY, double dirZ,
double upX, double upY, double upZ, Matrix3d dest) {
// Normalize direction
double invDirLength = Math.invsqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
dirX *= -invDirLength;
dirY *= -invDirLength;
dirZ *= -invDirLength;
// left = up x direction
double leftX, leftY, leftZ;
leftX = upY * dirZ - upZ * dirY;
leftY = upZ * dirX - upX * dirZ;
leftZ = upX * dirY - upY * dirX;
// normalize left
double invLeftLength = Math.invsqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
leftX *= invLeftLength;
leftY *= invLeftLength;
leftZ *= invLeftLength;
// up = direction x left
double upnX = dirY * leftZ - dirZ * leftY;
double upnY = dirZ * leftX - dirX * leftZ;
double upnZ = dirX * leftY - dirY * leftX;
// calculate right matrix elements
double rm00 = leftX;
double rm01 = upnX;
double rm02 = dirX;
double rm10 = leftY;
double rm11 = upnY;
double rm12 = dirY;
double rm20 = leftZ;
double rm21 = upnZ;
double rm22 = dirZ;
// perform optimized matrix multiplication
// introduce temporaries for dependent results
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
// set the rest of the matrix elements
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
return dest;
}
/**
* Apply a rotation transformation to this matrix to make <code>-z</code> point along <code>dir</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>
* In order to set the matrix to a lookalong transformation without post-multiplying it,
* use {@link #setLookAlong(double, double, double, double, double, double) setLookAlong()}
*
* @see #setLookAlong(double, double, double, double, double, double)
*
* @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
* @return this
*/
public Matrix3d lookAlong(double dirX, double dirY, double dirZ,
double upX, double upY, double upZ) {
return lookAlong(dirX, dirY, dirZ, upX, upY, upZ, this);
}
/**
* Set this matrix to a rotation transformation to make <code>-z</code>
* point along <code>dir</code>.
* <p>
* In order to apply the lookalong transformation to any previous existing transformation,
* use {@link #lookAlong(Vector3dc, Vector3dc)}.
*
* @see #setLookAlong(Vector3dc, Vector3dc)
* @see #lookAlong(Vector3dc, Vector3dc)
*
* @param dir
* the direction in space to look along
* @param up
* the direction of 'up'
* @return this
*/
public Matrix3d setLookAlong(Vector3dc dir, Vector3dc up) {
return setLookAlong(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z());
}
/**
* Set this matrix to a rotation transformation to make <code>-z</code>
* point along <code>dir</code>.
* <p>
* In order to apply the lookalong transformation to any previous existing transformation,
* use {@link #lookAlong(double, double, double, double, double, double) lookAlong()}
*
* @see #setLookAlong(double, double, double, double, double, double)
* @see #lookAlong(double, double, double, double, double, double)
*
* @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
* @return this
*/
public Matrix3d setLookAlong(double dirX, double dirY, double dirZ,
double upX, double upY, double upZ) {
// Normalize direction
double invDirLength = Math.invsqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
dirX *= -invDirLength;
dirY *= -invDirLength;
dirZ *= -invDirLength;
// left = up x direction
double leftX, leftY, leftZ;
leftX = upY * dirZ - upZ * dirY;
leftY = upZ * dirX - upX * dirZ;
leftZ = upX * dirY - upY * dirX;
// normalize left
double invLeftLength = Math.invsqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
leftX *= invLeftLength;
leftY *= invLeftLength;
leftZ *= invLeftLength;
// up = direction x left
double upnX = dirY * leftZ - dirZ * leftY;
double upnY = dirZ * leftX - dirX * leftZ;
double upnZ = dirX * leftY - dirY * leftX;
m00 = leftX;
m01 = upnX;
m02 = dirX;
m10 = leftY;
m11 = upnY;
m12 = dirY;
m20 = leftZ;
m21 = upnZ;
m22 = dirZ;
return this;
}
public Vector3d getScale(Vector3d dest) {
dest.x = Math.sqrt(m00 * m00 + m01 * m01 + m02 * m02);
dest.y = Math.sqrt(m10 * m10 + m11 * m11 + m12 * m12);
dest.z = Math.sqrt(m20 * m20 + m21 * m21 + m22 * m22);
return dest;
}
public Vector3d positiveZ(Vector3d dir) {
dir.x = m10 * m21 - m11 * m20;
dir.y = m20 * m01 - m21 * m00;
dir.z = m00 * m11 - m01 * m10;
return dir.normalize(dir);
}
public Vector3d normalizedPositiveZ(Vector3d dir) {
dir.x = m02;
dir.y = m12;
dir.z = m22;
return dir;
}
public Vector3d positiveX(Vector3d dir) {
dir.x = m11 * m22 - m12 * m21;
dir.y = m02 * m21 - m01 * m22;
dir.z = m01 * m12 - m02 * m11;
return dir.normalize(dir);
}
public Vector3d normalizedPositiveX(Vector3d dir) {
dir.x = m00;
dir.y = m10;
dir.z = m20;
return dir;
}
public Vector3d positiveY(Vector3d dir) {
dir.x = m12 * m20 - m10 * m22;
dir.y = m00 * m22 - m02 * m20;
dir.z = m02 * m10 - m00 * m12;
return dir.normalize(dir);
}
public Vector3d normalizedPositiveY(Vector3d dir) {
dir.x = m01;
dir.y = m11;
dir.z = m21;
return dir;
}
public int hashCode() {
final int prime = 31;
int result = 1;
long temp;
temp = Double.doubleToLongBits(m00);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m01);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m02);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m10);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m11);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m12);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m20);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m21);
result = prime * result + (int) (temp ^ (temp >>> 32));
temp = Double.doubleToLongBits(m22);
result = prime * result + (int) (temp ^ (temp >>> 32));
return result;
}
public boolean equals(Object obj) {
if (this == obj)
return true;
if (obj == null)
return false;
if (getClass() != obj.getClass())
return false;
Matrix3d other = (Matrix3d) obj;
if (Double.doubleToLongBits(m00) != Double.doubleToLongBits(other.m00))
return false;
if (Double.doubleToLongBits(m01) != Double.doubleToLongBits(other.m01))
return false;
if (Double.doubleToLongBits(m02) != Double.doubleToLongBits(other.m02))
return false;
if (Double.doubleToLongBits(m10) != Double.doubleToLongBits(other.m10))
return false;
if (Double.doubleToLongBits(m11) != Double.doubleToLongBits(other.m11))
return false;
if (Double.doubleToLongBits(m12) != Double.doubleToLongBits(other.m12))
return false;
if (Double.doubleToLongBits(m20) != Double.doubleToLongBits(other.m20))
return false;
if (Double.doubleToLongBits(m21) != Double.doubleToLongBits(other.m21))
return false;
if (Double.doubleToLongBits(m22) != Double.doubleToLongBits(other.m22))
return false;
return true;
}
public boolean equals(Matrix3dc m, double delta) {
if (this == m)
return true;
if (m == null)
return false;
if (!(m instanceof Matrix3d))
return false;
if (!Runtime.equals(m00, m.m00(), delta))
return false;
if (!Runtime.equals(m01, m.m01(), delta))
return false;
if (!Runtime.equals(m02, m.m02(), delta))
return false;
if (!Runtime.equals(m10, m.m10(), delta))
return false;
if (!Runtime.equals(m11, m.m11(), delta))
return false;
if (!Runtime.equals(m12, m.m12(), delta))
return false;
if (!Runtime.equals(m20, m.m20(), delta))
return false;
if (!Runtime.equals(m21, m.m21(), delta))
return false;
if (!Runtime.equals(m22, m.m22(), delta))
return false;
return true;
}
/**
* Exchange the values of <code>this</code> matrix with the given <code>other</code> matrix.
*
* @param other
* the other matrix to exchange the values with
* @return this
*/
public Matrix3d swap(Matrix3d other) {
double tmp;
tmp = m00; m00 = other.m00; other.m00 = tmp;
tmp = m01; m01 = other.m01; other.m01 = tmp;
tmp = m02; m02 = other.m02; other.m02 = tmp;
tmp = m10; m10 = other.m10; other.m10 = tmp;
tmp = m11; m11 = other.m11; other.m11 = tmp;
tmp = m12; m12 = other.m12; other.m12 = tmp;
tmp = m20; m20 = other.m20; other.m20 = tmp;
tmp = m21; m21 = other.m21; other.m21 = tmp;
tmp = m22; m22 = other.m22; other.m22 = tmp;
return this;
}
/**
* Component-wise add <code>this</code> and <code>other</code>.
*
* @param other
* the other addend
* @return this
*/
public Matrix3d add(Matrix3dc other) {
return add(other, this);
}
public Matrix3d add(Matrix3dc other, Matrix3d dest) {
dest.m00 = m00 + other.m00();
dest.m01 = m01 + other.m01();
dest.m02 = m02 + other.m02();
dest.m10 = m10 + other.m10();
dest.m11 = m11 + other.m11();
dest.m12 = m12 + other.m12();
dest.m20 = m20 + other.m20();
dest.m21 = m21 + other.m21();
dest.m22 = m22 + other.m22();
return dest;
}
/**
* Component-wise subtract <code>subtrahend</code> from <code>this</code>.
*
* @param subtrahend
* the subtrahend
* @return this
*/
public Matrix3d sub(Matrix3dc subtrahend) {
return sub(subtrahend, this);
}
public Matrix3d sub(Matrix3dc subtrahend, Matrix3d dest) {
dest.m00 = m00 - subtrahend.m00();
dest.m01 = m01 - subtrahend.m01();
dest.m02 = m02 - subtrahend.m02();
dest.m10 = m10 - subtrahend.m10();
dest.m11 = m11 - subtrahend.m11();
dest.m12 = m12 - subtrahend.m12();
dest.m20 = m20 - subtrahend.m20();
dest.m21 = m21 - subtrahend.m21();
dest.m22 = m22 - subtrahend.m22();
return dest;
}
/**
* Component-wise multiply <code>this</code> by <code>other</code>.
*
* @param other
* the other matrix
* @return this
*/
public Matrix3d mulComponentWise(Matrix3dc other) {
return mulComponentWise(other, this);
}
public Matrix3d mulComponentWise(Matrix3dc other, Matrix3d dest) {
dest.m00 = m00 * other.m00();
dest.m01 = m01 * other.m01();
dest.m02 = m02 * other.m02();
dest.m10 = m10 * other.m10();
dest.m11 = m11 * other.m11();
dest.m12 = m12 * other.m12();
dest.m20 = m20 * other.m20();
dest.m21 = m21 * other.m21();
dest.m22 = m22 * other.m22();
return dest;
}
/**
* Set this matrix to a skew-symmetric matrix using the following layout:
* <pre>
* 0, a, -b
* -a, 0, c
* b, -c, 0
* </pre>
*
* Reference: <a href="https://en.wikipedia.org/wiki/Skew-symmetric_matrix">https://en.wikipedia.org</a>
*
* @param a
* the value used for the matrix elements m01 and m10
* @param b
* the value used for the matrix elements m02 and m20
* @param c
* the value used for the matrix elements m12 and m21
* @return this
*/
public Matrix3d setSkewSymmetric(double a, double b, double c) {
m00 = m11 = m22 = 0;
m01 = -a;
m02 = b;
m10 = a;
m12 = -c;
m20 = -b;
m21 = c;
return this;
}
/**
* Linearly interpolate <code>this</code> and <code>other</code> using the given interpolation factor <code>t</code>
* and store the result in <code>this</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
* @return this
*/
public Matrix3d lerp(Matrix3dc other, double t) {
return lerp(other, t, this);
}
public Matrix3d lerp(Matrix3dc other, double t, Matrix3d dest) {
dest.m00 = Math.fma(other.m00() - m00, t, m00);
dest.m01 = Math.fma(other.m01() - m01, t, m01);
dest.m02 = Math.fma(other.m02() - m02, t, m02);
dest.m10 = Math.fma(other.m10() - m10, t, m10);
dest.m11 = Math.fma(other.m11() - m11, t, m11);
dest.m12 = Math.fma(other.m12() - m12, t, m12);
dest.m20 = Math.fma(other.m20() - m20, t, m20);
dest.m21 = Math.fma(other.m21() - m21, t, m21);
dest.m22 = Math.fma(other.m22() - m22, t, m22);
return 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>
* In order to set the matrix to a rotation transformation without post-multiplying it,
* use {@link #rotationTowards(Vector3dc, Vector3dc) rotationTowards()}.
* <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)
* @see #rotationTowards(Vector3dc, Vector3dc)
*
* @param direction
* the direction to rotate towards
* @param up
* the model's up vector
* @param dest
* will hold the result
* @return dest
*/
public Matrix3d rotateTowards(Vector3dc direction, Vector3dc up, Matrix3d dest) {
return rotateTowards(direction.x(), direction.y(), direction.z(), up.x(), up.y(), up.z(), 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>.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying it,
* use {@link #rotationTowards(Vector3dc, Vector3dc) rotationTowards()}.
* <p>
* This method is equivalent to calling: <code>mul(new Matrix3d().lookAlong(new Vector3d(dir).negate(), up).invert())</code>
*
* @see #rotateTowards(double, double, double, double, double, double)
* @see #rotationTowards(Vector3dc, Vector3dc)
*
* @param direction
* the direction to orient towards
* @param up
* the up vector
* @return this
*/
public Matrix3d rotateTowards(Vector3dc direction, Vector3dc up) {
return rotateTowards(direction.x(), direction.y(), direction.z(), up.x(), up.y(), up.z(), this);
}
/**
* 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>.
* <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>
* In order to set the matrix to a rotation transformation without post-multiplying it,
* use {@link #rotationTowards(double, double, double, double, double, double) rotationTowards()}.
* <p>
* This method is equivalent to calling: <code>mul(new Matrix3d().lookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert())</code>
*
* @see #rotateTowards(Vector3dc, Vector3dc)
* @see #rotationTowards(double, double, double, double, double, double)
*
* @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
* @return this
*/
public Matrix3d rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ) {
return rotateTowards(dirX, dirY, dirZ, upX, upY, upZ, this);
}
/**
* 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>
* In order to set the matrix to a rotation transformation without post-multiplying it,
* use {@link #rotationTowards(double, double, double, double, double, double) rotationTowards()}.
* <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)
* @see #rotationTowards(double, double, double, double, double, double)
*
* @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
*/
public Matrix3d rotateTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ, Matrix3d dest) {
// Normalize direction
double invDirLength = Math.invsqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
double ndirX = dirX * invDirLength;
double ndirY = dirY * invDirLength;
double ndirZ = dirZ * invDirLength;
// left = up x direction
double leftX, leftY, leftZ;
leftX = upY * ndirZ - upZ * ndirY;
leftY = upZ * ndirX - upX * ndirZ;
leftZ = upX * ndirY - upY * ndirX;
// normalize left
double invLeftLength = Math.invsqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
leftX *= invLeftLength;
leftY *= invLeftLength;
leftZ *= invLeftLength;
// up = direction x left
double upnX = ndirY * leftZ - ndirZ * leftY;
double upnY = ndirZ * leftX - ndirX * leftZ;
double upnZ = ndirX * leftY - ndirY * leftX;
double rm00 = leftX;
double rm01 = leftY;
double rm02 = leftZ;
double rm10 = upnX;
double rm11 = upnY;
double rm12 = upnZ;
double rm20 = ndirX;
double rm21 = ndirY;
double rm22 = ndirZ;
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
dest.m20 = m00 * rm20 + m10 * rm21 + m20 * rm22;
dest.m21 = m01 * rm20 + m11 * rm21 + m21 * rm22;
dest.m22 = m02 * rm20 + m12 * rm21 + m22 * rm22;
dest.m00 = nm00;
dest.m01 = nm01;
dest.m02 = nm02;
dest.m10 = nm10;
dest.m11 = nm11;
dest.m12 = nm12;
return dest;
}
/**
* Set this matrix to a model transformation for a right-handed coordinate system,
* that aligns the local <code>-z</code> axis with <code>center - eye</code>.
* <p>
* In order to apply the rotation transformation to a previous existing transformation,
* use {@link #rotateTowards(double, double, double, double, double, double) rotateTowards}.
* <p>
* This method is equivalent to calling: <code>setLookAlong(new Vector3d(dir).negate(), up).invert()</code>
*
* @see #rotationTowards(Vector3dc, Vector3dc)
* @see #rotateTowards(double, double, double, double, double, double)
*
* @param dir
* the direction to orient the local -z axis towards
* @param up
* the up vector
* @return this
*/
public Matrix3d rotationTowards(Vector3dc dir, Vector3dc up) {
return rotationTowards(dir.x(), dir.y(), dir.z(), up.x(), up.y(), up.z());
}
/**
* Set this matrix to a model transformation for a right-handed coordinate system,
* that aligns the local <code>-z</code> axis with <code>center - eye</code>.
* <p>
* In order to apply the rotation transformation to a previous existing transformation,
* use {@link #rotateTowards(double, double, double, double, double, double) rotateTowards}.
* <p>
* This method is equivalent to calling: <code>setLookAlong(-dirX, -dirY, -dirZ, upX, upY, upZ).invert()</code>
*
* @see #rotateTowards(Vector3dc, Vector3dc)
* @see #rotationTowards(double, double, double, double, double, double)
*
* @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
* @return this
*/
public Matrix3d rotationTowards(double dirX, double dirY, double dirZ, double upX, double upY, double upZ) {
// Normalize direction
double invDirLength = Math.invsqrt(dirX * dirX + dirY * dirY + dirZ * dirZ);
double ndirX = dirX * invDirLength;
double ndirY = dirY * invDirLength;
double ndirZ = dirZ * invDirLength;
// left = up x direction
double leftX, leftY, leftZ;
leftX = upY * ndirZ - upZ * ndirY;
leftY = upZ * ndirX - upX * ndirZ;
leftZ = upX * ndirY - upY * ndirX;
// normalize left
double invLeftLength = Math.invsqrt(leftX * leftX + leftY * leftY + leftZ * leftZ);
leftX *= invLeftLength;
leftY *= invLeftLength;
leftZ *= invLeftLength;
// up = direction x left
double upnX = ndirY * leftZ - ndirZ * leftY;
double upnY = ndirZ * leftX - ndirX * leftZ;
double upnZ = ndirX * leftY - ndirY * leftX;
this.m00 = leftX;
this.m01 = leftY;
this.m02 = leftZ;
this.m10 = upnX;
this.m11 = upnY;
this.m12 = upnZ;
this.m20 = ndirX;
this.m21 = ndirY;
this.m22 = ndirZ;
return this;
}
/**
* 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>
* 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 Matrix3d#rotateZYX(double, double, double)} 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 = ...; // <- matrix only representing rotation
* Matrix3d n = new Matrix3d();
* 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
*/
public Vector3d getEulerAnglesZYX(Vector3d dest) {
dest.x = (float) Math.atan2(m12, m22);
dest.y = (float) Math.atan2(-m02, Math.sqrt(m12 * m12 + m22 * m22));
dest.z = (float) Math.atan2(m01, m00);
return dest;
}
/**
* Apply an oblique projection transformation to this matrix with the given values for <code>a</code> and
* <code>b</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
* @return this
*/
public Matrix3d obliqueZ(double a, double b) {
this.m20 = m00 * a + m10 * b + m20;
this.m21 = m01 * a + m11 * b + m21;
this.m22 = m02 * a + m12 * b + m22;
return this;
}
/**
* 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
*/
public Matrix3d obliqueZ(double a, double b, Matrix3d dest) {
dest.m00 = m00;
dest.m01 = m01;
dest.m02 = m02;
dest.m10 = m10;
dest.m11 = m11;
dest.m12 = m12;
dest.m20 = m00 * a + m10 * b + m20;
dest.m21 = m01 * a + m11 * b + m21;
dest.m22 = m02 * a + m12 * b + m22;
return dest;
}
public Matrix3d reflect(double nx, double ny, double nz, Matrix3d dest) {
double da = nx + nx, db = ny + ny, dc = nz + nz;
double rm00 = 1.0 - da * nx;
double rm01 = -da * ny;
double rm02 = -da * nz;
double rm10 = -db * nx;
double rm11 = 1.0 - db * ny;
double rm12 = -db * nz;
double rm20 = -dc * nx;
double rm21 = -dc * ny;
double rm22 = 1.0 - dc * nz;
double nm00 = m00 * rm00 + m10 * rm01 + m20 * rm02;
double nm01 = m01 * rm00 + m11 * rm01 + m21 * rm02;
double nm02 = m02 * rm00 + m12 * rm01 + m22 * rm02;
double nm10 = m00 * rm10 + m10 * rm11 + m20 * rm12;
double nm11 = m01 * rm10 + m11 * rm11 + m21 * rm12;
double nm12 = m02 * rm10 + m12 * rm11 + m22 * rm12;
return dest
._m20(m00 * rm20 + m10 * rm21 + m20 * rm22)
._m21(m01 * rm20 + m11 * rm21 + m21 * rm22)
._m22(m02 * rm20 + m12 * rm21 + m22 * rm22)
._m00(nm00)
._m01(nm01)
._m02(nm02)
._m10(nm10)
._m11(nm11)
._m12(nm12);
}
/**
* Apply a mirror/reflection transformation to this matrix that reflects through the given plane
* specified via the plane normal.
* <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
* @return this
*/
public Matrix3d reflect(double nx, double ny, double nz) {
return reflect(nx, ny, nz, this);
}
/**
* Apply a mirror/reflection transformation to this matrix that reflects through the given plane
* specified via the plane normal.
* <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
* @return this
*/
public Matrix3d reflect(Vector3dc normal) {
return reflect(normal.x(), normal.y(), normal.z());
}
/**
* Apply a mirror/reflection transformation to this matrix that reflects about a plane
* specified via the plane orientation.
* <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
* @return this
*/
public Matrix3d reflect(Quaterniondc orientation) {
return reflect(orientation, this);
}
public Matrix3d reflect(Quaterniondc orientation, Matrix3d dest) {
double num1 = orientation.x() + orientation.x();
double num2 = orientation.y() + orientation.y();
double num3 = orientation.z() + orientation.z();
double normalX = (double) (orientation.x() * num3 + orientation.w() * num2);
double normalY = (double) (orientation.y() * num3 - orientation.w() * num1);
double normalZ = (double) (1.0 - (orientation.x() * num1 + orientation.y() * num2));
return reflect(normalX, normalY, normalZ, dest);
}
public Matrix3d reflect(Vector3dc normal, Matrix3d dest) {
return reflect(normal.x(), normal.y(), normal.z(), dest);
}
/**
* Set this matrix to a mirror/reflection transformation that reflects through the given plane
* specified via the plane normal.
*
* @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
* @return this
*/
public Matrix3d reflection(double nx, double ny, double nz) {
double da = nx + nx, db = ny + ny, dc = nz + nz;
this._m00(1.0 - da * nx);
this._m01(-da * ny);
this._m02(-da * nz);
this._m10(-db * nx);
this._m11(1.0 - db * ny);
this._m12(-db * nz);
this._m20(-dc * nx);
this._m21(-dc * ny);
this._m22(1.0 - dc * nz);
return this;
}
/**
* Set this matrix to a mirror/reflection transformation that reflects through the given plane
* specified via the plane normal.
*
* @param normal
* the plane normal
* @return this
*/
public Matrix3d reflection(Vector3dc normal) {
return reflection(normal.x(), normal.y(), normal.z());
}
/**
* Set this matrix to a mirror/reflection transformation that reflects through a plane
* specified via the plane orientation.
* <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>, offset by the given <code>point</code>.
*
* @param orientation
* the plane orientation
* @return this
*/
public Matrix3d reflection(Quaterniondc orientation) {
double num1 = orientation.x() + orientation.x();
double num2 = orientation.y() + orientation.y();
double num3 = orientation.z() + orientation.z();
double normalX = orientation.x() * num3 + orientation.w() * num2;
double normalY = orientation.y() * num3 - orientation.w() * num1;
double normalZ = 1.0 - (orientation.x() * num1 + orientation.y() * num2);
return reflection(normalX, normalY, normalZ);
}
public boolean isFinite() {
return Math.isFinite(m00) && Math.isFinite(m01) && Math.isFinite(m02) &&
Math.isFinite(m10) && Math.isFinite(m11) && Math.isFinite(m12) &&
Math.isFinite(m20) && Math.isFinite(m21) && Math.isFinite(m22);
}
}
