/*
* $RCSfile: Matrix3d.java,v $
*
* Copyright 1996-2008 Sun Microsystems, Inc. All Rights Reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Sun designates this
* particular file as subject to the "Classpath" exception as provided
* by Sun in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
* CA 95054 USA or visit www.sun.com if you need additional information or
* have any questions.
*
* $Revision: 1.8 $
* $Date: 2008/02/28 20:18:50 $
* $State: Exp $
*/
package javax.vecmath;
import java.lang.Math;
/**
* A double precision floating point 3 by 3 matrix. Primarily to support 3D
* rotations.
*
*/
public class Matrix3d implements java.io.Serializable, Cloneable {
// Compatible with 1.1
static final long serialVersionUID = 6837536777072402710L;
/**
* The first matrix element in the first row.
*/
public double m00;
/**
* The second matrix element in the first row.
*/
public double m01;
/**
* The third matrix element in the first row.
*/
public double m02;
/**
* The first matrix element in the second row.
*/
public double m10;
/**
* The second matrix element in the second row.
*/
public double m11;
/**
* The third matrix element in the second row.
*/
public double m12;
/**
* The first matrix element in the third row.
*/
public double m20;
/**
* The second matrix element in the third row.
*/
public double m21;
/**
* The third matrix element in the third row.
*/
public double m22;
// double[] tmp = new double[9]; // scratch matrix
// double[] tmp_rot = new double[9]; // scratch matrix
// double[] tmp_scale = new double[3]; // scratch matrix
private static final double EPS = 1.110223024E-16;
/**
* Constructs and initializes a Matrix3d from the specified nine values.
*
* @param m00
* the [0][0] element
* @param m01
* the [0][1] element
* @param m02
* the [0][2] element
* @param m10
* the [1][0] element
* @param m11
* the [1][1] element
* @param m12
* the [1][2] element
* @param m20
* the [2][0] element
* @param m21
* the [2][1] element
* @param m22
* the [2][2] element
*/
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;
}
/**
* Constructs and initializes a Matrix3d from the specified nine- element
* array.
*
* @param v
* the array of length 9 containing in order
*/
public Matrix3d(double[] v) {
this.m00 = v[0];
this.m01 = v[1];
this.m02 = v[2];
this.m10 = v[3];
this.m11 = v[4];
this.m12 = v[5];
this.m20 = v[6];
this.m21 = v[7];
this.m22 = v[8];
}
/**
* Constructs a new matrix with the same values as the Matrix3d parameter.
*
* @param m1
* the source matrix
*/
public Matrix3d(Matrix3d m1) {
this.m00 = m1.m00;
this.m01 = m1.m01;
this.m02 = m1.m02;
this.m10 = m1.m10;
this.m11 = m1.m11;
this.m12 = m1.m12;
this.m20 = m1.m20;
this.m21 = m1.m21;
this.m22 = m1.m22;
}
/**
* Constructs a new matrix with the same values as the Matrix3f parameter.
*
* @param m1
* the source matrix
*/
public Matrix3d(Matrix3f m1) {
this.m00 = m1.m00;
this.m01 = m1.m01;
this.m02 = m1.m02;
this.m10 = m1.m10;
this.m11 = m1.m11;
this.m12 = m1.m12;
this.m20 = m1.m20;
this.m21 = m1.m21;
this.m22 = m1.m22;
}
/**
* Constructs and initializes a Matrix3d to all zeros.
*/
public Matrix3d() {
this.m00 = 0.0;
this.m01 = 0.0;
this.m02 = 0.0;
this.m10 = 0.0;
this.m11 = 0.0;
this.m12 = 0.0;
this.m20 = 0.0;
this.m21 = 0.0;
this.m22 = 0.0;
}
/**
* Returns a string that contains the values of this Matrix3d.
*
* @return the String representation
*/
public String toString() {
return this.m00 + ", " + this.m01 + ", " + this.m02 + "\n" + this.m10
+ ", " + this.m11 + ", " + this.m12 + "\n" + this.m20 + ", " + this.m21
+ ", " + this.m22 + "\n";
}
/**
* Sets this Matrix3d to identity.
*/
public final void setIdentity() {
this.m00 = 1.0;
this.m01 = 0.0;
this.m02 = 0.0;
this.m10 = 0.0;
this.m11 = 1.0;
this.m12 = 0.0;
this.m20 = 0.0;
this.m21 = 0.0;
this.m22 = 1.0;
}
/**
* Sets the scale component of the current matrix by factoring out the current
* scale (by doing an SVD) and multiplying by the new scale.
*
* @param scale
* the new scale amount
*/
public final void setScale(double scale) {
double[] tmp_rot = new double[9]; // scratch matrix
double[] tmp_scale = new double[3]; // scratch matrix
getScaleRotate(tmp_scale, tmp_rot);
this.m00 = tmp_rot[0] * scale;
this.m01 = tmp_rot[1] * scale;
this.m02 = tmp_rot[2] * scale;
this.m10 = tmp_rot[3] * scale;
this.m11 = tmp_rot[4] * scale;
this.m12 = tmp_rot[5] * scale;
this.m20 = tmp_rot[6] * scale;
this.m21 = tmp_rot[7] * scale;
this.m22 = tmp_rot[8] * scale;
}
/**
* Sets the specified element of this matrix3f to the value provided.
*
* @param row
* the row number to be modified (zero indexed)
* @param column
* the column number to be modified (zero indexed)
* @param value
* the new value
*/
public final void setElement(int row, int column, double value) {
switch (row) {
case 0:
switch (column) {
case 0:
this.m00 = value;
break;
case 1:
this.m01 = value;
break;
case 2:
this.m02 = value;
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d0"));
}
break;
case 1:
switch (column) {
case 0:
this.m10 = value;
break;
case 1:
this.m11 = value;
break;
case 2:
this.m12 = value;
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d0"));
}
break;
case 2:
switch (column) {
case 0:
this.m20 = value;
break;
case 1:
this.m21 = value;
break;
case 2:
this.m22 = value;
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d0"));
}
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d0"));
}
}
/**
* Retrieves the value at the specified row and column of the specified
* matrix.
*
* @param row
* the row number to be retrieved (zero indexed)
* @param column
* the column number to be retrieved (zero indexed)
* @return the value at the indexed element.
*/
public final double getElement(int row, int column) {
switch (row) {
case 0:
switch (column) {
case 0:
return (this.m00);
case 1:
return (this.m01);
case 2:
return (this.m02);
default:
break;
}
break;
case 1:
switch (column) {
case 0:
return (this.m10);
case 1:
return (this.m11);
case 2:
return (this.m12);
default:
break;
}
break;
case 2:
switch (column) {
case 0:
return (this.m20);
case 1:
return (this.m21);
case 2:
return (this.m22);
default:
break;
}
break;
default:
break;
}
throw new ArrayIndexOutOfBoundsException(VecMathI18N.getString("Matrix3d1"));
}
/**
* Copies the matrix values in the specified row into the vector parameter.
*
* @param row
* the matrix row
* @param v
* the vector into which the matrix row values will be copied
*/
public final void getRow(int row, Vector3d v) {
if (row == 0) {
v.x = m00;
v.y = m01;
v.z = m02;
} else if (row == 1) {
v.x = m10;
v.y = m11;
v.z = m12;
} else if (row == 2) {
v.x = m20;
v.y = m21;
v.z = m22;
} else {
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d2"));
}
}
/**
* Copies the matrix values in the specified row into the array parameter.
*
* @param row
* the matrix row
* @param v
* the array into which the matrix row values will be copied
*/
public final void getRow(int row, double v[]) {
if (row == 0) {
v[0] = m00;
v[1] = m01;
v[2] = m02;
} else if (row == 1) {
v[0] = m10;
v[1] = m11;
v[2] = m12;
} else if (row == 2) {
v[0] = m20;
v[1] = m21;
v[2] = m22;
} else {
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d2"));
}
}
/**
* Copies the matrix values in the specified column into the vector parameter.
*
* @param column
* the matrix column
* @param v
* the vector into which the matrix row values will be copied
*/
public final void getColumn(int column, Vector3d v) {
if (column == 0) {
v.x = m00;
v.y = m10;
v.z = m20;
} else if (column == 1) {
v.x = m01;
v.y = m11;
v.z = m21;
} else if (column == 2) {
v.x = m02;
v.y = m12;
v.z = m22;
} else {
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d4"));
}
}
/**
* Copies the matrix values in the specified column into the array parameter.
*
* @param column
* the matrix column
* @param v
* the array into which the matrix row values will be copied
*/
public final void getColumn(int column, double v[]) {
if (column == 0) {
v[0] = m00;
v[1] = m10;
v[2] = m20;
} else if (column == 1) {
v[0] = m01;
v[1] = m11;
v[2] = m21;
} else if (column == 2) {
v[0] = m02;
v[1] = m12;
v[2] = m22;
} else {
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d4"));
}
}
/**
* Sets the specified row of this matrix3d to the 4 values provided.
*
* @param row
* the row number to be modified (zero indexed)
* @param x
* the first column element
* @param y
* the second column element
* @param z
* the third column element
*/
public final void setRow(int row, double x, double y, double z) {
switch (row) {
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 ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d6"));
}
}
/**
* Sets the specified row of this matrix3d to the Vector provided.
*
* @param row
* the row number to be modified (zero indexed)
* @param v
* the replacement row
*/
public final void setRow(int row, Vector3d v) {
switch (row) {
case 0:
this.m00 = v.x;
this.m01 = v.y;
this.m02 = v.z;
break;
case 1:
this.m10 = v.x;
this.m11 = v.y;
this.m12 = v.z;
break;
case 2:
this.m20 = v.x;
this.m21 = v.y;
this.m22 = v.z;
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d6"));
}
}
/**
* Sets the specified row of this matrix3d to the three values provided.
*
* @param row
* the row number to be modified (zero indexed)
* @param v
* the replacement row
*/
public final void setRow(int row, double v[]) {
switch (row) {
case 0:
this.m00 = v[0];
this.m01 = v[1];
this.m02 = v[2];
break;
case 1:
this.m10 = v[0];
this.m11 = v[1];
this.m12 = v[2];
break;
case 2:
this.m20 = v[0];
this.m21 = v[1];
this.m22 = v[2];
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d6"));
}
}
/**
* Sets the specified column of this matrix3d to the three values provided.
*
* @param column
* the column number to be modified (zero indexed)
* @param x
* the first row element
* @param y
* the second row element
* @param z
* the third row element
*/
public final void setColumn(int column, double x, double y, double z) {
switch (column) {
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 ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d9"));
}
}
/**
* Sets the specified column of this matrix3d to the vector provided.
*
* @param column
* the column number to be modified (zero indexed)
* @param v
* the replacement column
*/
public final void setColumn(int column, Vector3d v) {
switch (column) {
case 0:
this.m00 = v.x;
this.m10 = v.y;
this.m20 = v.z;
break;
case 1:
this.m01 = v.x;
this.m11 = v.y;
this.m21 = v.z;
break;
case 2:
this.m02 = v.x;
this.m12 = v.y;
this.m22 = v.z;
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d9"));
}
}
/**
* Sets the specified column of this matrix3d to the three values provided.
*
* @param column
* the column number to be modified (zero indexed)
* @param v
* the replacement column
*/
public final void setColumn(int column, double v[]) {
switch (column) {
case 0:
this.m00 = v[0];
this.m10 = v[1];
this.m20 = v[2];
break;
case 1:
this.m01 = v[0];
this.m11 = v[1];
this.m21 = v[2];
break;
case 2:
this.m02 = v[0];
this.m12 = v[1];
this.m22 = v[2];
break;
default:
throw new ArrayIndexOutOfBoundsException(VecMathI18N
.getString("Matrix3d9"));
}
}
/**
* Performs an SVD normalization of this matrix to calculate and return the
* uniform scale factor. If the matrix has non-uniform scale factors, the
* largest of the x, y, and z scale factors will be returned. This matrix is
* not modified.
*
* @return the scale factor of this matrix
*/
public final double getScale() {
double[] tmp_scale = new double[3]; // scratch matrix
double[] tmp_rot = new double[9]; // scratch matrix
getScaleRotate(tmp_scale, tmp_rot);
return (max3(tmp_scale));
}
/**
* Adds a scalar to each component of this matrix.
*
* @param scalar
* the scalar adder
*/
public final void add(double scalar) {
m00 += scalar;
m01 += scalar;
m02 += scalar;
m10 += scalar;
m11 += scalar;
m12 += scalar;
m20 += scalar;
m21 += scalar;
m22 += scalar;
}
/**
* Adds a scalar to each component of the matrix m1 and places the result into
* this. Matrix m1 is not modified.
*
* @param scalar
* the scalar adder
* @param m1
* the original matrix values
*/
public final void add(double scalar, Matrix3d m1) {
this.m00 = m1.m00 + scalar;
this.m01 = m1.m01 + scalar;
this.m02 = m1.m02 + scalar;
this.m10 = m1.m10 + scalar;
this.m11 = m1.m11 + scalar;
this.m12 = m1.m12 + scalar;
this.m20 = m1.m20 + scalar;
this.m21 = m1.m21 + scalar;
this.m22 = m1.m22 + scalar;
}
/**
* Sets the value of this matrix to the matrix sum of matrices m1 and m2.
*
* @param m1
* the first matrix
* @param m2
* the second matrix
*/
public final void add(Matrix3d m1, Matrix3d m2) {
this.m00 = m1.m00 + m2.m00;
this.m01 = m1.m01 + m2.m01;
this.m02 = m1.m02 + m2.m02;
this.m10 = m1.m10 + m2.m10;
this.m11 = m1.m11 + m2.m11;
this.m12 = m1.m12 + m2.m12;
this.m20 = m1.m20 + m2.m20;
this.m21 = m1.m21 + m2.m21;
this.m22 = m1.m22 + m2.m22;
}
/**
* Sets the value of this matrix to the sum of itself and matrix m1.
*
* @param m1
* the other matrix
*/
public final void add(Matrix3d m1) {
this.m00 += m1.m00;
this.m01 += m1.m01;
this.m02 += m1.m02;
this.m10 += m1.m10;
this.m11 += m1.m11;
this.m12 += m1.m12;
this.m20 += m1.m20;
this.m21 += m1.m21;
this.m22 += m1.m22;
}
/**
* Sets the value of this matrix to the matrix difference of matrices m1 and
* m2.
*
* @param m1
* the first matrix
* @param m2
* the second matrix
*/
public final void sub(Matrix3d m1, Matrix3d m2) {
this.m00 = m1.m00 - m2.m00;
this.m01 = m1.m01 - m2.m01;
this.m02 = m1.m02 - m2.m02;
this.m10 = m1.m10 - m2.m10;
this.m11 = m1.m11 - m2.m11;
this.m12 = m1.m12 - m2.m12;
this.m20 = m1.m20 - m2.m20;
this.m21 = m1.m21 - m2.m21;
this.m22 = m1.m22 - m2.m22;
}
/**
* Sets the value of this matrix to the matrix difference of itself and matrix
* m1 (this = this - m1).
*
* @param m1
* the other matrix
*/
public final void sub(Matrix3d m1) {
this.m00 -= m1.m00;
this.m01 -= m1.m01;
this.m02 -= m1.m02;
this.m10 -= m1.m10;
this.m11 -= m1.m11;
this.m12 -= m1.m12;
this.m20 -= m1.m20;
this.m21 -= m1.m21;
this.m22 -= m1.m22;
}
/**
* Sets the value of this matrix to its transpose.
*/
public final void transpose() {
double temp;
temp = this.m10;
this.m10 = this.m01;
this.m01 = temp;
temp = this.m20;
this.m20 = this.m02;
this.m02 = temp;
temp = this.m21;
this.m21 = this.m12;
this.m12 = temp;
}
/**
* Sets the value of this matrix to the transpose of the argument matrix.
*
* @param m1
* the matrix to be transposed
*/
public final void transpose(Matrix3d m1) {
if (this != m1) {
this.m00 = m1.m00;
this.m01 = m1.m10;
this.m02 = m1.m20;
this.m10 = m1.m01;
this.m11 = m1.m11;
this.m12 = m1.m21;
this.m20 = m1.m02;
this.m21 = m1.m12;
this.m22 = m1.m22;
} else
this.transpose();
}
/**
* Sets the value of this matrix to the matrix conversion of the double
* precision quaternion argument.
*
* @param q1
* the quaternion to be converted
*/
public final void set(Quat4d q1) {
this.m00 = (1.0 - 2.0 * q1.y * q1.y - 2.0 * q1.z * q1.z);
this.m10 = (2.0 * (q1.x * q1.y + q1.w * q1.z));
this.m20 = (2.0 * (q1.x * q1.z - q1.w * q1.y));
this.m01 = (2.0 * (q1.x * q1.y - q1.w * q1.z));
this.m11 = (1.0 - 2.0 * q1.x * q1.x - 2.0 * q1.z * q1.z);
this.m21 = (2.0 * (q1.y * q1.z + q1.w * q1.x));
this.m02 = (2.0 * (q1.x * q1.z + q1.w * q1.y));
this.m12 = (2.0 * (q1.y * q1.z - q1.w * q1.x));
this.m22 = (1.0 - 2.0 * q1.x * q1.x - 2.0 * q1.y * q1.y);
}
/**
* Sets the value of this matrix to the matrix conversion of the double
* precision axis and angle argument.
*
* @param a1
* the axis and angle to be converted
*/
public final void set(AxisAngle4d a1) {
double mag = Math.sqrt(a1.x * a1.x + a1.y * a1.y + a1.z * a1.z);
if (mag < EPS) {
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;
} else {
mag = 1.0 / mag;
double ax = a1.x * mag;
double ay = a1.y * mag;
double az = a1.z * mag;
double sinTheta = Math.sin(a1.angle);
double cosTheta = Math.cos(a1.angle);
double t = 1.0 - cosTheta;
double xz = ax * az;
double xy = ax * ay;
double yz = ay * az;
m00 = t * ax * ax + cosTheta;
m01 = t * xy - sinTheta * az;
m02 = t * xz + sinTheta * ay;
m10 = t * xy + sinTheta * az;
m11 = t * ay * ay + cosTheta;
m12 = t * yz - sinTheta * ax;
m20 = t * xz - sinTheta * ay;
m21 = t * yz + sinTheta * ax;
m22 = t * az * az + cosTheta;
}
}
/**
* Sets the value of this matrix to the matrix conversion of the single
* precision quaternion argument.
*
* @param q1
* the quaternion to be converted
*/
public final void set(Quat4f q1) {
this.m00 = (1.0 - 2.0 * q1.y * q1.y - 2.0 * q1.z * q1.z);
this.m10 = (2.0 * (q1.x * q1.y + q1.w * q1.z));
this.m20 = (2.0 * (q1.x * q1.z - q1.w * q1.y));
this.m01 = (2.0 * (q1.x * q1.y - q1.w * q1.z));
this.m11 = (1.0 - 2.0 * q1.x * q1.x - 2.0 * q1.z * q1.z);
this.m21 = (2.0 * (q1.y * q1.z + q1.w * q1.x));
this.m02 = (2.0 * (q1.x * q1.z + q1.w * q1.y));
this.m12 = (2.0 * (q1.y * q1.z - q1.w * q1.x));
this.m22 = (1.0 - 2.0 * q1.x * q1.x - 2.0 * q1.y * q1.y);
}
/**
* Sets the value of this matrix to the matrix conversion of the single
* precision axis and angle argument.
*
* @param a1
* the axis and angle to be converted
*/
public final void set(AxisAngle4f a1) {
double mag = Math.sqrt(a1.x * a1.x + a1.y * a1.y + a1.z * a1.z);
if (mag < EPS) {
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;
} else {
mag = 1.0 / mag;
double ax = a1.x * mag;
double ay = a1.y * mag;
double az = a1.z * mag;
double sinTheta = Math.sin(a1.angle);
double cosTheta = Math.cos(a1.angle);
double t = 1.0 - cosTheta;
double xz = ax * az;
double xy = ax * ay;
double yz = ay * az;
m00 = t * ax * ax + cosTheta;
m01 = t * xy - sinTheta * az;
m02 = t * xz + sinTheta * ay;
m10 = t * xy + sinTheta * az;
m11 = t * ay * ay + cosTheta;
m12 = t * yz - sinTheta * ax;
m20 = t * xz - sinTheta * ay;
m21 = t * yz + sinTheta * ax;
m22 = t * az * az + cosTheta;
}
}
/**
* Sets the value of this matrix to the double value of the Matrix3f argument.
*
* @param m1
* the matrix3d to be converted to double
*/
public final void set(Matrix3f m1) {
this.m00 = m1.m00;
this.m01 = m1.m01;
this.m02 = m1.m02;
this.m10 = m1.m10;
this.m11 = m1.m11;
this.m12 = m1.m12;
this.m20 = m1.m20;
this.m21 = m1.m21;
this.m22 = m1.m22;
}
/**
* Sets the value of this matrix to the value of the Matrix3d argument.
*
* @param m1
* the source matrix3d
*/
public final void set(Matrix3d m1) {
this.m00 = m1.m00;
this.m01 = m1.m01;
this.m02 = m1.m02;
this.m10 = m1.m10;
this.m11 = m1.m11;
this.m12 = m1.m12;
this.m20 = m1.m20;
this.m21 = m1.m21;
this.m22 = m1.m22;
}
/**
* Sets the values in this Matrix3d equal to the row-major array parameter
* (ie, the first three elements of the array will be copied into the first
* row of this matrix, etc.).
*
* @param m
* the double precision array of length 9
*/
public final void 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];
}
/**
* Sets the value of this matrix to the matrix inverse of the passed matrix
* m1.
*
* @param m1
* the matrix to be inverted
*/
public final void invert(Matrix3d m1) {
invertGeneral(m1);
}
/**
* Inverts this matrix in place.
*/
public final void invert() {
invertGeneral(this);
}
/**
* General invert routine. Inverts m1 and places the result in "this". Note
* that this routine handles both the "this" version and the non-"this"
* version.
*
* Also note that since this routine is slow anyway, we won't worry about
* allocating a little bit of garbage.
*/
private final void invertGeneral(Matrix3d m1) {
double result[] = new double[9];
int row_perm[] = new int[3];
int i;
double[] tmp = new double[9]; // scratch matrix
// Use LU decomposition and backsubstitution code specifically
// for floating-point 3x3 matrices.
// Copy source matrix to t1tmp
tmp[0] = m1.m00;
tmp[1] = m1.m01;
tmp[2] = m1.m02;
tmp[3] = m1.m10;
tmp[4] = m1.m11;
tmp[5] = m1.m12;
tmp[6] = m1.m20;
tmp[7] = m1.m21;
tmp[8] = m1.m22;
// Calculate LU decomposition: Is the matrix singular?
if (!luDecomposition(tmp, row_perm)) {
// Matrix has no inverse
throw new SingularMatrixException(VecMathI18N.getString("Matrix3d12"));
}
// Perform back substitution on the identity matrix
for (i = 0; i < 9; i++)
result[i] = 0.0;
result[0] = 1.0;
result[4] = 1.0;
result[8] = 1.0;
luBacksubstitution(tmp, row_perm, result);
this.m00 = result[0];
this.m01 = result[1];
this.m02 = result[2];
this.m10 = result[3];
this.m11 = result[4];
this.m12 = result[5];
this.m20 = result[6];
this.m21 = result[7];
this.m22 = result[8];
}
/**
* Given a 3x3 array "matrix0", this function replaces it with the LU
* decomposition of a row-wise permutation of itself. The input parameters are
* "matrix0" and "dimen". The array "matrix0" is also an output parameter. The
* vector "row_perm[3]" is an output parameter that contains the row
* permutations resulting from partial pivoting. The output parameter
* "even_row_xchg" is 1 when the number of row exchanges is even, or -1
* otherwise. Assumes data type is always double.
*
* This function is similar to luDecomposition, except that it is tuned
* specifically for 3x3 matrices.
*
* @return true if the matrix is nonsingular, or false otherwise.
*/
//
// Reference: Press, Flannery, Teukolsky, Vetterling,
// _Numerical_Recipes_in_C_, Cambridge University Press,
// 1988, pp 40-45.
//
static boolean luDecomposition(double[] matrix0, int[] row_perm) {
double row_scale[] = new double[3];
// Determine implicit scaling information by looping over rows
{
int i, j;
int ptr, rs;
double big, temp;
ptr = 0;
rs = 0;
// For each row ...
i = 3;
while (i-- != 0) {
big = 0.0;
// For each column, find the largest element in the row
j = 3;
while (j-- != 0) {
temp = matrix0[ptr++];
temp = Math.abs(temp);
if (temp > big) {
big = temp;
}
}
// Is the matrix singular?
if (big == 0.0) {
return false;
}
row_scale[rs++] = 1.0 / big;
}
}
{
int j;
int mtx;
mtx = 0;
// For all columns, execute Crout's method
for (j = 0; j < 3; j++) {
int i, imax, k;
int target, p1, p2;
double sum, big, temp;
// Determine elements of upper diagonal matrix U
for (i = 0; i < j; i++) {
target = mtx + (3 * i) + j;
sum = matrix0[target];
k = i;
p1 = mtx + (3 * i);
p2 = mtx + j;
while (k-- != 0) {
sum -= matrix0[p1] * matrix0[p2];
p1++;
p2 += 3;
}
matrix0[target] = sum;
}
// Search for largest pivot element and calculate
// intermediate elements of lower diagonal matrix L.
big = 0.0;
imax = -1;
for (i = j; i < 3; i++) {
target = mtx + (3 * i) + j;
sum = matrix0[target];
k = j;
p1 = mtx + (3 * i);
p2 = mtx + j;
while (k-- != 0) {
sum -= matrix0[p1] * matrix0[p2];
p1++;
p2 += 3;
}
matrix0[target] = sum;
// Is this the best pivot so far?
if ((temp = row_scale[i] * Math.abs(sum)) >= big) {
big = temp;
imax = i;
}
}
if (imax < 0) {
throw new RuntimeException(VecMathI18N.getString("Matrix3d13"));
}
// Is a row exchange necessary?
if (j != imax) {
// Yes: exchange rows
k = 3;
p1 = mtx + (3 * imax);
p2 = mtx + (3 * j);
while (k-- != 0) {
temp = matrix0[p1];
matrix0[p1++] = matrix0[p2];
matrix0[p2++] = temp;
}
// Record change in scale factor
row_scale[imax] = row_scale[j];
}
// Record row permutation
row_perm[j] = imax;
// Is the matrix singular
if (matrix0[(mtx + (3 * j) + j)] == 0.0) {
return false;
}
// Divide elements of lower diagonal matrix L by pivot
if (j != (3 - 1)) {
temp = 1.0 / (matrix0[(mtx + (3 * j) + j)]);
target = mtx + (3 * (j + 1)) + j;
i = 2 - j;
while (i-- != 0) {
matrix0[target] *= temp;
target += 3;
}
}
}
}
return true;
}
/**
* Solves a set of linear equations. The input parameters "matrix1", and
* "row_perm" come from luDecompostionD3x3 and do not change here. The
* parameter "matrix2" is a set of column vectors assembled into a 3x3 matrix
* of floating-point values. The procedure takes each column of "matrix2" in
* turn and treats it as the right-hand side of the matrix equation Ax = LUx =
* b. The solution vector replaces the original column of the matrix.
*
* If "matrix2" is the identity matrix, the procedure replaces its contents
* with the inverse of the matrix from which "matrix1" was originally derived.
*/
//
// Reference: Press, Flannery, Teukolsky, Vetterling,
// _Numerical_Recipes_in_C_, Cambridge University Press,
// 1988, pp 44-45.
//
static void luBacksubstitution(double[] matrix1, int[] row_perm,
double[] matrix2) {
int i, ii, ip, j, k;
int rp;
int cv, rv;
// rp = row_perm;
rp = 0;
// For each column vector of matrix2 ...
for (k = 0; k < 3; k++) {
// cv = &(matrix2[0][k]);
cv = k;
ii = -1;
// Forward substitution
for (i = 0; i < 3; i++) {
double sum;
ip = row_perm[rp + i];
sum = matrix2[cv + 3 * ip];
matrix2[cv + 3 * ip] = matrix2[cv + 3 * i];
if (ii >= 0) {
// rv = &(matrix1[i][0]);
rv = i * 3;
for (j = ii; j <= i - 1; j++) {
sum -= matrix1[rv + j] * matrix2[cv + 3 * j];
}
} else if (sum != 0.0) {
ii = i;
}
matrix2[cv + 3 * i] = sum;
}
// Backsubstitution
// rv = &(matrix1[3][0]);
rv = 2 * 3;
matrix2[cv + 3 * 2] /= matrix1[rv + 2];
rv -= 3;
matrix2[cv + 3 * 1] = (matrix2[cv + 3 * 1] - matrix1[rv + 2]
* matrix2[cv + 3 * 2])
/ matrix1[rv + 1];
rv -= 3;
matrix2[cv + 4 * 0] = (matrix2[cv + 3 * 0] - matrix1[rv + 1]
* matrix2[cv + 3 * 1] - matrix1[rv + 2] * matrix2[cv + 3 * 2])
/ matrix1[rv + 0];
}
}
/**
* Computes the determinant of this matrix.
*
* @return the determinant of the matrix
*/
public final double determinant() {
double total;
total = this.m00 * (this.m11 * this.m22 - this.m12 * this.m21) + this.m01
* (this.m12 * this.m20 - this.m10 * this.m22) + this.m02
* (this.m10 * this.m21 - this.m11 * this.m20);
return total;
}
/**
* Sets the value of this matrix to a scale matrix with the passed scale
* amount.
*
* @param scale
* the scale factor for the matrix
*/
public final void set(double scale) {
this.m00 = scale;
this.m01 = 0.0;
this.m02 = 0.0;
this.m10 = 0.0;
this.m11 = scale;
this.m12 = 0.0;
this.m20 = 0.0;
this.m21 = 0.0;
this.m22 = scale;
}
/**
* Sets the value of this matrix to a counter clockwise rotation about the x
* axis.
*
* @param angle
* the angle to rotate about the X axis in radians
*/
public final void rotX(double angle) {
double sinAngle, cosAngle;
sinAngle = Math.sin(angle);
cosAngle = Math.cos(angle);
this.m00 = 1.0;
this.m01 = 0.0;
this.m02 = 0.0;
this.m10 = 0.0;
this.m11 = cosAngle;
this.m12 = -sinAngle;
this.m20 = 0.0;
this.m21 = sinAngle;
this.m22 = cosAngle;
}
/**
* Sets the value of this matrix to a counter clockwise rotation about the y
* axis.
*
* @param angle
* the angle to rotate about the Y axis in radians
*/
public final void rotY(double angle) {
double sinAngle, cosAngle;
sinAngle = Math.sin(angle);
cosAngle = Math.cos(angle);
this.m00 = cosAngle;
this.m01 = 0.0;
this.m02 = sinAngle;
this.m10 = 0.0;
this.m11 = 1.0;
this.m12 = 0.0;
this.m20 = -sinAngle;
this.m21 = 0.0;
this.m22 = cosAngle;
}
/**
* Sets the value of this matrix to a counter clockwise rotation about the z
* axis.
*
* @param angle
* the angle to rotate about the Z axis in radians
*/
public final void rotZ(double angle) {
double sinAngle, cosAngle;
sinAngle = Math.sin(angle);
cosAngle = Math.cos(angle);
this.m00 = cosAngle;
this.m01 = -sinAngle;
this.m02 = 0.0;
this.m10 = sinAngle;
this.m11 = cosAngle;
this.m12 = 0.0;
this.m20 = 0.0;
this.m21 = 0.0;
this.m22 = 1.0;
}
/**
* Multiplies each element of this matrix by a scalar.
*
* @param scalar
* The scalar multiplier.
*/
public final void mul(double scalar) {
m00 *= scalar;
m01 *= scalar;
m02 *= scalar;
m10 *= scalar;
m11 *= scalar;
m12 *= scalar;
m20 *= scalar;
m21 *= scalar;
m22 *= scalar;
}
/**
* Multiplies each element of matrix m1 by a scalar and places the result into
* this. Matrix m1 is not modified.
*
* @param scalar
* the scalar multiplier
* @param m1
* the original matrix
*/
public final void mul(double scalar, Matrix3d m1) {
this.m00 = scalar * m1.m00;
this.m01 = scalar * m1.m01;
this.m02 = scalar * m1.m02;
this.m10 = scalar * m1.m10;
this.m11 = scalar * m1.m11;
this.m12 = scalar * m1.m12;
this.m20 = scalar * m1.m20;
this.m21 = scalar * m1.m21;
this.m22 = scalar * m1.m22;
}
/**
* Sets the value of this matrix to the result of multiplying itself with
* matrix m1.
*
* @param m1
* the other matrix
*/
public final void mul(Matrix3d m1) {
double m00, m01, m02, m10, m11, m12, m20, m21, m22;
m00 = this.m00 * m1.m00 + this.m01 * m1.m10 + this.m02 * m1.m20;
m01 = this.m00 * m1.m01 + this.m01 * m1.m11 + this.m02 * m1.m21;
m02 = this.m00 * m1.m02 + this.m01 * m1.m12 + this.m02 * m1.m22;
m10 = this.m10 * m1.m00 + this.m11 * m1.m10 + this.m12 * m1.m20;
m11 = this.m10 * m1.m01 + this.m11 * m1.m11 + this.m12 * m1.m21;
m12 = this.m10 * m1.m02 + this.m11 * m1.m12 + this.m12 * m1.m22;
m20 = this.m20 * m1.m00 + this.m21 * m1.m10 + this.m22 * m1.m20;
m21 = this.m20 * m1.m01 + this.m21 * m1.m11 + this.m22 * m1.m21;
m22 = this.m20 * m1.m02 + this.m21 * m1.m12 + this.m22 * m1.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;
}
/**
* Sets the value of this matrix to the result of multiplying the two argument
* matrices together.
*
* @param m1
* the first matrix
* @param m2
* the second matrix
*/
public final void mul(Matrix3d m1, Matrix3d m2) {
if (this != m1 && this != m2) {
this.m00 = m1.m00 * m2.m00 + m1.m01 * m2.m10 + m1.m02 * m2.m20;
this.m01 = m1.m00 * m2.m01 + m1.m01 * m2.m11 + m1.m02 * m2.m21;
this.m02 = m1.m00 * m2.m02 + m1.m01 * m2.m12 + m1.m02 * m2.m22;
this.m10 = m1.m10 * m2.m00 + m1.m11 * m2.m10 + m1.m12 * m2.m20;
this.m11 = m1.m10 * m2.m01 + m1.m11 * m2.m11 + m1.m12 * m2.m21;
this.m12 = m1.m10 * m2.m02 + m1.m11 * m2.m12 + m1.m12 * m2.m22;
this.m20 = m1.m20 * m2.m00 + m1.m21 * m2.m10 + m1.m22 * m2.m20;
this.m21 = m1.m20 * m2.m01 + m1.m21 * m2.m11 + m1.m22 * m2.m21;
this.m22 = m1.m20 * m2.m02 + m1.m21 * m2.m12 + m1.m22 * m2.m22;
} else {
double m00, m01, m02, m10, m11, m12, m20, m21, m22; // vars for temp
// result matrix
m00 = m1.m00 * m2.m00 + m1.m01 * m2.m10 + m1.m02 * m2.m20;
m01 = m1.m00 * m2.m01 + m1.m01 * m2.m11 + m1.m02 * m2.m21;
m02 = m1.m00 * m2.m02 + m1.m01 * m2.m12 + m1.m02 * m2.m22;
m10 = m1.m10 * m2.m00 + m1.m11 * m2.m10 + m1.m12 * m2.m20;
m11 = m1.m10 * m2.m01 + m1.m11 * m2.m11 + m1.m12 * m2.m21;
m12 = m1.m10 * m2.m02 + m1.m11 * m2.m12 + m1.m12 * m2.m22;
m20 = m1.m20 * m2.m00 + m1.m21 * m2.m10 + m1.m22 * m2.m20;
m21 = m1.m20 * m2.m01 + m1.m21 * m2.m11 + m1.m22 * m2.m21;
m22 = m1.m20 * m2.m02 + m1.m21 * m2.m12 + m1.m22 * m2.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;
}
}
/**
* Multiplies this matrix by matrix m1, does an SVD normalization of the
* result, and places the result back into this matrix this =
* SVDnorm(this*m1).
*
* @param m1
* the matrix on the right hand side of the multiplication
*/
public final void mulNormalize(Matrix3d m1) {
double[] tmp = new double[9]; // scratch matrix
double[] tmp_rot = new double[9]; // scratch matrix
double[] tmp_scale = new double[3]; // scratch matrix
tmp[0] = this.m00 * m1.m00 + this.m01 * m1.m10 + this.m02 * m1.m20;
tmp[1] = this.m00 * m1.m01 + this.m01 * m1.m11 + this.m02 * m1.m21;
tmp[2] = this.m00 * m1.m02 + this.m01 * m1.m12 + this.m02 * m1.m22;
tmp[3] = this.m10 * m1.m00 + this.m11 * m1.m10 + this.m12 * m1.m20;
tmp[4] = this.m10 * m1.m01 + this.m11 * m1.m11 + this.m12 * m1.m21;
tmp[5] = this.m10 * m1.m02 + this.m11 * m1.m12 + this.m12 * m1.m22;
tmp[6] = this.m20 * m1.m00 + this.m21 * m1.m10 + this.m22 * m1.m20;
tmp[7] = this.m20 * m1.m01 + this.m21 * m1.m11 + this.m22 * m1.m21;
tmp[8] = this.m20 * m1.m02 + this.m21 * m1.m12 + this.m22 * m1.m22;
compute_svd(tmp, tmp_scale, tmp_rot);
this.m00 = tmp_rot[0];
this.m01 = tmp_rot[1];
this.m02 = tmp_rot[2];
this.m10 = tmp_rot[3];
this.m11 = tmp_rot[4];
this.m12 = tmp_rot[5];
this.m20 = tmp_rot[6];
this.m21 = tmp_rot[7];
this.m22 = tmp_rot[8];
}
/**
* Multiplies matrix m1 by matrix m2, does an SVD normalization of the result,
* and places the result into this matrix this = SVDnorm(m1*m2).
*
* @param m1
* the matrix on the left hand side of the multiplication
* @param m2
* the matrix on the right hand side of the multiplication
*/
public final void mulNormalize(Matrix3d m1, Matrix3d m2) {
double[] tmp = new double[9]; // scratch matrix
double[] tmp_rot = new double[9]; // scratch matrix
double[] tmp_scale = new double[3]; // scratch matrix
tmp[0] = m1.m00 * m2.m00 + m1.m01 * m2.m10 + m1.m02 * m2.m20;
tmp[1] = m1.m00 * m2.m01 + m1.m01 * m2.m11 + m1.m02 * m2.m21;
tmp[2] = m1.m00 * m2.m02 + m1.m01 * m2.m12 + m1.m02 * m2.m22;
tmp[3] = m1.m10 * m2.m00 + m1.m11 * m2.m10 + m1.m12 * m2.m20;
tmp[4] = m1.m10 * m2.m01 + m1.m11 * m2.m11 + m1.m12 * m2.m21;
tmp[5] = m1.m10 * m2.m02 + m1.m11 * m2.m12 + m1.m12 * m2.m22;
tmp[6] = m1.m20 * m2.m00 + m1.m21 * m2.m10 + m1.m22 * m2.m20;
tmp[7] = m1.m20 * m2.m01 + m1.m21 * m2.m11 + m1.m22 * m2.m21;
tmp[8] = m1.m20 * m2.m02 + m1.m21 * m2.m12 + m1.m22 * m2.m22;
compute_svd(tmp, tmp_scale, tmp_rot);
this.m00 = tmp_rot[0];
this.m01 = tmp_rot[1];
this.m02 = tmp_rot[2];
this.m10 = tmp_rot[3];
this.m11 = tmp_rot[4];
this.m12 = tmp_rot[5];
this.m20 = tmp_rot[6];
this.m21 = tmp_rot[7];
this.m22 = tmp_rot[8];
}
/**
* Multiplies the transpose of matrix m1 times the transpose of matrix m2, and
* places the result into this.
*
* @param m1
* the matrix on the left hand side of the multiplication
* @param m2
* the matrix on the right hand side of the multiplication
*/
public final void mulTransposeBoth(Matrix3d m1, Matrix3d m2) {
if (this != m1 && this != m2) {
this.m00 = m1.m00 * m2.m00 + m1.m10 * m2.m01 + m1.m20 * m2.m02;
this.m01 = m1.m00 * m2.m10 + m1.m10 * m2.m11 + m1.m20 * m2.m12;
this.m02 = m1.m00 * m2.m20 + m1.m10 * m2.m21 + m1.m20 * m2.m22;
this.m10 = m1.m01 * m2.m00 + m1.m11 * m2.m01 + m1.m21 * m2.m02;
this.m11 = m1.m01 * m2.m10 + m1.m11 * m2.m11 + m1.m21 * m2.m12;
this.m12 = m1.m01 * m2.m20 + m1.m11 * m2.m21 + m1.m21 * m2.m22;
this.m20 = m1.m02 * m2.m00 + m1.m12 * m2.m01 + m1.m22 * m2.m02;
this.m21 = m1.m02 * m2.m10 + m1.m12 * m2.m11 + m1.m22 * m2.m12;
this.m22 = m1.m02 * m2.m20 + m1.m12 * m2.m21 + m1.m22 * m2.m22;
} else {
double m00, m01, m02, m10, m11, m12, m20, m21, m22; // vars for temp
// result matrix
m00 = m1.m00 * m2.m00 + m1.m10 * m2.m01 + m1.m20 * m2.m02;
m01 = m1.m00 * m2.m10 + m1.m10 * m2.m11 + m1.m20 * m2.m12;
m02 = m1.m00 * m2.m20 + m1.m10 * m2.m21 + m1.m20 * m2.m22;
m10 = m1.m01 * m2.m00 + m1.m11 * m2.m01 + m1.m21 * m2.m02;
m11 = m1.m01 * m2.m10 + m1.m11 * m2.m11 + m1.m21 * m2.m12;
m12 = m1.m01 * m2.m20 + m1.m11 * m2.m21 + m1.m21 * m2.m22;
m20 = m1.m02 * m2.m00 + m1.m12 * m2.m01 + m1.m22 * m2.m02;
m21 = m1.m02 * m2.m10 + m1.m12 * m2.m11 + m1.m22 * m2.m12;
m22 = m1.m02 * m2.m20 + m1.m12 * m2.m21 + m1.m22 * m2.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;
}
}
/**
* Multiplies matrix m1 times the transpose of matrix m2, and places the
* result into this.
*
* @param m1
* the matrix on the left hand side of the multiplication
* @param m2
* the matrix on the right hand side of the multiplication
*/
public final void mulTransposeRight(Matrix3d m1, Matrix3d m2) {
if (this != m1 && this != m2) {
this.m00 = m1.m00 * m2.m00 + m1.m01 * m2.m01 + m1.m02 * m2.m02;
this.m01 = m1.m00 * m2.m10 + m1.m01 * m2.m11 + m1.m02 * m2.m12;
this.m02 = m1.m00 * m2.m20 + m1.m01 * m2.m21 + m1.m02 * m2.m22;
this.m10 = m1.m10 * m2.m00 + m1.m11 * m2.m01 + m1.m12 * m2.m02;
this.m11 = m1.m10 * m2.m10 + m1.m11 * m2.m11 + m1.m12 * m2.m12;
this.m12 = m1.m10 * m2.m20 + m1.m11 * m2.m21 + m1.m12 * m2.m22;
this.m20 = m1.m20 * m2.m00 + m1.m21 * m2.m01 + m1.m22 * m2.m02;
this.m21 = m1.m20 * m2.m10 + m1.m21 * m2.m11 + m1.m22 * m2.m12;
this.m22 = m1.m20 * m2.m20 + m1.m21 * m2.m21 + m1.m22 * m2.m22;
} else {
double m00, m01, m02, m10, m11, m12, m20, m21, m22; // vars for temp
// result matrix
m00 = m1.m00 * m2.m00 + m1.m01 * m2.m01 + m1.m02 * m2.m02;
m01 = m1.m00 * m2.m10 + m1.m01 * m2.m11 + m1.m02 * m2.m12;
m02 = m1.m00 * m2.m20 + m1.m01 * m2.m21 + m1.m02 * m2.m22;
m10 = m1.m10 * m2.m00 + m1.m11 * m2.m01 + m1.m12 * m2.m02;
m11 = m1.m10 * m2.m10 + m1.m11 * m2.m11 + m1.m12 * m2.m12;
m12 = m1.m10 * m2.m20 + m1.m11 * m2.m21 + m1.m12 * m2.m22;
m20 = m1.m20 * m2.m00 + m1.m21 * m2.m01 + m1.m22 * m2.m02;
m21 = m1.m20 * m2.m10 + m1.m21 * m2.m11 + m1.m22 * m2.m12;
m22 = m1.m20 * m2.m20 + m1.m21 * m2.m21 + m1.m22 * m2.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;
}
}
/**
* Multiplies the transpose of matrix m1 times matrix m2, and places the
* result into this.
*
* @param m1
* the matrix on the left hand side of the multiplication
* @param m2
* the matrix on the right hand side of the multiplication
*/
public final void mulTransposeLeft(Matrix3d m1, Matrix3d m2) {
if (this != m1 && this != m2) {
this.m00 = m1.m00 * m2.m00 + m1.m10 * m2.m10 + m1.m20 * m2.m20;
this.m01 = m1.m00 * m2.m01 + m1.m10 * m2.m11 + m1.m20 * m2.m21;
this.m02 = m1.m00 * m2.m02 + m1.m10 * m2.m12 + m1.m20 * m2.m22;
this.m10 = m1.m01 * m2.m00 + m1.m11 * m2.m10 + m1.m21 * m2.m20;
this.m11 = m1.m01 * m2.m01 + m1.m11 * m2.m11 + m1.m21 * m2.m21;
this.m12 = m1.m01 * m2.m02 + m1.m11 * m2.m12 + m1.m21 * m2.m22;
this.m20 = m1.m02 * m2.m00 + m1.m12 * m2.m10 + m1.m22 * m2.m20;
this.m21 = m1.m02 * m2.m01 + m1.m12 * m2.m11 + m1.m22 * m2.m21;
this.m22 = m1.m02 * m2.m02 + m1.m12 * m2.m12 + m1.m22 * m2.m22;
} else {
double m00, m01, m02, m10, m11, m12, m20, m21, m22; // vars for temp
// result matrix
m00 = m1.m00 * m2.m00 + m1.m10 * m2.m10 + m1.m20 * m2.m20;
m01 = m1.m00 * m2.m01 + m1.m10 * m2.m11 + m1.m20 * m2.m21;
m02 = m1.m00 * m2.m02 + m1.m10 * m2.m12 + m1.m20 * m2.m22;
m10 = m1.m01 * m2.m00 + m1.m11 * m2.m10 + m1.m21 * m2.m20;
m11 = m1.m01 * m2.m01 + m1.m11 * m2.m11 + m1.m21 * m2.m21;
m12 = m1.m01 * m2.m02 + m1.m11 * m2.m12 + m1.m21 * m2.m22;
m20 = m1.m02 * m2.m00 + m1.m12 * m2.m10 + m1.m22 * m2.m20;
m21 = m1.m02 * m2.m01 + m1.m12 * m2.m11 + m1.m22 * m2.m21;
m22 = m1.m02 * m2.m02 + m1.m12 * m2.m12 + m1.m22 * m2.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;
}
}
/**
* Performs singular value decomposition normalization of this matrix.
*/
public final void normalize() {
double[] tmp_rot = new double[9]; // scratch matrix
double[] tmp_scale = new double[3]; // scratch matrix
getScaleRotate(tmp_scale, tmp_rot);
this.m00 = tmp_rot[0];
this.m01 = tmp_rot[1];
this.m02 = tmp_rot[2];
this.m10 = tmp_rot[3];
this.m11 = tmp_rot[4];
this.m12 = tmp_rot[5];
this.m20 = tmp_rot[6];
this.m21 = tmp_rot[7];
this.m22 = tmp_rot[8];
}
/**
* Perform singular value decomposition normalization of matrix m1 and place
* the normalized values into this.
*
* @param m1
* Provides the matrix values to be normalized
*/
public final void normalize(Matrix3d m1) {
double[] tmp = new double[9]; // scratch matrix
double[] tmp_rot = new double[9]; // scratch matrix
double[] tmp_scale = new double[3]; // scratch matrix
tmp[0] = m1.m00;
tmp[1] = m1.m01;
tmp[2] = m1.m02;
tmp[3] = m1.m10;
tmp[4] = m1.m11;
tmp[5] = m1.m12;
tmp[6] = m1.m20;
tmp[7] = m1.m21;
tmp[8] = m1.m22;
compute_svd(tmp, tmp_scale, tmp_rot);
this.m00 = tmp_rot[0];
this.m01 = tmp_rot[1];
this.m02 = tmp_rot[2];
this.m10 = tmp_rot[3];
this.m11 = tmp_rot[4];
this.m12 = tmp_rot[5];
this.m20 = tmp_rot[6];
this.m21 = tmp_rot[7];
this.m22 = tmp_rot[8];
}
/**
* Perform cross product normalization of this matrix.
*/
public final void normalizeCP() {
double mag = 1.0 / Math.sqrt(m00 * m00 + m10 * m10 + m20 * m20);
m00 = m00 * mag;
m10 = m10 * mag;
m20 = m20 * mag;
mag = 1.0 / Math.sqrt(m01 * m01 + m11 * m11 + m21 * m21);
m01 = m01 * mag;
m11 = m11 * mag;
m21 = m21 * mag;
m02 = m10 * m21 - m11 * m20;
m12 = m01 * m20 - m00 * m21;
m22 = m00 * m11 - m01 * m10;
}
/**
* Perform cross product normalization of matrix m1 and place the normalized
* values into this.
*
* @param m1
* Provides the matrix values to be normalized
*/
public final void normalizeCP(Matrix3d m1) {
double mag = 1.0 / Math.sqrt(m1.m00 * m1.m00 + m1.m10 * m1.m10 + m1.m20
* m1.m20);
m00 = m1.m00 * mag;
m10 = m1.m10 * mag;
m20 = m1.m20 * mag;
mag = 1.0 / Math.sqrt(m1.m01 * m1.m01 + m1.m11 * m1.m11 + m1.m21 * m1.m21);
m01 = m1.m01 * mag;
m11 = m1.m11 * mag;
m21 = m1.m21 * mag;
m02 = m10 * m21 - m11 * m20;
m12 = m01 * m20 - m00 * m21;
m22 = m00 * m11 - m01 * m10;
}
/**
* Returns true if all of the data members of Matrix3d m1 are equal to the
* corresponding data members in this Matrix3d.
*
* @param m1
* the matrix with which the comparison is made
* @return true or false
*/
public boolean equals(Matrix3d m1) {
try {
return (this.m00 == m1.m00 && this.m01 == m1.m01 && this.m02 == m1.m02
&& this.m10 == m1.m10 && this.m11 == m1.m11 && this.m12 == m1.m12
&& this.m20 == m1.m20 && this.m21 == m1.m21 && this.m22 == m1.m22);
} catch (NullPointerException e2) {
return false;
}
}
/**
* Returns true if the Object t1 is of type Matrix3d and all of the data
* members of t1 are equal to the corresponding data members in this Matrix3d.
*
* @param t1
* the matrix with which the comparison is made
* @return true or false
*/
public boolean equals(Object t1) {
try {
Matrix3d m2 = (Matrix3d) t1;
return (this.m00 == m2.m00 && this.m01 == m2.m01 && this.m02 == m2.m02
&& this.m10 == m2.m10 && this.m11 == m2.m11 && this.m12 == m2.m12
&& this.m20 == m2.m20 && this.m21 == m2.m21 && this.m22 == m2.m22);
} catch (ClassCastException e1) {
return false;
} catch (NullPointerException e2) {
return false;
}
}
/**
* Returns true if the L-infinite distance between this matrix and matrix m1
* is less than or equal to the epsilon parameter, otherwise returns false.
* The L-infinite distance is equal to MAX[i=0,1,2 ; j=0,1,2 ; abs(this.m(i,j)
* - m1.m(i,j)]
*
* @param m1
* the matrix to be compared to this matrix
* @param epsilon
* the threshold value
*/
public boolean epsilonEquals(Matrix3d m1, double epsilon) {
double diff;
diff = m00 - m1.m00;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m01 - m1.m01;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m02 - m1.m02;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m10 - m1.m10;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m11 - m1.m11;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m12 - m1.m12;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m20 - m1.m20;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m21 - m1.m21;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
diff = m22 - m1.m22;
if ((diff < 0 ? -diff : diff) > epsilon)
return false;
return true;
}
/**
* Returns a hash code value based on the data values in this object. Two
* different Matrix3d objects with identical data values (i.e.,
* Matrix3d.equals returns true) will return the same hash code value. Two
* objects with different data members may return the same hash value,
* although this is not likely.
*
* @return the integer hash code value
*/
public int hashCode() {
long bits = 1L;
bits = 31L * bits + VecMathUtil.doubleToLongBits(m00);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m01);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m02);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m10);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m11);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m12);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m20);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m21);
bits = 31L * bits + VecMathUtil.doubleToLongBits(m22);
return (int) (bits ^ (bits >> 32));
}
/**
* Sets this matrix to all zeros.
*/
public final void setZero() {
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;
}
/**
* Negates the value of this matrix: this = -this.
*/
public final void negate() {
this.m00 = -this.m00;
this.m01 = -this.m01;
this.m02 = -this.m02;
this.m10 = -this.m10;
this.m11 = -this.m11;
this.m12 = -this.m12;
this.m20 = -this.m20;
this.m21 = -this.m21;
this.m22 = -this.m22;
}
/**
* Sets the value of this matrix equal to the negation of of the Matrix3d
* parameter.
*
* @param m1
* the source matrix
*/
public final void negate(Matrix3d m1) {
this.m00 = -m1.m00;
this.m01 = -m1.m01;
this.m02 = -m1.m02;
this.m10 = -m1.m10;
this.m11 = -m1.m11;
this.m12 = -m1.m12;
this.m20 = -m1.m20;
this.m21 = -m1.m21;
this.m22 = -m1.m22;
}
/**
* Multiply this matrix by the tuple t and place the result back into the
* tuple (t = this*t).
*
* @param t
* the tuple to be multiplied by this matrix and then replaced
*/
public final void transform(Tuple3d t) {
double x, y, z;
x = m00 * t.x + m01 * t.y + m02 * t.z;
y = m10 * t.x + m11 * t.y + m12 * t.z;
z = m20 * t.x + m21 * t.y + m22 * t.z;
t.set(x, y, z);
}
/**
* Multiply this matrix by the tuple t and and place the result into the tuple
* "result" (result = this*t).
*
* @param t
* the tuple to be multiplied by this matrix
* @param result
* the tuple into which the product is placed
*/
public final void transform(Tuple3d t, Tuple3d result) {
double x, y;
x = m00 * t.x + m01 * t.y + m02 * t.z;
y = m10 * t.x + m11 * t.y + m12 * t.z;
result.z = m20 * t.x + m21 * t.y + m22 * t.z;
result.x = x;
result.y = y;
}
/**
* perform SVD (if necessary to get rotational component
*/
final void getScaleRotate(double scales[], double rots[]) {
double[] tmp = new double[9]; // scratch matrix
tmp[0] = m00;
tmp[1] = m01;
tmp[2] = m02;
tmp[3] = m10;
tmp[4] = m11;
tmp[5] = m12;
tmp[6] = m20;
tmp[7] = m21;
tmp[8] = m22;
compute_svd(tmp, scales, rots);
return;
}
static void compute_svd(double[] m, double[] outScale, double[] outRot) {
int i;
double g;
double[] u1 = new double[9];
double[] v1 = new double[9];
double[] t1 = new double[9];
double[] t2 = new double[9];
double[] tmp = t1;
double[] single_values = t2;
double[] rot = new double[9];
double[] e = new double[3];
double[] scales = new double[3];
int negCnt = 0;
double c1, c2, c3, c4;
double s1, s2, s3, s4;
for (i = 0; i < 9; i++)
rot[i] = m[i];
// u1
if (m[3] * m[3] < EPS) {
u1[0] = 1.0;
u1[1] = 0.0;
u1[2] = 0.0;
u1[3] = 0.0;
u1[4] = 1.0;
u1[5] = 0.0;
u1[6] = 0.0;
u1[7] = 0.0;
u1[8] = 1.0;
} else if (m[0] * m[0] < EPS) {
tmp[0] = m[0];
tmp[1] = m[1];
tmp[2] = m[2];
m[0] = m[3];
m[1] = m[4];
m[2] = m[5];
m[3] = -tmp[0]; // zero
m[4] = -tmp[1];
m[5] = -tmp[2];
u1[0] = 0.0;
u1[1] = 1.0;
u1[2] = 0.0;
u1[3] = -1.0;
u1[4] = 0.0;
u1[5] = 0.0;
u1[6] = 0.0;
u1[7] = 0.0;
u1[8] = 1.0;
} else {
g = 1.0 / Math.sqrt(m[0] * m[0] + m[3] * m[3]);
c1 = m[0] * g;
s1 = m[3] * g;
tmp[0] = c1 * m[0] + s1 * m[3];
tmp[1] = c1 * m[1] + s1 * m[4];
tmp[2] = c1 * m[2] + s1 * m[5];
m[3] = -s1 * m[0] + c1 * m[3]; // zero
m[4] = -s1 * m[1] + c1 * m[4];
m[5] = -s1 * m[2] + c1 * m[5];
m[0] = tmp[0];
m[1] = tmp[1];
m[2] = tmp[2];
u1[0] = c1;
u1[1] = s1;
u1[2] = 0.0;
u1[3] = -s1;
u1[4] = c1;
u1[5] = 0.0;
u1[6] = 0.0;
u1[7] = 0.0;
u1[8] = 1.0;
}
// u2
if (m[6] * m[6] < EPS) {
} else if (m[0] * m[0] < EPS) {
tmp[0] = m[0];
tmp[1] = m[1];
tmp[2] = m[2];
m[0] = m[6];
m[1] = m[7];
m[2] = m[8];
m[6] = -tmp[0]; // zero
m[7] = -tmp[1];
m[8] = -tmp[2];
tmp[0] = u1[0];
tmp[1] = u1[1];
tmp[2] = u1[2];
u1[0] = u1[6];
u1[1] = u1[7];
u1[2] = u1[8];
u1[6] = -tmp[0]; // zero
u1[7] = -tmp[1];
u1[8] = -tmp[2];
} else {
g = 1.0 / Math.sqrt(m[0] * m[0] + m[6] * m[6]);
c2 = m[0] * g;
s2 = m[6] * g;
tmp[0] = c2 * m[0] + s2 * m[6];
tmp[1] = c2 * m[1] + s2 * m[7];
tmp[2] = c2 * m[2] + s2 * m[8];
m[6] = -s2 * m[0] + c2 * m[6];
m[7] = -s2 * m[1] + c2 * m[7];
m[8] = -s2 * m[2] + c2 * m[8];
m[0] = tmp[0];
m[1] = tmp[1];
m[2] = tmp[2];
tmp[0] = c2 * u1[0];
tmp[1] = c2 * u1[1];
u1[2] = s2;
tmp[6] = -u1[0] * s2;
tmp[7] = -u1[1] * s2;
u1[8] = c2;
u1[0] = tmp[0];
u1[1] = tmp[1];
u1[6] = tmp[6];
u1[7] = tmp[7];
}
// v1
if (m[2] * m[2] < EPS) {
v1[0] = 1.0;
v1[1] = 0.0;
v1[2] = 0.0;
v1[3] = 0.0;
v1[4] = 1.0;
v1[5] = 0.0;
v1[6] = 0.0;
v1[7] = 0.0;
v1[8] = 1.0;
} else if (m[1] * m[1] < EPS) {
tmp[2] = m[2];
tmp[5] = m[5];
tmp[8] = m[8];
m[2] = -m[1];
m[5] = -m[4];
m[8] = -m[7];
m[1] = tmp[2]; // zero
m[4] = tmp[5];
m[7] = tmp[8];
v1[0] = 1.0;
v1[1] = 0.0;
v1[2] = 0.0;
v1[3] = 0.0;
v1[4] = 0.0;
v1[5] = -1.0;
v1[6] = 0.0;
v1[7] = 1.0;
v1[8] = 0.0;
} else {
g = 1.0 / Math.sqrt(m[1] * m[1] + m[2] * m[2]);
c3 = m[1] * g;
s3 = m[2] * g;
tmp[1] = c3 * m[1] + s3 * m[2]; // can assign to m[1]?
m[2] = -s3 * m[1] + c3 * m[2]; // zero
m[1] = tmp[1];
tmp[4] = c3 * m[4] + s3 * m[5];
m[5] = -s3 * m[4] + c3 * m[5];
m[4] = tmp[4];
tmp[7] = c3 * m[7] + s3 * m[8];
m[8] = -s3 * m[7] + c3 * m[8];
m[7] = tmp[7];
v1[0] = 1.0;
v1[1] = 0.0;
v1[2] = 0.0;
v1[3] = 0.0;
v1[4] = c3;
v1[5] = -s3;
v1[6] = 0.0;
v1[7] = s3;
v1[8] = c3;
}
// u3
if (m[7] * m[7] < EPS) {
} else if (m[4] * m[4] < EPS) {
tmp[3] = m[3];
tmp[4] = m[4];
tmp[5] = m[5];
m[3] = m[6]; // zero
m[4] = m[7];
m[5] = m[8];
m[6] = -tmp[3]; // zero
m[7] = -tmp[4]; // zero
m[8] = -tmp[5];
tmp[3] = u1[3];
tmp[4] = u1[4];
tmp[5] = u1[5];
u1[3] = u1[6];
u1[4] = u1[7];
u1[5] = u1[8];
u1[6] = -tmp[3]; // zero
u1[7] = -tmp[4];
u1[8] = -tmp[5];
} else {
g = 1.0 / Math.sqrt(m[4] * m[4] + m[7] * m[7]);
c4 = m[4] * g;
s4 = m[7] * g;
tmp[3] = c4 * m[3] + s4 * m[6];
m[6] = -s4 * m[3] + c4 * m[6]; // zero
m[3] = tmp[3];
tmp[4] = c4 * m[4] + s4 * m[7];
m[7] = -s4 * m[4] + c4 * m[7];
m[4] = tmp[4];
tmp[5] = c4 * m[5] + s4 * m[8];
m[8] = -s4 * m[5] + c4 * m[8];
m[5] = tmp[5];
tmp[3] = c4 * u1[3] + s4 * u1[6];
u1[6] = -s4 * u1[3] + c4 * u1[6];
u1[3] = tmp[3];
tmp[4] = c4 * u1[4] + s4 * u1[7];
u1[7] = -s4 * u1[4] + c4 * u1[7];
u1[4] = tmp[4];
tmp[5] = c4 * u1[5] + s4 * u1[8];
u1[8] = -s4 * u1[5] + c4 * u1[8];
u1[5] = tmp[5];
}
single_values[0] = m[0];
single_values[1] = m[4];
single_values[2] = m[8];
e[0] = m[1];
e[1] = m[5];
if (e[0] * e[0] < EPS && e[1] * e[1] < EPS) {
} else {
compute_qr(single_values, e, u1, v1);
}
scales[0] = single_values[0];
scales[1] = single_values[1];
scales[2] = single_values[2];
// Do some optimization here. If scale is unity, simply return the rotation
// matric.
if (almostEqual(Math.abs(scales[0]), 1.0)
&& almostEqual(Math.abs(scales[1]), 1.0)
&& almostEqual(Math.abs(scales[2]), 1.0)) {
// System.out.println("Scale components almost to 1.0");
for (i = 0; i < 3; i++)
if (scales[i] < 0.0)
negCnt++;
if ((negCnt == 0) || (negCnt == 2)) {
// System.out.println("Optimize!!");
outScale[0] = outScale[1] = outScale[2] = 1.0;
for (i = 0; i < 9; i++)
outRot[i] = rot[i];
return;
}
}
transpose_mat(u1, t1);
transpose_mat(v1, t2);
/*
* System.out.println("t1 is \n" + t1);
* System.out.println("t1="+t1[0]+" "+t1[1]+" "+t1[2]);
* System.out.println("t1="+t1[3]+" "+t1[4]+" "+t1[5]);
* System.out.println("t1="+t1[6]+" "+t1[7]+" "+t1[8]);
*
* System.out.println("t2 is \n" + t2);
* System.out.println("t2="+t2[0]+" "+t2[1]+" "+t2[2]);
* System.out.println("t2="+t2[3]+" "+t2[4]+" "+t2[5]);
* System.out.println("t2="+t2[6]+" "+t2[7]+" "+t2[8]);
*/
svdReorder(m, t1, t2, scales, outRot, outScale);
}
static void svdReorder(double[] m, double[] t1, double[] t2, double[] scales,
double[] outRot, double[] outScale) {
int[] out = new int[3];
int in0, in1, in2, index, i;
double[] mag = new double[3];
double[] rot = new double[9];
// check for rotation information in the scales
if (scales[0] < 0.0) { // move the rotation info to rotation matrix
scales[0] = -scales[0];
t2[0] = -t2[0];
t2[1] = -t2[1];
t2[2] = -t2[2];
}
if (scales[1] < 0.0) { // move the rotation info to rotation matrix
scales[1] = -scales[1];
t2[3] = -t2[3];
t2[4] = -t2[4];
t2[5] = -t2[5];
}
if (scales[2] < 0.0) { // move the rotation info to rotation matrix
scales[2] = -scales[2];
t2[6] = -t2[6];
t2[7] = -t2[7];
t2[8] = -t2[8];
}
mat_mul(t1, t2, rot);
// check for equal scales case and do not reorder
if (almostEqual(Math.abs(scales[0]), Math.abs(scales[1]))
&& almostEqual(Math.abs(scales[1]), Math.abs(scales[2]))) {
for (i = 0; i < 9; i++) {
outRot[i] = rot[i];
}
for (i = 0; i < 3; i++) {
outScale[i] = scales[i];
}
} else {
// sort the order of the results of SVD
if (scales[0] > scales[1]) {
if (scales[0] > scales[2]) {
if (scales[2] > scales[1]) {
out[0] = 0;
out[1] = 2;
out[2] = 1; // xzy
} else {
out[0] = 0;
out[1] = 1;
out[2] = 2; // xyz
}
} else {
out[0] = 2;
out[1] = 0;
out[2] = 1; // zxy
}
} else { // y > x
if (scales[1] > scales[2]) {
if (scales[2] > scales[0]) {
out[0] = 1;
out[1] = 2;
out[2] = 0; // yzx
} else {
out[0] = 1;
out[1] = 0;
out[2] = 2; // yxz
}
} else {
out[0] = 2;
out[1] = 1;
out[2] = 0; // zyx
}
}
/*
* System.out.println("\nscales="+scales[0]+" "+scales[1]+" "+scales[2]);
* System.out.println("\nrot="+rot[0]+" "+rot[1]+" "+rot[2]);
* System.out.println("rot="+rot[3]+" "+rot[4]+" "+rot[5]);
* System.out.println("rot="+rot[6]+" "+rot[7]+" "+rot[8]);
*/
// sort the order of the input matrix
mag[0] = (m[0] * m[0] + m[1] * m[1] + m[2] * m[2]);
mag[1] = (m[3] * m[3] + m[4] * m[4] + m[5] * m[5]);
mag[2] = (m[6] * m[6] + m[7] * m[7] + m[8] * m[8]);
if (mag[0] > mag[1]) {
if (mag[0] > mag[2]) {
if (mag[2] > mag[1]) {
// 0 - 2 - 1
in0 = 0;
in2 = 1;
in1 = 2;// xzy
} else {
// 0 - 1 - 2
in0 = 0;
in1 = 1;
in2 = 2; // xyz
}
} else {
// 2 - 0 - 1
in2 = 0;
in0 = 1;
in1 = 2; // zxy
}
} else { // y > x 1>0
if (mag[1] > mag[2]) {
if (mag[2] > mag[0]) {
// 1 - 2 - 0
in1 = 0;
in2 = 1;
in0 = 2; // yzx
} else {
// 1 - 0 - 2
in1 = 0;
in0 = 1;
in2 = 2; // yxz
}
} else {
// 2 - 1 - 0
in2 = 0;
in1 = 1;
in0 = 2; // zyx
}
}
index = out[in0];
outScale[0] = scales[index];
index = out[in1];
outScale[1] = scales[index];
index = out[in2];
outScale[2] = scales[index];
index = out[in0];
outRot[0] = rot[index];
index = out[in0] + 3;
outRot[0 + 3] = rot[index];
index = out[in0] + 6;
outRot[0 + 6] = rot[index];
index = out[in1];
outRot[1] = rot[index];
index = out[in1] + 3;
outRot[1 + 3] = rot[index];
index = out[in1] + 6;
outRot[1 + 6] = rot[index];
index = out[in2];
outRot[2] = rot[index];
index = out[in2] + 3;
outRot[2 + 3] = rot[index];
index = out[in2] + 6;
outRot[2 + 6] = rot[index];
}
}
static int compute_qr(double[] s, double[] e, double[] u, double[] v) {
int k;
boolean converged;
double shift, r;
double[] cosl = new double[2];
double[] cosr = new double[2];
double[] sinl = new double[2];
double[] sinr = new double[2];
double[] m = new double[9];
double utemp, vtemp;
double f, g;
final int MAX_INTERATIONS = 10;
final double CONVERGE_TOL = 4.89E-15;
double c_b48 = 1.;
int first;
converged = false;
first = 1;
if (Math.abs(e[1]) < CONVERGE_TOL || Math.abs(e[0]) < CONVERGE_TOL)
converged = true;
for (k = 0; k < MAX_INTERATIONS && !converged; k++) {
shift = compute_shift(s[1], e[1], s[2]);
f = (Math.abs(s[0]) - shift) * (d_sign(c_b48, s[0]) + shift / s[0]);
g = e[0];
r = compute_rot(f, g, sinr, cosr, 0, first);
f = cosr[0] * s[0] + sinr[0] * e[0];
e[0] = cosr[0] * e[0] - sinr[0] * s[0];
g = sinr[0] * s[1];
s[1] = cosr[0] * s[1];
r = compute_rot(f, g, sinl, cosl, 0, first);
first = 0;
s[0] = r;
f = cosl[0] * e[0] + sinl[0] * s[1];
s[1] = cosl[0] * s[1] - sinl[0] * e[0];
g = sinl[0] * e[1];
e[1] = cosl[0] * e[1];
r = compute_rot(f, g, sinr, cosr, 1, first);
e[0] = r;
f = cosr[1] * s[1] + sinr[1] * e[1];
e[1] = cosr[1] * e[1] - sinr[1] * s[1];
g = sinr[1] * s[2];
s[2] = cosr[1] * s[2];
r = compute_rot(f, g, sinl, cosl, 1, first);
s[1] = r;
f = cosl[1] * e[1] + sinl[1] * s[2];
s[2] = cosl[1] * s[2] - sinl[1] * e[1];
e[1] = f;
// update u matrices
utemp = u[0];
u[0] = cosl[0] * utemp + sinl[0] * u[3];
u[3] = -sinl[0] * utemp + cosl[0] * u[3];
utemp = u[1];
u[1] = cosl[0] * utemp + sinl[0] * u[4];
u[4] = -sinl[0] * utemp + cosl[0] * u[4];
utemp = u[2];
u[2] = cosl[0] * utemp + sinl[0] * u[5];
u[5] = -sinl[0] * utemp + cosl[0] * u[5];
utemp = u[3];
u[3] = cosl[1] * utemp + sinl[1] * u[6];
u[6] = -sinl[1] * utemp + cosl[1] * u[6];
utemp = u[4];
u[4] = cosl[1] * utemp + sinl[1] * u[7];
u[7] = -sinl[1] * utemp + cosl[1] * u[7];
utemp = u[5];
u[5] = cosl[1] * utemp + sinl[1] * u[8];
u[8] = -sinl[1] * utemp + cosl[1] * u[8];
// update v matrices
vtemp = v[0];
v[0] = cosr[0] * vtemp + sinr[0] * v[1];
v[1] = -sinr[0] * vtemp + cosr[0] * v[1];
vtemp = v[3];
v[3] = cosr[0] * vtemp + sinr[0] * v[4];
v[4] = -sinr[0] * vtemp + cosr[0] * v[4];
vtemp = v[6];
v[6] = cosr[0] * vtemp + sinr[0] * v[7];
v[7] = -sinr[0] * vtemp + cosr[0] * v[7];
vtemp = v[1];
v[1] = cosr[1] * vtemp + sinr[1] * v[2];
v[2] = -sinr[1] * vtemp + cosr[1] * v[2];
vtemp = v[4];
v[4] = cosr[1] * vtemp + sinr[1] * v[5];
v[5] = -sinr[1] * vtemp + cosr[1] * v[5];
vtemp = v[7];
v[7] = cosr[1] * vtemp + sinr[1] * v[8];
v[8] = -sinr[1] * vtemp + cosr[1] * v[8];
m[0] = s[0];
m[1] = e[0];
m[2] = 0.0;
m[3] = 0.0;
m[4] = s[1];
m[5] = e[1];
m[6] = 0.0;
m[7] = 0.0;
m[8] = s[2];
if (Math.abs(e[1]) < CONVERGE_TOL || Math.abs(e[0]) < CONVERGE_TOL)
converged = true;
}
if (Math.abs(e[1]) < CONVERGE_TOL) {
compute_2X2(s[0], e[0], s[1], s, sinl, cosl, sinr, cosr, 0);
utemp = u[0];
u[0] = cosl[0] * utemp + sinl[0] * u[3];
u[3] = -sinl[0] * utemp + cosl[0] * u[3];
utemp = u[1];
u[1] = cosl[0] * utemp + sinl[0] * u[4];
u[4] = -sinl[0] * utemp + cosl[0] * u[4];
utemp = u[2];
u[2] = cosl[0] * utemp + sinl[0] * u[5];
u[5] = -sinl[0] * utemp + cosl[0] * u[5];
// update v matrices
vtemp = v[0];
v[0] = cosr[0] * vtemp + sinr[0] * v[1];
v[1] = -sinr[0] * vtemp + cosr[0] * v[1];
vtemp = v[3];
v[3] = cosr[0] * vtemp + sinr[0] * v[4];
v[4] = -sinr[0] * vtemp + cosr[0] * v[4];
vtemp = v[6];
v[6] = cosr[0] * vtemp + sinr[0] * v[7];
v[7] = -sinr[0] * vtemp + cosr[0] * v[7];
} else {
compute_2X2(s[1], e[1], s[2], s, sinl, cosl, sinr, cosr, 1);
utemp = u[3];
u[3] = cosl[0] * utemp + sinl[0] * u[6];
u[6] = -sinl[0] * utemp + cosl[0] * u[6];
utemp = u[4];
u[4] = cosl[0] * utemp + sinl[0] * u[7];
u[7] = -sinl[0] * utemp + cosl[0] * u[7];
utemp = u[5];
u[5] = cosl[0] * utemp + sinl[0] * u[8];
u[8] = -sinl[0] * utemp + cosl[0] * u[8];
// update v matrices
vtemp = v[1];
v[1] = cosr[0] * vtemp + sinr[0] * v[2];
v[2] = -sinr[0] * vtemp + cosr[0] * v[2];
vtemp = v[4];
v[4] = cosr[0] * vtemp + sinr[0] * v[5];
v[5] = -sinr[0] * vtemp + cosr[0] * v[5];
vtemp = v[7];
v[7] = cosr[0] * vtemp + sinr[0] * v[8];
v[8] = -sinr[0] * vtemp + cosr[0] * v[8];
}
return (0);
}
static double max(double a, double b) {
if (a > b)
return (a);
else
return (b);
}
static double min(double a, double b) {
if (a < b)
return (a);
else
return (b);
}
static double d_sign(double a, double b) {
double x;
x = (a >= 0 ? a : -a);
return (b >= 0 ? x : -x);
}
static double compute_shift(double f, double g, double h) {
double d__1, d__2;
double fhmn, fhmx, c, fa, ga, ha, as, at, au;
double ssmin;
fa = Math.abs(f);
ga = Math.abs(g);
ha = Math.abs(h);
fhmn = min(fa, ha);
fhmx = max(fa, ha);
if (fhmn == 0.) {
ssmin = 0.;
if (fhmx == 0.) {
} else {
d__1 = min(fhmx, ga) / max(fhmx, ga);
}
} else {
if (ga < fhmx) {
as = fhmn / fhmx + 1.;
at = (fhmx - fhmn) / fhmx;
d__1 = ga / fhmx;
au = d__1 * d__1;
c = 2. / (Math.sqrt(as * as + au) + Math.sqrt(at * at + au));
ssmin = fhmn * c;
} else {
au = fhmx / ga;
if (au == 0.) {
ssmin = fhmn * fhmx / ga;
} else {
as = fhmn / fhmx + 1.;
at = (fhmx - fhmn) / fhmx;
d__1 = as * au;
d__2 = at * au;
c = 1. / (Math.sqrt(d__1 * d__1 + 1.) + Math.sqrt(d__2 * d__2 + 1.));
ssmin = fhmn * c * au;
ssmin += ssmin;
}
}
}
return (ssmin);
}
static int compute_2X2(double f, double g, double h, double[] single_values,
double[] snl, double[] csl, double[] snr, double[] csr, int index) {
double c_b3 = 2.;
double c_b4 = 1.;
double d__1;
int pmax;
double temp;
boolean swap;
double a, d, l, m, r, s, t, tsign, fa, ga, ha;
double ft, gt, ht, mm;
boolean gasmal;
double tt, clt, crt, slt, srt;
double ssmin, ssmax;
ssmax = single_values[0];
ssmin = single_values[1];
clt = 0.0;
crt = 0.0;
slt = 0.0;
srt = 0.0;
tsign = 0.0;
ft = f;
fa = Math.abs(ft);
ht = h;
ha = Math.abs(h);
pmax = 1;
if (ha > fa)
swap = true;
else
swap = false;
if (swap) {
pmax = 3;
temp = ft;
ft = ht;
ht = temp;
temp = fa;
fa = ha;
ha = temp;
}
gt = g;
ga = Math.abs(gt);
if (ga == 0.) {
single_values[1] = ha;
single_values[0] = fa;
clt = 1.;
crt = 1.;
slt = 0.;
srt = 0.;
} else {
gasmal = true;
if (ga > fa) {
pmax = 2;
if (fa / ga < EPS) {
gasmal = false;
ssmax = ga;
if (ha > 1.) {
ssmin = fa / (ga / ha);
} else {
ssmin = fa / ga * ha;
}
clt = 1.;
slt = ht / gt;
srt = 1.;
crt = ft / gt;
}
}
if (gasmal) {
d = fa - ha;
if (d == fa) {
l = 1.;
} else {
l = d / fa;
}
m = gt / ft;
t = 2. - l;
mm = m * m;
tt = t * t;
s = Math.sqrt(tt + mm);
if (l == 0.) {
r = Math.abs(m);
} else {
r = Math.sqrt(l * l + mm);
}
a = (s + r) * .5;
if (ga > fa) {
pmax = 2;
if (fa / ga < EPS) {
gasmal = false;
ssmax = ga;
if (ha > 1.) {
ssmin = fa / (ga / ha);
} else {
ssmin = fa / ga * ha;
}
clt = 1.;
slt = ht / gt;
srt = 1.;
crt = ft / gt;
}
}
if (gasmal) {
d = fa - ha;
if (d == fa) {
l = 1.;
} else {
l = d / fa;
}
m = gt / ft;
t = 2. - l;
mm = m * m;
tt = t * t;
s = Math.sqrt(tt + mm);
if (l == 0.) {
r = Math.abs(m);
} else {
r = Math.sqrt(l * l + mm);
}
a = (s + r) * .5;
ssmin = ha / a;
ssmax = fa * a;
if (mm == 0.) {
if (l == 0.) {
t = d_sign(c_b3, ft) * d_sign(c_b4, gt);
} else {
t = gt / d_sign(d, ft) + m / t;
}
} else {
t = (m / (s + t) + m / (r + l)) * (a + 1.);
}
l = Math.sqrt(t * t + 4.);
crt = 2. / l;
srt = t / l;
clt = (crt + srt * m) / a;
slt = ht / ft * srt / a;
}
}
if (swap) {
csl[0] = srt;
snl[0] = crt;
csr[0] = slt;
snr[0] = clt;
} else {
csl[0] = clt;
snl[0] = slt;
csr[0] = crt;
snr[0] = srt;
}
if (pmax == 1) {
tsign = d_sign(c_b4, csr[0]) * d_sign(c_b4, csl[0]) * d_sign(c_b4, f);
}
if (pmax == 2) {
tsign = d_sign(c_b4, snr[0]) * d_sign(c_b4, csl[0]) * d_sign(c_b4, g);
}
if (pmax == 3) {
tsign = d_sign(c_b4, snr[0]) * d_sign(c_b4, snl[0]) * d_sign(c_b4, h);
}
single_values[index] = d_sign(ssmax, tsign);
d__1 = tsign * d_sign(c_b4, f) * d_sign(c_b4, h);
single_values[index + 1] = d_sign(ssmin, d__1);
}
return 0;
}
static double compute_rot(double f, double g, double[] sin, double[] cos,
int index, int first) {
double cs, sn;
int i;
double scale;
int count;
double f1, g1;
double r;
final double safmn2 = 2.002083095183101E-146;
final double safmx2 = 4.994797680505588E+145;
if (g == 0.) {
cs = 1.;
sn = 0.;
r = f;
} else if (f == 0.) {
cs = 0.;
sn = 1.;
r = g;
} else {
f1 = f;
g1 = g;
scale = max(Math.abs(f1), Math.abs(g1));
if (scale >= safmx2) {
count = 0;
while (scale >= safmx2) {
++count;
f1 *= safmn2;
g1 *= safmn2;
scale = max(Math.abs(f1), Math.abs(g1));
}
r = Math.sqrt(f1 * f1 + g1 * g1);
cs = f1 / r;
sn = g1 / r;
for (i = 1; i <= count; ++i) {
r *= safmx2;
}
} else if (scale <= safmn2) {
count = 0;
while (scale <= safmn2) {
++count;
f1 *= safmx2;
g1 *= safmx2;
scale = max(Math.abs(f1), Math.abs(g1));
}
r = Math.sqrt(f1 * f1 + g1 * g1);
cs = f1 / r;
sn = g1 / r;
for (i = 1; i <= count; ++i) {
r *= safmn2;
}
} else {
r = Math.sqrt(f1 * f1 + g1 * g1);
cs = f1 / r;
sn = g1 / r;
}
if (Math.abs(f) > Math.abs(g) && cs < 0.) {
cs = -cs;
sn = -sn;
r = -r;
}
}
sin[index] = sn;
cos[index] = cs;
return r;
}
static void print_mat(double[] mat) {
int i;
for (i = 0; i < 3; i++) {
System.out.println(mat[i * 3 + 0] + " " + mat[i * 3 + 1] + " "
+ mat[i * 3 + 2] + "\n");
}
}
static void print_det(double[] mat) {
double det;
det = mat[0] * mat[4] * mat[8] + mat[1] * mat[5] * mat[6] + mat[2] * mat[3]
* mat[7] - mat[2] * mat[4] * mat[6] - mat[0] * mat[5] * mat[7] - mat[1]
* mat[3] * mat[8];
System.out.println("det= " + det);
}
static void mat_mul(double[] m1, double[] m2, double[] m3) {
int i;
double[] tmp = new double[9];
tmp[0] = m1[0] * m2[0] + m1[1] * m2[3] + m1[2] * m2[6];
tmp[1] = m1[0] * m2[1] + m1[1] * m2[4] + m1[2] * m2[7];
tmp[2] = m1[0] * m2[2] + m1[1] * m2[5] + m1[2] * m2[8];
tmp[3] = m1[3] * m2[0] + m1[4] * m2[3] + m1[5] * m2[6];
tmp[4] = m1[3] * m2[1] + m1[4] * m2[4] + m1[5] * m2[7];
tmp[5] = m1[3] * m2[2] + m1[4] * m2[5] + m1[5] * m2[8];
tmp[6] = m1[6] * m2[0] + m1[7] * m2[3] + m1[8] * m2[6];
tmp[7] = m1[6] * m2[1] + m1[7] * m2[4] + m1[8] * m2[7];
tmp[8] = m1[6] * m2[2] + m1[7] * m2[5] + m1[8] * m2[8];
for (i = 0; i < 9; i++) {
m3[i] = tmp[i];
}
}
static void transpose_mat(double[] in, double[] out) {
out[0] = in[0];
out[1] = in[3];
out[2] = in[6];
out[3] = in[1];
out[4] = in[4];
out[5] = in[7];
out[6] = in[2];
out[7] = in[5];
out[8] = in[8];
}
static double max3(double[] values) {
if (values[0] > values[1]) {
if (values[0] > values[2])
return (values[0]);
else
return (values[2]);
} else {
if (values[1] > values[2])
return (values[1]);
else
return (values[2]);
}
}
private static final boolean almostEqual(double a, double b) {
if (a == b)
return true;
final double EPSILON_ABSOLUTE = 1.0e-6;
final double EPSILON_RELATIVE = 1.0e-4;
double diff = Math.abs(a - b);
double absA = Math.abs(a);
double absB = Math.abs(b);
double max = (absA >= absB) ? absA : absB;
if (diff < EPSILON_ABSOLUTE)
return true;
if ((diff / max) < EPSILON_RELATIVE)
return true;
return false;
}
/**
* Get the first matrix element in the first row.
*
* @return Returns the m00.
* @since vecmath 1.5
*/
public final double getM00() {
return m00;
}
/**
* Set the first matrix element in the first row.
*
* @param m00
* The m00 to set.
*
* @since vecmath 1.5
*/
public final void setM00(double m00) {
this.m00 = m00;
}
/**
* Get the second matrix element in the first row.
*
* @return Returns the m01.
*
* @since vecmath 1.5
*/
public final double getM01() {
return m01;
}
/**
* Set the second matrix element in the first row.
*
* @param m01
* The m01 to set.
*
* @since vecmath 1.5
*/
public final void setM01(double m01) {
this.m01 = m01;
}
/**
* Get the third matrix element in the first row.
*
* @return Returns the m02.
*
* @since vecmath 1.5
*/
public final double getM02() {
return m02;
}
/**
* Set the third matrix element in the first row.
*
* @param m02
* The m02 to set.
*
* @since vecmath 1.5
*/
public final void setM02(double m02) {
this.m02 = m02;
}
/**
* Get first matrix element in the second row.
*
* @return Returns the m10.
*
* @since vecmath 1.5
*/
public final double getM10() {
return m10;
}
/**
* Set first matrix element in the second row.
*
* @param m10
* The m10 to set.
*
* @since vecmath 1.5
*/
public final void setM10(double m10) {
this.m10 = m10;
}
/**
* Get second matrix element in the second row.
*
* @return Returns the m11.
*
* @since vecmath 1.5
*/
public final double getM11() {
return m11;
}
/**
* Set the second matrix element in the second row.
*
* @param m11
* The m11 to set.
*
* @since vecmath 1.5
*/
public final void setM11(double m11) {
this.m11 = m11;
}
/**
* Get the third matrix element in the second row.
*
* @return Returns the m12.
*
* @since vecmath 1.5
*/
public final double getM12() {
return m12;
}
/**
* Set the third matrix element in the second row.
*
* @param m12
* The m12 to set.
*
* @since vecmath 1.5
*/
public final void setM12(double m12) {
this.m12 = m12;
}
/**
* Get the first matrix element in the third row.
*
* @return Returns the m20.
*
* @since vecmath 1.5
*/
public final double getM20() {
return m20;
}
/**
* Set the first matrix element in the third row.
*
* @param m20
* The m20 to set.
*
* @since vecmath 1.5
*/
public final void setM20(double m20) {
this.m20 = m20;
}
/**
* Get the second matrix element in the third row.
*
* @return Returns the m21.
*
* @since vecmath 1.5
*/
public final double getM21() {
return m21;
}
/**
* Set the second matrix element in the third row.
*
* @param m21
* The m21 to set.
*
* @since vecmath 1.5
*/
public final void setM21(double m21) {
this.m21 = m21;
}
/**
* Get the third matrix element in the third row .
*
* @return Returns the m22.
*
* @since vecmath 1.5
*/
public final double getM22() {
return m22;
}
/**
* Set the third matrix element in the third row.
*
* @param m22
* The m22 to set.
*
* @since vecmath 1.5
*/
public final void setM22(double m22) {
this.m22 = m22;
}
}