369 lines
12 KiB
Java
369 lines
12 KiB
Java
/*
|
|
* WorldEdit, a Minecraft world manipulation toolkit
|
|
* Copyright (C) sk89q <http://www.sk89q.com>
|
|
* Copyright (C) WorldEdit team and contributors
|
|
*
|
|
* This program is free software: you can redistribute it and/or modify
|
|
* it under the terms of the GNU General Public License as published by
|
|
* the Free Software Foundation, either version 3 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* This program 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 for more details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License
|
|
* along with this program. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
package com.sk89q.worldedit.math.transform;
|
|
|
|
import com.sk89q.worldedit.math.BlockVector3;
|
|
import com.sk89q.worldedit.math.MathUtils;
|
|
import com.sk89q.worldedit.math.Vector3;
|
|
|
|
import java.io.Serializable;
|
|
|
|
/**
|
|
* An affine transform.
|
|
*
|
|
* <p>This class is from the
|
|
* <a href="http://geom-java.sourceforge.net/index.html">JavaGeom project</a>,
|
|
* which is licensed under LGPL v2.1.</p>
|
|
*/
|
|
public class AffineTransform implements Transform, Serializable {
|
|
|
|
/**
|
|
* coefficients for x coordinate.
|
|
*/
|
|
private final double m00; // x-only
|
|
private final double m01; // x-y
|
|
private final double m02; // x-z
|
|
private final double m03; // translation
|
|
|
|
/**
|
|
* coefficients for y coordinate.
|
|
*/
|
|
private final double m10; // x-y
|
|
private final double m11; // y-only
|
|
private final double m12; // y-z
|
|
private final double m13; // translation
|
|
|
|
/**
|
|
* coefficients for z coordinate.
|
|
*/
|
|
private final double m20; // x-z
|
|
private final double m21; // y-z
|
|
private final double m22; // z-only
|
|
private final double m23; // translation
|
|
|
|
// ===================================================================
|
|
// constructors
|
|
|
|
/**
|
|
* Creates a new affine transform3D set to the identity.
|
|
*/
|
|
public AffineTransform() {
|
|
// init to identity matrix
|
|
m00 = m11 = m22 = 1;
|
|
m01 = m02 = m03 = 0;
|
|
m10 = m12 = m13 = 0;
|
|
m20 = m21 = m23 = 0;
|
|
}
|
|
|
|
public AffineTransform(double[] coefs) {
|
|
if (coefs.length == 9) {
|
|
m00 = coefs[0];
|
|
m01 = coefs[1];
|
|
m02 = coefs[2];
|
|
m10 = coefs[3];
|
|
m11 = coefs[4];
|
|
m12 = coefs[5];
|
|
m20 = coefs[6];
|
|
m21 = coefs[7];
|
|
m22 = coefs[8];
|
|
m03 = m13 = m23 = 0;
|
|
} else if (coefs.length == 12) {
|
|
m00 = coefs[0];
|
|
m01 = coefs[1];
|
|
m02 = coefs[2];
|
|
m03 = coefs[3];
|
|
m10 = coefs[4];
|
|
m11 = coefs[5];
|
|
m12 = coefs[6];
|
|
m13 = coefs[7];
|
|
m20 = coefs[8];
|
|
m21 = coefs[9];
|
|
m22 = coefs[10];
|
|
m23 = coefs[11];
|
|
} else {
|
|
throw new IllegalArgumentException(
|
|
"Input array must have 9 or 12 elements");
|
|
}
|
|
}
|
|
|
|
public AffineTransform(double xx, double yx, double zx, double tx,
|
|
double xy, double yy, double zy, double ty, double xz, double yz,
|
|
double zz, double tz) {
|
|
m00 = xx;
|
|
m01 = yx;
|
|
m02 = zx;
|
|
m03 = tx;
|
|
m10 = xy;
|
|
m11 = yy;
|
|
m12 = zy;
|
|
m13 = ty;
|
|
m20 = xz;
|
|
m21 = yz;
|
|
m22 = zz;
|
|
m23 = tz;
|
|
}
|
|
|
|
// ===================================================================
|
|
// accessors
|
|
|
|
@Override
|
|
public boolean isIdentity() {
|
|
return m00 == m11 && m11 == m22 && m22 == 1
|
|
&& m01 == m02 && m02 == m03 && m03 == 0
|
|
&& m10 == m12 && m12 == m13 && m13 == 0
|
|
&& m20 == m21 && m21 == m23 && m23 == 0;
|
|
}
|
|
|
|
/**
|
|
* Returns the affine coefficients of the transform. Result is an array of
|
|
* 12 double.
|
|
*/
|
|
public double[] coefficients() {
|
|
return new double[]{m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23};
|
|
}
|
|
|
|
public boolean isOffAxis() {
|
|
double[] c = coefficients();
|
|
for (int i = 0; i < c.length; i++) {
|
|
if ((i + 1) % 4 != 0) {
|
|
if (Math.abs(c[i]) != 1 && c[i] != 0) {
|
|
return true;
|
|
}
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
* Computes the determinant of this transform. Can be zero.
|
|
*
|
|
* @return the determinant of the transform.
|
|
*/
|
|
private double determinant() {
|
|
return m00 * (m11 * m22 - m12 * m21) - m01 * (m10 * m22 - m20 * m12)
|
|
+ m02 * (m10 * m21 - m20 * m11);
|
|
}
|
|
|
|
/**
|
|
* Computes the inverse affine transform.
|
|
*/
|
|
@Override
|
|
public AffineTransform inverse() {
|
|
double det = this.determinant();
|
|
return new AffineTransform(
|
|
(m11 * m22 - m21 * m12) / det,
|
|
(m21 * m02 - m01 * m22) / det,
|
|
(m01 * m12 - m11 * m02) / det,
|
|
(m01 * (m22 * m13 - m12 * m23) + m02 * (m11 * m23 - m21 * m13)
|
|
- m03 * (m11 * m22 - m21 * m12)) / det,
|
|
(m20 * m12 - m10 * m22) / det,
|
|
(m00 * m22 - m20 * m02) / det,
|
|
(m10 * m02 - m00 * m12) / det,
|
|
(m00 * (m12 * m23 - m22 * m13) - m02 * (m10 * m23 - m20 * m13)
|
|
+ m03 * (m10 * m22 - m20 * m12)) / det,
|
|
(m10 * m21 - m20 * m11) / det,
|
|
(m20 * m01 - m00 * m21) / det,
|
|
(m00 * m11 - m10 * m01) / det,
|
|
(m00 * (m21 * m13 - m11 * m23) + m01 * (m10 * m23 - m20 * m13)
|
|
- m03 * (m10 * m21 - m20 * m11)) / det);
|
|
}
|
|
|
|
// ===================================================================
|
|
// general methods
|
|
|
|
/**
|
|
* Returns the affine transform created by applying first the affine
|
|
* transform given by {@code that}, then this affine transform.
|
|
*
|
|
* @param that the transform to apply first
|
|
* @return the composition this * that
|
|
*/
|
|
public AffineTransform concatenate(AffineTransform that) {
|
|
double n00 = m00 * that.m00 + m01 * that.m10 + m02 * that.m20;
|
|
double n01 = m00 * that.m01 + m01 * that.m11 + m02 * that.m21;
|
|
double n02 = m00 * that.m02 + m01 * that.m12 + m02 * that.m22;
|
|
double n03 = m00 * that.m03 + m01 * that.m13 + m02 * that.m23 + m03;
|
|
double n10 = m10 * that.m00 + m11 * that.m10 + m12 * that.m20;
|
|
double n11 = m10 * that.m01 + m11 * that.m11 + m12 * that.m21;
|
|
double n12 = m10 * that.m02 + m11 * that.m12 + m12 * that.m22;
|
|
double n13 = m10 * that.m03 + m11 * that.m13 + m12 * that.m23 + m13;
|
|
double n20 = m20 * that.m00 + m21 * that.m10 + m22 * that.m20;
|
|
double n21 = m20 * that.m01 + m21 * that.m11 + m22 * that.m21;
|
|
double n22 = m20 * that.m02 + m21 * that.m12 + m22 * that.m22;
|
|
double n23 = m20 * that.m03 + m21 * that.m13 + m22 * that.m23 + m23;
|
|
return new AffineTransform(
|
|
n00, n01, n02, n03,
|
|
n10, n11, n12, n13,
|
|
n20, n21, n22, n23);
|
|
}
|
|
|
|
/**
|
|
* Return the affine transform created by applying first this affine
|
|
* transform, then the affine transform given by {@code that}.
|
|
*
|
|
* @param that the transform to apply in a second step
|
|
* @return the composition that * this
|
|
*/
|
|
public AffineTransform preConcatenate(AffineTransform that) {
|
|
double n00 = that.m00 * m00 + that.m01 * m10 + that.m02 * m20;
|
|
double n01 = that.m00 * m01 + that.m01 * m11 + that.m02 * m21;
|
|
double n02 = that.m00 * m02 + that.m01 * m12 + that.m02 * m22;
|
|
double n03 = that.m00 * m03 + that.m01 * m13 + that.m02 * m23 + that.m03;
|
|
double n10 = that.m10 * m00 + that.m11 * m10 + that.m12 * m20;
|
|
double n11 = that.m10 * m01 + that.m11 * m11 + that.m12 * m21;
|
|
double n12 = that.m10 * m02 + that.m11 * m12 + that.m12 * m22;
|
|
double n13 = that.m10 * m03 + that.m11 * m13 + that.m12 * m23 + that.m13;
|
|
double n20 = that.m20 * m00 + that.m21 * m10 + that.m22 * m20;
|
|
double n21 = that.m20 * m01 + that.m21 * m11 + that.m22 * m21;
|
|
double n22 = that.m20 * m02 + that.m21 * m12 + that.m22 * m22;
|
|
double n23 = that.m20 * m03 + that.m21 * m13 + that.m22 * m23 + that.m23;
|
|
return new AffineTransform(
|
|
n00, n01, n02, n03,
|
|
n10, n11, n12, n13,
|
|
n20, n21, n22, n23);
|
|
}
|
|
|
|
public AffineTransform translate(Vector3 vec) {
|
|
return translate(vec.getX(), vec.getY(), vec.getZ());
|
|
}
|
|
|
|
public AffineTransform translate(BlockVector3 vec) {
|
|
return translate(vec.getX(), vec.getY(), vec.getZ());
|
|
}
|
|
|
|
public AffineTransform translate(double x, double y, double z) {
|
|
return concatenate(new AffineTransform(1, 0, 0, x, 0, 1, 0, y, 0, 0, 1, z));
|
|
}
|
|
|
|
public AffineTransform rotateX(double theta) {
|
|
double cot = MathUtils.dCos(theta);
|
|
double sit = MathUtils.dSin(theta);
|
|
return concatenate(
|
|
new AffineTransform(
|
|
1, 0, 0, 0,
|
|
0, cot, -sit, 0,
|
|
0, sit, cot, 0));
|
|
}
|
|
|
|
public AffineTransform rotateY(double theta) {
|
|
double cot = MathUtils.dCos(theta);
|
|
double sit = MathUtils.dSin(theta);
|
|
return concatenate(
|
|
new AffineTransform(
|
|
cot, 0, sit, 0,
|
|
0, 1, 0, 0,
|
|
-sit, 0, cot, 0));
|
|
}
|
|
|
|
public AffineTransform rotateZ(double theta) {
|
|
double cot = MathUtils.dCos(theta);
|
|
double sit = MathUtils.dSin(theta);
|
|
return concatenate(
|
|
new AffineTransform(
|
|
cot, -sit, 0, 0,
|
|
sit, cot, 0, 0,
|
|
0, 0, 1, 0));
|
|
}
|
|
|
|
public AffineTransform scale(double s) {
|
|
return scale(s, s, s);
|
|
}
|
|
|
|
public AffineTransform scale(double sx, double sy, double sz) {
|
|
return concatenate(new AffineTransform(sx, 0, 0, 0, 0, sy, 0, 0, 0, 0, sz, 0));
|
|
}
|
|
|
|
public AffineTransform scale(Vector3 vec) {
|
|
return scale(vec.getX(), vec.getY(), vec.getZ());
|
|
}
|
|
|
|
public boolean isScaled(Vector3 vector) {
|
|
boolean flip = vector.getX() != 0 && m00 < 0;
|
|
if (vector.getY() != 0 && m11 < 0) {
|
|
flip = !flip;
|
|
}
|
|
if (vector.getZ() != 0 && m22 < 0) {
|
|
flip = !flip;
|
|
}
|
|
if (flip) {
|
|
return true;
|
|
}
|
|
// Check for flip-and-rotate
|
|
if (vector.getX() != 0 && vector.getY() != 0 && ((m01 < 0 && m10 < 0) || (m01 > 0 && m10 > 0))) {
|
|
flip = true;
|
|
}
|
|
if (vector.getX() != 0 && vector.getZ() != 0 && ((m02 < 0 && m20 < 0) || (m02 > 0 && m20 > 0))) {
|
|
flip = !flip;
|
|
}
|
|
if (vector.getY() != 0 && vector.getZ() != 0 && ((m12 < 0 && m21 < 0) || (m12 > 0 && m21 > 0))) {
|
|
flip = !flip;
|
|
}
|
|
return flip;
|
|
}
|
|
|
|
@Override
|
|
public Vector3 apply(Vector3 vector) {
|
|
double x = (vector.getX() * m00 + vector.getY() * m01 + vector.getZ() * m02 + m03);
|
|
double y = (vector.getX() * m10 + vector.getY() * m11 + vector.getZ() * m12 + m13);
|
|
double z = (vector.getX() * m20 + vector.getY() * m21 + vector.getZ() * m22 + m23);
|
|
vector = vector.mutX(x);
|
|
vector = vector.mutY(y);
|
|
vector = vector.mutZ(z);
|
|
return vector;
|
|
}
|
|
|
|
public AffineTransform combine(AffineTransform other) {
|
|
return concatenate(other);
|
|
}
|
|
|
|
@Override
|
|
public Transform combine(Transform other) {
|
|
if (other instanceof Identity || other.isIdentity()) {
|
|
return this;
|
|
} else if (other instanceof AffineTransform) {
|
|
return concatenate((AffineTransform) other);
|
|
} else {
|
|
return new CombinedTransform(this, other);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Returns if this affine transform represents a horizontal flip.
|
|
*/
|
|
public boolean isHorizontalFlip() {
|
|
// use the determinant of the x-z submatrix to check if this is a horizontal flip
|
|
return m00 * m22 - m02 * m20 < 0;
|
|
}
|
|
|
|
/**
|
|
* Returns if this affine transform represents a vertical flip.
|
|
*/
|
|
public boolean isVerticalFlip() {
|
|
return m11 < 0;
|
|
}
|
|
|
|
@Override
|
|
public String toString() {
|
|
return String.format("Affine[%g %g %g %g, %g %g %g %g, %g %g %g %g]}", m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23);
|
|
}
|
|
|
|
|
|
}
|