AffineTransform.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 Lesser 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 Lesser General Public License
 * for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program. If not, see <http://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;

/**
 * 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 {

    /**
     * coefficients for x coordinate.
     */
    private double m00, m01, m02, m03;

    /**
     * coefficients for y coordinate.
     */
    private double m10, m11, m12, m13;

    /**
     * coefficients for z coordinate.
     */
    private double m20, m21, m22, m23;

    // ===================================================================
    // constructors

    /**
     * Creates a new affine transform3D set to 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];
        } 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() {
        if (m00 != 1)
            return false;
        if (m11 != 1)
            return false;
        if (m22 != 1)
            return false;
        if (m01 != 0)
            return false;
        if (m02 != 0)
            return false;
        if (m03 != 0)
            return false;
        if (m10 != 0)
            return false;
        if (m12 != 0)
            return false;
        if (m13 != 0)
            return false;
        if (m20 != 0)
            return false;
        if (m21 != 0)
            return false;
        if (m23 != 0)
            return false;
        return true;
    }

    /**
     * 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};
    }

    /**
     * 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());
    }

    @Override
    public Vector3 apply(Vector3 vector) {
        return Vector3.at(
                vector.getX() * m00 + vector.getY() * m01 + vector.getZ() * m02 + m03,
                vector.getX() * m10 + vector.getY() * m11 + vector.getZ() * m12 + m13,
                vector.getX() * m20 + vector.getY() * m21 + vector.getZ() * m22 + m23);
    }

    public AffineTransform combine(AffineTransform other) {
        return concatenate(other);
    }

    @Override
    public Transform combine(Transform other) {
        if (other instanceof AffineTransform) {
            return concatenate((AffineTransform) other);
        } else {
            return new CombinedTransform(this, other);
        }
    }

    @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);
    }


}