PMatrix2D.java

/* -*- mode: java; c-basic-offset: 2; indent-tabs-mode: nil -*- */

/*
  Part of the Processing project - http://processing.org

  Copyright (c) 2005-08 Ben Fry and Casey Reas

  This library 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 2.1 of the License, or (at your option) any later version.

  This library 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 library; if not, write to the
  Free Software Foundation, Inc., 59 Temple Place, Suite 330,
  Boston, MA  02111-1307  USA
*/

package processing.core;


/**
 * 3x2 affine matrix implementation.
 * Matrices are used to describe a transformation; see {@link PMatrix} for a
 * general description. This matrix looks like the following when multiplying
 * a vector (x, y) in {@code mult()}.
 * <pre>
 * [m00 m01 m02][x]   [m00*x + m01*y + m02*1]   [x']
 * [m10 m11 m12][y] = [m10*x + m11*y + m12*1] = [y']
 * [ 0   0   1 ][1]   [ 0*x  +  0*y  +  1*1 ]   [ 1]</pre>
 * (x', y') is returned. The values in the matrix determine the transformation.
 * They are modified by the various transformation functions.
 */
public class PMatrix2D implements PMatrix {

  public float m00, m01, m02;
  public float m10, m11, m12;


  /**
   * Create a new matrix, set to the identity matrix.
   */
  public PMatrix2D() {
    reset();
  }


  public PMatrix2D(float m00, float m01, float m02,
                   float m10, float m11, float m12) {
    set(m00, m01, m02,
        m10, m11, m12);
  }


  public PMatrix2D(PMatrix matrix) {
    set(matrix);
  }


  public void reset() {
    set(1, 0, 0,
        0, 1, 0);
  }


  /**
   * Returns a copy of this PMatrix.
   */
  public PMatrix2D get() {
    PMatrix2D outgoing = new PMatrix2D();
    outgoing.set(this);
    return outgoing;
  }


  /**
   * Copies the matrix contents into a 6 entry float array.
   * If target is null (or not the correct size), a new array will be created.
   * Returned in the order {@code {m00, m01, m02, m10, m11, m12}}.
   */
  public float[] get(float[] target) {
    if ((target == null) || (target.length != 6)) {
      target = new float[6];
    }
    target[0] = m00;
    target[1] = m01;
    target[2] = m02;

    target[3] = m10;
    target[4] = m11;
    target[5] = m12;

    return target;
  }


  /**
   * If matrix is a PMatrix2D, sets this matrix to be a copy of it.
   * @throws IllegalArgumentException If <tt>matrix</tt> is not 2D.
   */
  public void set(PMatrix matrix) {
    if (matrix instanceof PMatrix2D) {
      PMatrix2D src = (PMatrix2D) matrix;
      set(src.m00, src.m01, src.m02,
          src.m10, src.m11, src.m12);
    } else {
      throw new IllegalArgumentException("PMatrix2D.set() only accepts PMatrix2D objects.");
    }
  }


  /**
   * Unavailable in 2D. Does nothing.
   */
  public void set(PMatrix3D src) {
  }


  public void set(float[] source) {
    m00 = source[0];
    m01 = source[1];
    m02 = source[2];

    m10 = source[3];
    m11 = source[4];
    m12 = source[5];
  }


  /**
   * Sets the matrix content.
   */
  public void set(float m00, float m01, float m02,
                  float m10, float m11, float m12) {
    this.m00 = m00; this.m01 = m01; this.m02 = m02;
    this.m10 = m10; this.m11 = m11; this.m12 = m12;
  }


  /**
   * Unavailable in 2D. Does nothing.
   */
  public void set(float m00, float m01, float m02, float m03,
                  float m10, float m11, float m12, float m13,
                  float m20, float m21, float m22, float m23,
                  float m30, float m31, float m32, float m33) {

  }


  public void translate(float tx, float ty) {
    m02 = tx*m00 + ty*m01 + m02;
    m12 = tx*m10 + ty*m11 + m12;
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void translate(float x, float y, float z) {
    throw new IllegalArgumentException("Cannot use translate(x, y, z) on a PMatrix2D.");
  }


  // Implementation roughly based on AffineTransform.
  public void rotate(float angle) {
    float s = sin(angle);
    float c = cos(angle);

    float temp1 = m00;
    float temp2 = m01;
    m00 =  c * temp1 + s * temp2;
    m01 = -s * temp1 + c * temp2;
    temp1 = m10;
    temp2 = m11;
    m10 =  c * temp1 + s * temp2;
    m11 = -s * temp1 + c * temp2;
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void rotateX(float angle) {
    throw new IllegalArgumentException("Cannot use rotateX() on a PMatrix2D.");
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void rotateY(float angle) {
    throw new IllegalArgumentException("Cannot use rotateY() on a PMatrix2D.");
  }


  public void rotateZ(float angle) {
    rotate(angle);
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void rotate(float angle, float v0, float v1, float v2) {
    throw new IllegalArgumentException("Cannot use this version of rotate() on a PMatrix2D.");
  }


  public void scale(float s) {
    scale(s, s);
  }


  public void scale(float sx, float sy) {
    m00 *= sx;  m01 *= sy;
    m10 *= sx;  m11 *= sy;
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void scale(float x, float y, float z) {
    throw new IllegalArgumentException("Cannot use this version of scale() on a PMatrix2D.");
  }


  public void shearX(float angle) {
    apply(1, 0, 1,  tan(angle), 0, 0);
  }


  public void shearY(float angle) {
    apply(1, 0, 1,  0, tan(angle), 0);
  }


  public void apply(PMatrix source) {
    if (source instanceof PMatrix2D) {
      apply((PMatrix2D) source);
    } else if (source instanceof PMatrix3D) {
      apply((PMatrix3D) source);
    }
  }


  public void apply(PMatrix2D source) {
    apply(source.m00, source.m01, source.m02,
          source.m10, source.m11, source.m12);
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void apply(PMatrix3D source) {
    throw new IllegalArgumentException("Cannot use apply(PMatrix3D) on a PMatrix2D.");
  }


  public void apply(float n00, float n01, float n02,
                    float n10, float n11, float n12) {
    float t0 = m00;
    float t1 = m01;
    m00  = n00 * t0 + n10 * t1;
    m01  = n01 * t0 + n11 * t1;
    m02 += n02 * t0 + n12 * t1;

    t0 = m10;
    t1 = m11;
    m10  = n00 * t0 + n10 * t1;
    m11  = n01 * t0 + n11 * t1;
    m12 += n02 * t0 + n12 * t1;
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void apply(float n00, float n01, float n02, float n03,
                    float n10, float n11, float n12, float n13,
                    float n20, float n21, float n22, float n23,
                    float n30, float n31, float n32, float n33) {
    throw new IllegalArgumentException("Cannot use this version of apply() on a PMatrix2D.");
  }


  /**
   * Apply another matrix to the left of this one.
   */
  public void preApply(PMatrix source) {
    if (source instanceof PMatrix2D) {
      preApply((PMatrix2D) source);
    } else if (source instanceof PMatrix3D) {
      preApply((PMatrix3D) source);
    }
  }


  public void preApply(PMatrix2D left) {
    preApply(left.m00, left.m01, left.m02,
             left.m10, left.m11, left.m12);
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void preApply(PMatrix3D left) {
    throw new IllegalArgumentException("Cannot use preApply(PMatrix3D) on a PMatrix2D.");
  }


  public void preApply(float n00, float n01, float n02,
                       float n10, float n11, float n12) {
    float t0 = m02;
    float t1 = m12;
    n02 += t0 * n00 + t1 * n01;
    n12 += t0 * n10 + t1 * n11;

    m02 = n02;
    m12 = n12;

    t0 = m00;
    t1 = m10;
    m00 = t0 * n00 + t1 * n01;
    m10 = t0 * n10 + t1 * n11;

    t0 = m01;
    t1 = m11;
    m01 = t0 * n00 + t1 * n01;
    m11 = t0 * n10 + t1 * n11;
  }


  /**
   * Unavailable in 2D.
   * @throws IllegalArgumentException
   */
  public void preApply(float n00, float n01, float n02, float n03,
                       float n10, float n11, float n12, float n13,
                       float n20, float n21, float n22, float n23,
                       float n30, float n31, float n32, float n33) {
    throw new IllegalArgumentException("Cannot use this version of preApply() on a PMatrix2D.");
  }


  //////////////////////////////////////////////////////////////


  /**
   * {@inheritDoc}
   * Ignores any z component.
   */
  public PVector mult(PVector source, PVector target) {
    if (target == null) {
      target = new PVector();
    }
    target.x = m00*source.x + m01*source.y + m02;
    target.y = m10*source.x + m11*source.y + m12;
    return target;
  }


  /**
   * Multiply a two element vector against this matrix.
   * If out is null or not length four, a new float array will be returned.
   * The values for vec and out can be the same (though that's less efficient).
   */
  public float[] mult(float vec[], float out[]) {
    if (out == null || out.length != 2) {
      out = new float[2];
    }

    if (vec == out) {
      float tx = m00*vec[0] + m01*vec[1] + m02;
      float ty = m10*vec[0] + m11*vec[1] + m12;

      out[0] = tx;
      out[1] = ty;

    } else {
      out[0] = m00*vec[0] + m01*vec[1] + m02;
      out[1] = m10*vec[0] + m11*vec[1] + m12;
    }

    return out;
  }


  /**
   * Returns the x-coordinate of the result of multiplying the point (x, y)
   * by this matrix.
   */
  public float multX(float x, float y) {
    return m00*x + m01*y + m02;
  }


  /**
   * Returns the y-coordinate of the result of multiplying the point (x, y)
   * by this matrix.
   */
  public float multY(float x, float y) {
    return m10*x + m11*y + m12;
  }



  /**
   * Unavailable in 2D. Does nothing.
   */
  public void transpose() {
  }


  /*
   * Implementation stolen from OpenJDK.
   */
  public boolean invert() {
    float determinant = determinant();
    if (Math.abs(determinant) <= Float.MIN_VALUE) {
      return false;
    }

    float t00 = m00;
    float t01 = m01;
    float t02 = m02;
    float t10 = m10;
    float t11 = m11;
    float t12 = m12;

    m00 =  t11 / determinant;
    m10 = -t10 / determinant;
    m01 = -t01 / determinant;
    m11 =  t00 / determinant;
    m02 = (t01 * t12 - t11 * t02) / determinant;
    m12 = (t10 * t02 - t00 * t12) / determinant;

    return true;
  }


  /**
   * @return the determinant of the matrix
   */
  public float determinant() {
    return m00 * m11 - m01 * m10;
  }


  //////////////////////////////////////////////////////////////


  public void print() {
    int big = (int) abs(max(PApplet.max(abs(m00), abs(m01), abs(m02)),
                            PApplet.max(abs(m10), abs(m11), abs(m12))));

    int digits = 1;
    if (Float.isNaN(big) || Float.isInfinite(big)) {  // avoid infinite loop
      digits = 5;
    } else {
      while ((big /= 10) != 0) digits++;  // cheap log()
    }

    System.out.println(PApplet.nfs(m00, digits, 4) + " " +
                       PApplet.nfs(m01, digits, 4) + " " +
                       PApplet.nfs(m02, digits, 4));

    System.out.println(PApplet.nfs(m10, digits, 4) + " " +
                       PApplet.nfs(m11, digits, 4) + " " +
                       PApplet.nfs(m12, digits, 4));

    System.out.println();
  }


  //////////////////////////////////////////////////////////////

  // TODO these need to be added as regular API, but the naming and
  // implementation needs to be improved first. (e.g. actually keeping track
  // of whether the matrix is in fact identity internally.)


  protected boolean isIdentity() {
    return ((m00 == 1) && (m01 == 0) && (m02 == 0) &&
            (m10 == 0) && (m11 == 1) && (m12 == 0));
  }


  // TODO make this more efficient, or move into PMatrix2D
  protected boolean isWarped() {
    return ((m00 != 1) || (m01 != 0) &&
            (m10 != 0) || (m11 != 1));
  }


  //////////////////////////////////////////////////////////////


  static private final float max(float a, float b) {
    return (a > b) ? a : b;
  }

  static private final float abs(float a) {
    return (a < 0) ? -a : a;
  }

  static private final float sin(float angle) {
    return (float)Math.sin(angle);
  }

  static private final float cos(float angle) {
    return (float)Math.cos(angle);
  }

  static private final float tan(float angle) {
    return (float)Math.tan(angle);
  }
}