gcc/libjava/java/awt/geom/QuadCurve2D.java

/* QuadCurve2D.java -- represents a parameterized quadratic curve in 2-D space
   Copyright (C) 2002, 2003, 2004 Free Software Foundation

This file is part of GNU Classpath.

GNU Classpath 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 2, or (at your option)
any later version.

GNU Classpath 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
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02111-1307 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
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permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
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terms of your choice, provided that you also meet, for each linked
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this exception to your version of the library, but you are not
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exception statement from your version. */

package java.awt.geom;

import java.awt.Rectangle;
import java.awt.Shape;
import java.util.NoSuchElementException;


/**
 * A two-dimensional curve that is parameterized with a quadratic
 * function.
 *
 * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180"
 * alt="A drawing of a QuadCurve2D" />
 *
 * @author Eric Blake (ebb9@email.byu.edu)
 * @author Graydon Hoare (graydon@redhat.com)
 * @author Sascha Brawer (brawer@dandelis.ch)
 * @author Sven de Marothy (sven@physto.se)
 *
 * @since 1.2
 */
public abstract class QuadCurve2D implements Shape, Cloneable
{
  private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0;
  private static final double EPSILON = 1E-10;

  /**
   * Constructs a new QuadCurve2D. Typical users will want to
   * construct instances of a subclass, such as {@link
   * QuadCurve2D.Float} or {@link QuadCurve2D.Double}.
   */
  protected QuadCurve2D()
  {
  }

  /**
   * Returns the <i>x</i> coordinate of the curve&#x2019;s start
   * point.
   */
  public abstract double getX1();

  /**
   * Returns the <i>y</i> coordinate of the curve&#x2019;s start
   * point.
   */
  public abstract double getY1();

  /**
   * Returns the curve&#x2019;s start point.
   */
  public abstract Point2D getP1();

  /**
   * Returns the <i>x</i> coordinate of the curve&#x2019;s control
   * point.
   */
  public abstract double getCtrlX();

  /**
   * Returns the <i>y</i> coordinate of the curve&#x2019;s control
   * point.
   */
  public abstract double getCtrlY();

  /**
   * Returns the curve&#x2019;s control point.
   */
  public abstract Point2D getCtrlPt();

  /**
   * Returns the <i>x</i> coordinate of the curve&#x2019;s end
   * point.
   */
  public abstract double getX2();

  /**
   * Returns the <i>y</i> coordinate of the curve&#x2019;s end
   * point.
   */
  public abstract double getY2();

  /**
   * Returns the curve&#x2019;s end point.
   */
  public abstract Point2D getP2();

  /**
   * Changes the curve geometry, separately specifying each coordinate
   * value.
   *
   * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new start
   * point.
   *
   * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
   * point.
   *
   * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
   * control point.
   *
   * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
   * control point.
   *
   * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
   * point.
   *
   * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new end
   * point.
   */
  public abstract void setCurve(double x1, double y1, double cx, double cy,
                                double x2, double y2);

  /**
   * Changes the curve geometry, passing coordinate values in an
   * array.
   *
   * @param coords an array containing the new coordinate values.  The
   * <i>x</i> coordinate of the new start point is located at
   * <code>coords[offset]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
   * new control point is located at <code>coords[offset + 2]</code>,
   * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The
   * <i>x</i> coordinate of the new end point is located at
   * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 5]</code>.
   *
   * @param offset the offset of the first coordinate value in
   * <code>coords</code>.
   */
  public void setCurve(double[] coords, int offset)
  {
    setCurve(coords[offset++], coords[offset++], coords[offset++],
             coords[offset++], coords[offset++], coords[offset++]);
  }

  /**
   * Changes the curve geometry, specifying coordinate values in
   * separate Point objects.
   *
   * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180"
   * alt="A drawing of a QuadCurve2D" />
   *
   * <p>The curve does not keep any reference to the passed point
   * objects. Therefore, a later change to <code>p1</code>,
   * <code>c</code> <code>p2</code> will not affect the curve
   * geometry.
   *
   * @param p1 the new start point.
   * @param c the new control point.
   * @param p2 the new end point.
   */
  public void setCurve(Point2D p1, Point2D c, Point2D p2)
  {
    setCurve(p1.getX(), p1.getY(), c.getX(), c.getY(), p2.getX(), p2.getY());
  }

  /**
   * Changes the curve geometry, specifying coordinate values in an
   * array of Point objects.
   *
   * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180"
   * alt="A drawing of a QuadCurve2D" />
   *
   * <p>The curve does not keep references to the passed point
   * objects. Therefore, a later change to the <code>pts</code> array
   * or any of its elements will not affect the curve geometry.
   *
   * @param pts an array containing the points. The new start point
   * is located at <code>pts[offset]</code>, the new control
   * point at <code>pts[offset + 1]</code>, and the new end point
   * at <code>pts[offset + 2]</code>.
   *
   * @param offset the offset of the start point in <code>pts</code>.
   */
  public void setCurve(Point2D[] pts, int offset)
  {
    setCurve(pts[offset].getX(), pts[offset].getY(), pts[offset + 1].getX(),
             pts[offset + 1].getY(), pts[offset + 2].getX(),
             pts[offset + 2].getY());
  }

  /**
   * Changes the geometry of the curve to that of another curve.
   *
   * @param c the curve whose coordinates will be copied.
   */
  public void setCurve(QuadCurve2D c)
  {
    setCurve(c.getX1(), c.getY1(), c.getCtrlX(), c.getCtrlY(), c.getX2(),
             c.getY2());
  }

  /**
   * Calculates the squared flatness of a quadratic curve, directly
   * specifying each coordinate value. The flatness is the distance of
   * the control point to the line between start and end point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the square of the distance between C and the gray line, i.e.
   * the squared length of the red line.
   *
   * @param x1 the <i>x</i> coordinate of the start point P1.
   * @param y1 the <i>y</i> coordinate of the start point P1.
   * @param cx the <i>x</i> coordinate of the control point C.
   * @param cy the <i>y</i> coordinate of the control point C.
   * @param x2 the <i>x</i> coordinate of the end point P2.
   * @param y2 the <i>y</i> coordinate of the end point P2.
   */
  public static double getFlatnessSq(double x1, double y1, double cx,
                                     double cy, double x2, double y2)
  {
    return Line2D.ptSegDistSq(x1, y1, x2, y2, cx, cy);
  }

  /**
   * Calculates the flatness of a quadratic curve, directly specifying
   * each coordinate value. The flatness is the distance of the
   * control point to the line between start and end point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the distance between C and the gray line, i.e. the length of
   * the red line.
   *
   * @param x1 the <i>x</i> coordinate of the start point P1.
   * @param y1 the <i>y</i> coordinate of the start point P1.
   * @param cx the <i>x</i> coordinate of the control point C.
   * @param cy the <i>y</i> coordinate of the control point C.
   * @param x2 the <i>x</i> coordinate of the end point P2.
   * @param y2 the <i>y</i> coordinate of the end point P2.
   */
  public static double getFlatness(double x1, double y1, double cx, double cy,
                                   double x2, double y2)
  {
    return Line2D.ptSegDist(x1, y1, x2, y2, cx, cy);
  }

  /**
   * Calculates the squared flatness of a quadratic curve, specifying
   * the coordinate values in an array. The flatness is the distance
   * of the control point to the line between start and end point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the square of the distance between C and the gray line, i.e.
   * the squared length of the red line.
   *
   * @param coords an array containing the coordinate values.  The
   * <i>x</i> coordinate of the start point P1 is located at
   * <code>coords[offset]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
   * control point C is located at <code>coords[offset + 2]</code>,
   * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The
   * <i>x</i> coordinate of the end point P2 is located at
   * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 5]</code>.
   *
   * @param offset the offset of the first coordinate value in
   * <code>coords</code>.
   */
  public static double getFlatnessSq(double[] coords, int offset)
  {
    return Line2D.ptSegDistSq(coords[offset], coords[offset + 1],
                              coords[offset + 4], coords[offset + 5],
                              coords[offset + 2], coords[offset + 3]);
  }

  /**
   * Calculates the flatness of a quadratic curve, specifying the
   * coordinate values in an array. The flatness is the distance of
   * the control point to the line between start and end point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the the distance between C and the gray line, i.e.  the length of
   * the red line.
   *
   * @param coords an array containing the coordinate values.  The
   * <i>x</i> coordinate of the start point P1 is located at
   * <code>coords[offset]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
   * control point C is located at <code>coords[offset + 2]</code>,
   * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The
   * <i>x</i> coordinate of the end point P2 is located at
   * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at
   * <code>coords[offset + 5]</code>.
   *
   * @param offset the offset of the first coordinate value in
   * <code>coords</code>.
   */
  public static double getFlatness(double[] coords, int offset)
  {
    return Line2D.ptSegDist(coords[offset], coords[offset + 1],
                            coords[offset + 4], coords[offset + 5],
                            coords[offset + 2], coords[offset + 3]);
  }

  /**
   * Calculates the squared flatness of this curve. The flatness is
   * the distance of the control point to the line between start and
   * end point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the square of the distance between C and the gray line, i.e. the
   * squared length of the red line.
   */
  public double getFlatnessSq()
  {
    return Line2D.ptSegDistSq(getX1(), getY1(), getX2(), getY2(), getCtrlX(),
                              getCtrlY());
  }

  /**
   * Calculates the flatness of this curve. The flatness is the
   * distance of the control point to the line between start and end
   * point.
   *
   * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180"
   * alt="A drawing that illustrates the flatness" />
   *
   * <p>In the above drawing, the straight line connecting start point
   * P1 and end point P2 is depicted in gray.  The result will be the
   * the distance between C and the gray line, i.e.  the length of the
   * red line.
   */
  public double getFlatness()
  {
    return Line2D.ptSegDist(getX1(), getY1(), getX2(), getY2(), getCtrlX(),
                            getCtrlY());
  }

  /**
   * Subdivides this curve into two halves.
   *
   * <p><img src="doc-files/QuadCurve2D-3.png" width="700"
   * height="180" alt="A drawing that illustrates the effects of
   * subdividing a QuadCurve2D" />
   *
   * @param left a curve whose geometry will be set to the left half
   * of this curve, or <code>null</code> if the caller is not
   * interested in the left half.
   *
   * @param right a curve whose geometry will be set to the right half
   * of this curve, or <code>null</code> if the caller is not
   * interested in the right half.
   */
  public void subdivide(QuadCurve2D left, QuadCurve2D right)
  {
    // Use empty slots at end to share single array.
    double[] d = new double[]
                 {
                   getX1(), getY1(), getCtrlX(), getCtrlY(), getX2(), getY2(),
                   0, 0, 0, 0
                 };
    subdivide(d, 0, d, 0, d, 4);
    if (left != null)
      left.setCurve(d, 0);
    if (right != null)
      right.setCurve(d, 4);
  }

  /**
   * Subdivides a quadratic curve into two halves.
   *
   * <p><img src="doc-files/QuadCurve2D-3.png" width="700"
   * height="180" alt="A drawing that illustrates the effects of
   * subdividing a QuadCurve2D" />
   *
   * @param src the curve to be subdivided.
   *
   * @param left a curve whose geometry will be set to the left half
   * of <code>src</code>, or <code>null</code> if the caller is not
   * interested in the left half.
   *
   * @param right a curve whose geometry will be set to the right half
   * of <code>src</code>, or <code>null</code> if the caller is not
   * interested in the right half.
   */
  public static void subdivide(QuadCurve2D src, QuadCurve2D left,
                               QuadCurve2D right)
  {
    src.subdivide(left, right);
  }

  /**
   * Subdivides a quadratic curve into two halves, passing all
   * coordinates in an array.
   *
   * <p><img src="doc-files/QuadCurve2D-3.png" width="700"
   * height="180" alt="A drawing that illustrates the effects of
   * subdividing a QuadCurve2D" />
   *
   * <p>The left end point and the right start point will always be
   * identical. Memory-concious programmers thus may want to pass the
   * same array for both <code>left</code> and <code>right</code>, and
   * set <code>rightOff</code> to <code>leftOff + 4</code>.
   *
   * @param src an array containing the coordinates of the curve to be
   * subdivided.  The <i>x</i> coordinate of the start point is
   * located at <code>src[srcOff]</code>, its <i>y</i> at
   * <code>src[srcOff + 1]</code>.  The <i>x</i> coordinate of the
   * control point is located at <code>src[srcOff + 2]</code>, its
   * <i>y</i> at <code>src[srcOff + 3]</code>.  The <i>x</i>
   * coordinate of the end point is located at <code>src[srcOff +
   * 4]</code>, its <i>y</i> at <code>src[srcOff + 5]</code>.
   *
   * @param srcOff an offset into <code>src</code>, specifying
   * the index of the start point&#x2019;s <i>x</i> coordinate.
   *
   * @param left an array that will receive the coordinates of the
   * left half of <code>src</code>. It is acceptable to pass
   * <code>src</code>. A caller who is not interested in the left half
   * can pass <code>null</code>.
   *
   * @param leftOff an offset into <code>left</code>, specifying the
   * index where the start point&#x2019;s <i>x</i> coordinate will be
   * stored.
   *
   * @param right an array that will receive the coordinates of the
   * right half of <code>src</code>. It is acceptable to pass
   * <code>src</code> or <code>left</code>. A caller who is not
   * interested in the right half can pass <code>null</code>.
   *
   * @param rightOff an offset into <code>right</code>, specifying the
   * index where the start point&#x2019;s <i>x</i> coordinate will be
   * stored.
   */
  public static void subdivide(double[] src, int srcOff, double[] left,
                               int leftOff, double[] right, int rightOff)
  {
    double x1;
    double y1;
    double xc;
    double yc;
    double x2;
    double y2;

    x1 = src[srcOff];
    y1 = src[srcOff + 1];
    xc = src[srcOff + 2];
    yc = src[srcOff + 3];
    x2 = src[srcOff + 4];
    y2 = src[srcOff + 5];

    if (left != null)
      {
	left[leftOff] = x1;
	left[leftOff + 1] = y1;
      }

    if (right != null)
      {
	right[rightOff + 4] = x2;
	right[rightOff + 5] = y2;
      }

    x1 = (x1 + xc) / 2;
    x2 = (xc + x2) / 2;
    xc = (x1 + x2) / 2;
    y1 = (y1 + yc) / 2;
    y2 = (y2 + yc) / 2;
    yc = (y1 + y2) / 2;

    if (left != null)
      {
	left[leftOff + 2] = x1;
	left[leftOff + 3] = y1;
	left[leftOff + 4] = xc;
	left[leftOff + 5] = yc;
      }

    if (right != null)
      {
	right[rightOff] = xc;
	right[rightOff + 1] = yc;
	right[rightOff + 2] = x2;
	right[rightOff + 3] = y2;
      }
  }

  /**
   * Finds the non-complex roots of a quadratic equation, placing the
   * results into the same array as the equation coefficients. The
   * following equation is being solved:
   *
   * <blockquote><code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
   * + <code>eqn[1]</code> &#xb7; <i>x</i>
   * + <code>eqn[0]</code>
   * = 0
   * </blockquote>
   *
   * <p>For some background about solving quadratic equations, see the
   * article <a href=
   * "http://planetmath.org/encyclopedia/QuadraticFormula.html"
   * >&#x201c;Quadratic Formula&#x201d;</a> in <a href=
   * "http://planetmath.org/">PlanetMath</a>. For an extensive library
   * of numerical algorithms written in the C programming language,
   * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific
   * Library</a>.
   *
   * @see #solveQuadratic(double[], double[])
   * @see CubicCurve2D#solveCubic(double[], double[])
   *
   * @param eqn an array with the coefficients of the equation. When
   * this procedure has returned, <code>eqn</code> will contain the
   * non-complex solutions of the equation, in no particular order.
   *
   * @return the number of non-complex solutions. A result of 0
   * indicates that the equation has no non-complex solutions. A
   * result of -1 indicates that the equation is constant (i.e.,
   * always or never zero).
   *
   * @author <a href="mailto:bjg@network-theory.com">Brian Gough</a>
   * (original C implementation in the <a href=
   * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
   *
   * @author <a href="mailto:brawer@dandelis.ch">Sascha Brawer</a>
   * (adaptation to Java)
   */
  public static int solveQuadratic(double[] eqn)
  {
    return solveQuadratic(eqn, eqn);
  }

  /**
   * Finds the non-complex roots of a quadratic equation. The
   * following equation is being solved:
   *
   * <blockquote><code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
   * + <code>eqn[1]</code> &#xb7; <i>x</i>
   * + <code>eqn[0]</code>
   * = 0
   * </blockquote>
   *
   * <p>For some background about solving quadratic equations, see the
   * article <a href=
   * "http://planetmath.org/encyclopedia/QuadraticFormula.html"
   * >&#x201c;Quadratic Formula&#x201d;</a> in <a href=
   * "http://planetmath.org/">PlanetMath</a>. For an extensive library
   * of numerical algorithms written in the C programming language,
   * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific
   * Library</a>.
   *
   * @see CubicCurve2D#solveCubic(double[],double[])
   *
   * @param eqn an array with the coefficients of the equation.
   *
   * @param res an array into which the non-complex roots will be
   * stored.  The results may be in an arbitrary order. It is safe to
   * pass the same array object reference for both <code>eqn</code>
   * and <code>res</code>.
   *
   * @return the number of non-complex solutions. A result of 0
   * indicates that the equation has no non-complex solutions. A
   * result of -1 indicates that the equation is constant (i.e.,
   * always or never zero).
   *
   * @author <a href="mailto:bjg@network-theory.com">Brian Gough</a>
   * (original C implementation in the <a href=
   * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
   *
   * @author <a href="mailto:brawer@dandelis.ch">Sascha Brawer</a>
   * (adaptation to Java)
   */
  public static int solveQuadratic(double[] eqn, double[] res)
  {
    // Taken from poly/solve_quadratic.c in the GNU Scientific Library
    // (GSL), cvs revision 1.7 of 2003-07-26. For the original source,
    // see http://www.gnu.org/software/gsl/
    //
    // Brian Gough, the author of that code, has granted the
    // permission to use it in GNU Classpath under the GNU Classpath
    // license, and has assigned the copyright to the Free Software
    // Foundation.
    //
    // The Java implementation is very similar to the GSL code, but
    // not a strict one-to-one copy. For example, GSL would sort the
    // result.
    double a;
    double b;
    double c;
    double disc;

    c = eqn[0];
    b = eqn[1];
    a = eqn[2];

    // Check for linear or constant functions. This is not done by the
    // GNU Scientific Library.  Without this special check, we
    // wouldn't return -1 for constant functions, and 2 instead of 1
    // for linear functions.
    if (a == 0)
      {
	if (b == 0)
	  return -1;

	res[0] = -c / b;
	return 1;
      }

    disc = b * b - 4 * a * c;

    if (disc < 0)
      return 0;

    if (disc == 0)
      {
	// The GNU Scientific Library returns two identical results here.
	// We just return one.
	res[0] = -0.5 * b / a;
	return 1;
      }

    // disc > 0
    if (b == 0)
      {
	double r;

	r = Math.abs(0.5 * Math.sqrt(disc) / a);
	res[0] = -r;
	res[1] = r;
      }
    else
      {
	double sgnb;
	double temp;

	sgnb = (b > 0 ? 1 : -1);
	temp = -0.5 * (b + sgnb * Math.sqrt(disc));

	// The GNU Scientific Library sorts the result here. We don't.
	res[0] = temp / a;
	res[1] = c / temp;
      }
    return 2;
  }

  /**
   * Determines whether a point is inside the area bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; a QuadCurve2D.
   */
  public boolean contains(double x, double y)
  {
    if (! getBounds2D().contains(x, y))
      return false;

    return ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0);
  }

  /**
   * Determines whether a point is inside the area bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; a QuadCurve2D.
   */
  public boolean contains(Point2D p)
  {
    return contains(p.getX(), p.getY());
  }

  /**
   * Determines whether any part of a rectangle is inside the area bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; in a CubicCurve2D.
   */
  public boolean intersects(double x, double y, double w, double h)
  {
    if (! getBounds2D().contains(x, y, w, h))
      return false;

    /* Does any edge intersect? */
    if (getAxisIntersections(x, y, true, w) != 0 /* top */
        || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
        || getAxisIntersections(x + w, y, false, h) != 0 /* right */
        || getAxisIntersections(x, y, false, h) != 0) /* left */
      return true;

    /* No intersections, is any point inside? */
    if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
      return true;

    return false;
  }

  /**
   * Determines whether any part of a Rectangle2D is inside the area bounded 
   * by the curve and the straight line connecting its end points.
   * @see #intersects(double, double, double, double)
   */
  public boolean intersects(Rectangle2D r)
  {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Determines whether a rectangle is entirely inside the area bounded
   * by the curve and the straight line connecting its end points.
   *
   * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180"
   * alt="A drawing of the area spanned by the curve" />
   *
   * <p>The above drawing illustrates in which area points are
   * considered &#x201c;inside&#x201d; a QuadCurve2D.
   * @see #contains(double, double)
   */
  public boolean contains(double x, double y, double w, double h)
  {
    if (! getBounds2D().intersects(x, y, w, h))
      return false;

    /* Does any edge intersect? */
    if (getAxisIntersections(x, y, true, w) != 0 /* top */
        || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
        || getAxisIntersections(x + w, y, false, h) != 0 /* right */
        || getAxisIntersections(x, y, false, h) != 0) /* left */
      return false;

    /* No intersections, is any point inside? */
    if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
      return true;

    return false;
  }

  /**
   * Determines whether a Rectangle2D is entirely inside the area that is 
   * bounded by the curve and the straight line connecting its end points.
   * @see #contains(double, double, double, double)
   */
  public boolean contains(Rectangle2D r)
  {
    return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Determines the smallest rectangle that encloses the
   * curve&#x2019;s start, end and control point. As the illustration
   * below shows, the invisible control point may cause the bounds to
   * be much larger than the area that is actually covered by the
   * curve.
   *
   * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180"
   * alt="An illustration of the bounds of a QuadCurve2D" />
   */
  public Rectangle getBounds()
  {
    return getBounds2D().getBounds();
  }

  public PathIterator getPathIterator(final AffineTransform at)
  {
    return new PathIterator()
      {
	/** Current coordinate. */
	private int current = 0;

	public int getWindingRule()
	{
	  return WIND_NON_ZERO;
	}

	public boolean isDone()
	{
	  return current >= 2;
	}

	public void next()
	{
	  current++;
	}

	public int currentSegment(float[] coords)
	{
	  int result;
	  switch (current)
	    {
	    case 0:
	      coords[0] = (float) getX1();
	      coords[1] = (float) getY1();
	      result = SEG_MOVETO;
	      break;
	    case 1:
	      coords[0] = (float) getCtrlX();
	      coords[1] = (float) getCtrlY();
	      coords[2] = (float) getX2();
	      coords[3] = (float) getY2();
	      result = SEG_QUADTO;
	      break;
	    default:
	      throw new NoSuchElementException("quad iterator out of bounds");
	    }
	  if (at != null)
	    at.transform(coords, 0, coords, 0, 2);
	  return result;
	}

	public int currentSegment(double[] coords)
	{
	  int result;
	  switch (current)
	    {
	    case 0:
	      coords[0] = getX1();
	      coords[1] = getY1();
	      result = SEG_MOVETO;
	      break;
	    case 1:
	      coords[0] = getCtrlX();
	      coords[1] = getCtrlY();
	      coords[2] = getX2();
	      coords[3] = getY2();
	      result = SEG_QUADTO;
	      break;
	    default:
	      throw new NoSuchElementException("quad iterator out of bounds");
	    }
	  if (at != null)
	    at.transform(coords, 0, coords, 0, 2);
	  return result;
	}
      };
  }

  public PathIterator getPathIterator(AffineTransform at, double flatness)
  {
    return new FlatteningPathIterator(getPathIterator(at), flatness);
  }

  /**
   * Creates a new curve with the same contents as this one.
   *
   * @return the clone.
   */
  public Object clone()
  {
    try
      {
	return super.clone();
      }
    catch (CloneNotSupportedException e)
      {
	throw (Error) new InternalError().initCause(e); // Impossible
      }
  }

  /**
   * Helper method used by contains() and intersects() methods
   * Return the number of curve/line intersections on a given axis
   * extending from a certain point. useYaxis is true for using the Y axis,
   * @param x x coordinate of the origin point
   * @param y y coordinate of the origin point
   * @param useYaxis axis to follow, if true the positive Y axis is used,
   * false uses the positive X axis.
   *
   * This is an implementation of the line-crossings algorithm,
   * Detailed in an article on Eric Haines' page:
   * http://www.acm.org/tog/editors/erich/ptinpoly/
   */
  private int getAxisIntersections(double x, double y, boolean useYaxis,
                                   double distance)
  {
    int nCrossings = 0;
    double a0;
    double a1;
    double a2;
    double b0;
    double b1;
    double b2;
    double[] r = new double[3];
    int nRoots;

    a0 = a2 = 0.0;

    if (useYaxis)
      {
	a0 = getY1() - y;
	a1 = getCtrlY() - y;
	a2 = getY2() - y;
	b0 = getX1() - x;
	b1 = getCtrlX() - x;
	b2 = getX2() - x;
      }
    else
      {
	a0 = getX1() - x;
	a1 = getCtrlX() - x;
	a2 = getX2() - x;
	b0 = getY1() - y;
	b1 = getCtrlY() - y;
	b2 = getY2() - y;
      }

    /* If the axis intersects a start/endpoint, shift it up by some small 
       amount to guarantee the line is 'inside'
       If this is not done,bad behaviour may result for points on that axis. */
    if (a0 == 0.0 || a2 == 0.0)
      {
	double small = getFlatness() * EPSILON;
	if (a0 == 0.0)
	  a0 -= small;

	if (a2 == 0.0)
	  a2 -= small;
      }

    r[0] = a0;
    r[1] = 2 * (a1 - a0);
    r[2] = (a2 - 2 * a1 + a0);

    nRoots = solveQuadratic(r);
    for (int i = 0; i < nRoots; i++)
      {
	double t = r[i];
	if (t >= 0.0 && t <= 1.0)
	  {
	    double crossing = t * t * (b2 - 2 * b1 + b0) + 2 * t * (b1 - b0)
	                      + b0;
	    /* single root is always doubly degenerate in quads */
	    if (crossing > 0 && crossing < distance)
	      nCrossings += (nRoots == 1) ? 2 : 1;
	  }
      }

    if (useYaxis)
      {
	if (Line2D.linesIntersect(b0, a0, b2, a2, EPSILON, 0.0, distance, 0.0))
	  nCrossings++;
      }
    else
      {
	if (Line2D.linesIntersect(a0, b0, a2, b2, 0.0, EPSILON, 0.0, distance))
	  nCrossings++;
      }

    return (nCrossings);
  }

  /**
   * A two-dimensional curve that is parameterized with a quadratic
   * function and stores coordinate values in double-precision
   * floating-point format.
   *
   * @see QuadCurve2D.Float
   *
   * @author Eric Blake (ebb9@email.byu.edu)
   * @author Sascha Brawer (brawer@dandelis.ch)
   */
  public static class Double extends QuadCurve2D
  {
    /**
     * The <i>x</i> coordinate of the curve&#x2019;s start point.
     */
    public double x1;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s start point.
     */
    public double y1;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s control point.
     */
    public double ctrlx;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s control point.
     */
    public double ctrly;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s end point.
     */
    public double x2;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s end point.
     */
    public double y2;

    /**
     * Constructs a new QuadCurve2D that stores its coordinate values
     * in double-precision floating-point format. All points are
     * initially at position (0, 0).
     */
    public Double()
    {
    }

    /**
     * Constructs a new QuadCurve2D that stores its coordinate values
     * in double-precision floating-point format, specifying the
     * initial position of each point.
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param cx the <i>x</i> coordinate of the curve&#x2019;s control
     * point.
     *
     * @param cy the <i>y</i> coordinate of the curve&#x2019;s control
     * point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
     * point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public Double(double x1, double y1, double cx, double cy, double x2,
                  double y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      ctrlx = cx;
      ctrly = cy;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getX1()
    {
      return x1;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getY1()
    {
      return y1;
    }

    /**
     * Returns the curve&#x2019;s start point.
     */
    public Point2D getP1()
    {
      return new Point2D.Double(x1, y1);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s control
     * point.
     */
    public double getCtrlX()
    {
      return ctrlx;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s control
     * point.
     */
    public double getCtrlY()
    {
      return ctrly;
    }

    /**
     * Returns the curve&#x2019;s control point.
     */
    public Point2D getCtrlPt()
    {
      return new Point2D.Double(ctrlx, ctrly);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public double getX2()
    {
      return x2;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public double getY2()
    {
      return y2;
    }

    /**
     * Returns the curve&#x2019;s end point.
     */
    public Point2D getP2()
    {
      return new Point2D.Double(x2, y2);
    }

    /**
     * Changes the geometry of the curve.
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
     * end point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new
     * end point.
     */
    public void setCurve(double x1, double y1, double cx, double cy,
                         double x2, double y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      ctrlx = cx;
      ctrly = cy;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Determines the smallest rectangle that encloses the
     * curve&#x2019;s start, end and control point. As the
     * illustration below shows, the invisible control point may cause
     * the bounds to be much larger than the area that is actually
     * covered by the curve.
     *
     * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180"
     * alt="An illustration of the bounds of a QuadCurve2D" />
     */
    public Rectangle2D getBounds2D()
    {
      double nx1 = Math.min(Math.min(x1, ctrlx), x2);
      double ny1 = Math.min(Math.min(y1, ctrly), y2);
      double nx2 = Math.max(Math.max(x1, ctrlx), x2);
      double ny2 = Math.max(Math.max(y1, ctrly), y2);
      return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1);
    }
  }

  /**
   * A two-dimensional curve that is parameterized with a quadratic
   * function and stores coordinate values in single-precision
   * floating-point format.
   *
   * @see QuadCurve2D.Double
   *
   * @author Eric Blake (ebb9@email.byu.edu)
   * @author Sascha Brawer (brawer@dandelis.ch)
   */
  public static class Float extends QuadCurve2D
  {
    /**
     * The <i>x</i> coordinate of the curve&#x2019;s start point.
     */
    public float x1;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s start point.
     */
    public float y1;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s control point.
     */
    public float ctrlx;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s control point.
     */
    public float ctrly;

    /**
     * The <i>x</i> coordinate of the curve&#x2019;s end point.
     */
    public float x2;

    /**
     * The <i>y</i> coordinate of the curve&#x2019;s end point.
     */
    public float y2;

    /**
     * Constructs a new QuadCurve2D that stores its coordinate values
     * in single-precision floating-point format. All points are
     * initially at position (0, 0).
     */
    public Float()
    {
    }

    /**
     * Constructs a new QuadCurve2D that stores its coordinate values
     * in single-precision floating-point format, specifying the
     * initial position of each point.
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     *
     * @param cx the <i>x</i> coordinate of the curve&#x2019;s control
     * point.
     *
     * @param cy the <i>y</i> coordinate of the curve&#x2019;s control
     * point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
     * point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public Float(float x1, float y1, float cx, float cy, float x2, float y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      ctrlx = cx;
      ctrly = cy;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getX1()
    {
      return x1;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s start
     * point.
     */
    public double getY1()
    {
      return y1;
    }

    /**
     * Returns the curve&#x2019;s start point.
     */
    public Point2D getP1()
    {
      return new Point2D.Float(x1, y1);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s control
     * point.
     */
    public double getCtrlX()
    {
      return ctrlx;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s control
     * point.
     */
    public double getCtrlY()
    {
      return ctrly;
    }

    /**
     * Returns the curve&#x2019;s control point.
     */
    public Point2D getCtrlPt()
    {
      return new Point2D.Float(ctrlx, ctrly);
    }

    /**
     * Returns the <i>x</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public double getX2()
    {
      return x2;
    }

    /**
     * Returns the <i>y</i> coordinate of the curve&#x2019;s end
     * point.
     */
    public double getY2()
    {
      return y2;
    }

    /**
     * Returns the curve&#x2019;s end point.
     */
    public Point2D getP2()
    {
      return new Point2D.Float(x2, y2);
    }

    /**
     * Changes the geometry of the curve, specifying coordinate values
     * as double-precision floating-point numbers.
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
     * end point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new
     * end point.
     */
    public void setCurve(double x1, double y1, double cx, double cy,
                         double x2, double y2)
    {
      this.x1 = (float) x1;
      this.y1 = (float) y1;
      ctrlx = (float) cx;
      ctrly = (float) cy;
      this.x2 = (float) x2;
      this.y2 = (float) y2;
    }

    /**
     * Changes the geometry of the curve, specifying coordinate values
     * as single-precision floating-point numbers.
     *
     * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
     * start point.
     *
     * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
     * control point.
     *
     * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
     * end point.
     *
     * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new
     * end point.
     */
    public void setCurve(float x1, float y1, float cx, float cy, float x2,
                         float y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      ctrlx = cx;
      ctrly = cy;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Determines the smallest rectangle that encloses the
     * curve&#x2019;s start, end and control point. As the
     * illustration below shows, the invisible control point may cause
     * the bounds to be much larger than the area that is actually
     * covered by the curve.
     *
     * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180"
     * alt="An illustration of the bounds of a QuadCurve2D" />
     */
    public Rectangle2D getBounds2D()
    {
      float nx1 = (float) Math.min(Math.min(x1, ctrlx), x2);
      float ny1 = (float) Math.min(Math.min(y1, ctrly), y2);
      float nx2 = (float) Math.max(Math.max(x1, ctrlx), x2);
      float ny2 = (float) Math.max(Math.max(y1, ctrly), y2);
      return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
    }
  }
}