/*
 * @(#)QuadCurve2D.java	1.22 00/02/02
 *
 * Copyright 1997-2000 Sun Microsystems, Inc. All Rights Reserved.
 * 
 * This software is the proprietary information of Sun Microsystems, Inc.  
 * Use is subject to license terms.
 * 
 */

package java.awt.geom;

import java.awt.Shape;
import java.awt.Rectangle;

/**
 * The <code>QuadCurve2D</code> class defines a quadratic parametric curve
 * segment in (x, y) coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects that
 * store a 2D quadratic curve segment.
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @version 	1.22, 02/02/00
 * @author	Jim Graham
 */
public abstract class QuadCurve2D implements Shape, Cloneable {
    /**
     * A quadratic parametric curve segment specified with 
     * <code>float</code> coordinates.
     */

    public static class Float extends QuadCurve2D {

	/**
	 * The x coordinate of the start point of the quadratic curve
         * segment.
	 */
	public float x1;

	/**
	 * The y coordinate of the start point of the quadratic curve
         * segment.
	 */
	public float y1;

	/**
	 * The x coordinate of the control point of the quadratic curve
         * segment.
	 */
	public float ctrlx;

	/**
	 * The y coordinate of the control point of the quadratic curve
         * segment.
	 */
	public float ctrly;

	/**
	 * The x coordinate of the end point of the quadratic curve
         * segment.
	 */
	public float x2;

	/**
	 * The y coordinate of the end point of the quadratic curve
         * segment.
	 */
	public float y2;

	/**
	 * Constructs and initializes a <code>QuadCurve2D</code> with
         * coordinates (0, 0, 0, 0, 0, 0).
	 */
	public Float() {
	}

	/**
	 * Constructs and initializes a <code>QuadCurve2D</code> from the
         * specified coordinates.
         * @param x1, y1 the starting point coordinates
         * @param ctrlx, ctrly the coordinates of the control point
         * @param x2, y2 the ending point coordinates
	 */
	public Float(float x1, float y1,
		     float ctrlx, float ctrly,
		     float x2, float y2) {
	    setCurve(x1, y1, ctrlx, ctrly, x2, y2);
	}

	/**
	 * Returns the x coordinate of the start point in 
         * <code>double</code> precision.
         * @return the x coordinate of the starting point.
	 */
	public double getX1() {
	    return (double) x1;
	}

	/**
	 * Returns the y coordinate of the start point in 
         * <code>double</code> precision.
         * @return the y coordinate of the starting point.
	 */
	public double getY1() {
	    return (double) y1;
	}

	/**
	 * Returns the start point.
         * @return a {@link Point2D} object that is the starting point
         *		of this <code>QuadCurve2D</code>.
	 */
	public Point2D getP1() {
	    return new Point2D.Float(x1, y1);
	}

	/**
	 * Returns the x coordinate of the control point in 
         * <code>double</code> precision.
         * @return the x coordinate of the control point.
	 */
	public double getCtrlX() {
	    return (double) ctrlx;
	}

	/**
	 * Returns the y coordinate of the control point in 
         * <code>double</code> precision.
         * @return the y coordiante of the control point.
	 */
	public double getCtrlY() {
	    return (double) ctrly;
	}

	/**
	 * Returns the control point.
         * @return a <code>Point2D</code> that is the control point of
         *	this <code>QuadCurve2D</code>.
	 */
	public Point2D getCtrlPt() {
	    return new Point2D.Float(ctrlx, ctrly);
	}

	/**
	 * Returns the x coordinate of the end point in 
         * <code>double</code> precision.
         * @return the x coordinate of the end point.
	 */
	public double getX2() {
	    return (double) x2;
	}

	/**
	 * Returns the y coordinate of the end point in 
         * <code>double</code> precision.
         * @return the y coordiante of the end point.
	 */
	public double getY2() {
	    return (double) y2;
	}

	/**
	 * Returns the end point.
         * @return a <code>Point2D</code> that is the end point of this
         * 		<code>QuadCurve2D</code>.
	 */
	public Point2D getP2() {
	    return new Point2D.Float(x2, y2);
	}

	/**
	 * Sets the location of the endpoints and controlpoint of this 
         * <code>QuadCurve2D</code> to the specified <code>double</code>
         * coordinates.
         * @param x1, y1 the coordinates of the starting point
         * @param ctrlx, ctrly the coordinates of the control point
         * @param x2 y2 the coordinates of the ending point
	 */
	public void setCurve(double x1, double y1,
			     double ctrlx, double ctrly,
			     double x2, double y2) {
	    this.x1    = (float) x1;
	    this.y1    = (float) y1;
	    this.ctrlx = (float) ctrlx;
	    this.ctrly = (float) ctrly;
	    this.x2    = (float) x2;
	    this.y2    = (float) y2;
	}

	/**
	 * Sets the location of the endpoints and controlpoint of this curve
	 * to the specified <code>float</code> coordinates.
         * @param x1, y1 the coordinates of the starting point
         * @param ctrlx, ctrly the coordinates of the control point
         * @param x2, y2 the coordinates of the ending point
	 */
	public void setCurve(float x1, float y1,
			     float ctrlx, float ctrly,
			     float x2, float y2) {
	    this.x1    = x1;
	    this.y1    = y1;
	    this.ctrlx = ctrlx;
	    this.ctrly = ctrly;
	    this.x2    = x2;
	    this.y2    = y2;
	}

	/**
	 * Returns the bounding box of this <code>QuadCurve2D</code>.
         * @return a {@link Rectangle2D} that is the bounding box
         *		of the shape of this <code>QuadCurve2D</code>.
	 */
	public Rectangle2D getBounds2D() {
	    float left   = Math.min(Math.min(x1, x2), ctrlx);
	    float top    = Math.min(Math.min(y1, y2), ctrly);
	    float right  = Math.max(Math.max(x1, x2), ctrlx);
	    float bottom = Math.max(Math.max(y1, y2), ctrly);
	    return new Rectangle2D.Float(left, top,
					 right - left, bottom - top);
	}
    }

    /**
     * A quadratic parametric curve segment specified with 
     * <code>double</code> coordinates.
     */
    public static class Double extends QuadCurve2D {
	/**
	 * The x coordinate of the start point of the quadratic curve
         * segment.
	 */
	public double x1;

	/**
	 * The x coordinate of the start point of the quadratic curve
         * segment.
	 */
	public double y1;

	/**
	 * The x coordinate of the control point of the quadratic curve
         * segment.
	 */
	public double ctrlx;

	/**
	 * The y coordinate of the control point of the quadratic curve
         * segment.
	 */
	public double ctrly;

	/**
	 * The x coordinate of the end point of the quadratic curve
         * segment.
	 */
	public double x2;

	/**
	 * The y coordinate of the end point of the quadratic curve
         * segment.
	 */
	public double y2;

	/**
	 * Constructs and initializes a <code>QuadCurve2D</code> with
         * coordinates (0, 0, 0, 0, 0, 0).
	 */
	public Double() {
	}

	/**
	 * Constructs and initializes a <code>QuadCurve2D</code> from the
         * specified coordinates.
         * @param x1, y1 the coordinates of the starting point
         * @param ctrlx, ctrly the coordinates of the control point
         * @param x2, y1 the coordinates of the ending point
	 */
	public Double(double x1, double y1,
		      double ctrlx, double ctrly,
		      double x2, double y2) {
	    setCurve(x1, y1, ctrlx, ctrly, x2, y2);
	}

	/**
	 * Returns the x coordinate of the start point in 
         * <code>double</code> precision.
         * @return the x coordinate of the starting point.
	 */
	public double getX1() {
	    return x1;
	}

	/**
	 * Returns the y coordinate of the start point in 
         * <code>double</code> precision.
         * @return the y coordiante of the starting point.
	 */
	public double getY1() {
	    return y1;
	}

	/**
	 * Returns the start point.
         * @return a <code>Point2D</code> that is the starting point
         *		of this <code>QuadCurve2D</code>.
	 */
	public Point2D getP1() {
	    return new Point2D.Double(x1, y1);
	}

	/**
	 * Returns the x coordinate of the control point in 
         * <code>double</code> precision.
         * @return the x coordinate of the control point.
	 */
	public double getCtrlX() {
	    return ctrlx;
	}

	/**
	 * Returns the y coordinate of the control point in 
         * <code>double</code> precision.
         * @return the y coordiante of the control point.
	 */
	public double getCtrlY() {
	    return ctrly;
	}

	/**
	 * Returns the control point.
         * @return a <code>Point2D</code> object that is the control
         * point of this <code>QuadCurve2D</code>. 
	 */
	public Point2D getCtrlPt() {
	    return new Point2D.Double(ctrlx, ctrly);
	}

	/**
	 * Returns the x coordinate of the end point in 
         * <code>double</code> precision.
         * @return the x coordiante of the end point.
	 */
	public double getX2() {
	    return x2;
	}

	/**
	 * Returns the y coordinate of the end point in 
         * <code>double</code> precision.
         * @return the y coordiante of the end point.
	 */
	public double getY2() {
	    return y2;
	}

	/**
	 * Returns the end point.
         * @return a <code>Point2D</code> that is the end point
         *	of this <code>QuadCurve2D</code>.
	 */
	public Point2D getP2() {
	    return new Point2D.Double(x2, y2);
	}

	/**
	 * Sets the location of the endpoints and controlpoint of this curve
	 * to the specified <code>double</code> coordinates.
         * @param x1, y1 the coordinates of the starting point
         * @param ctrlx, ctrly the coordinates of the control point
         * @param x2, y1 the coordinates of the ending point
	 */
	public void setCurve(double x1, double y1,
			     double ctrlx, double ctrly,
			     double x2, double y2) {
	    this.x1    = x1;
	    this.y1    = y1;
	    this.ctrlx = ctrlx;
	    this.ctrly = ctrly;
	    this.x2    = x2;
	    this.y2    = y2;
	}

	/**
	 * Returns the bounding box of this <code>QuadCurve2D</code>.
         * @return a <code>Rectangle2D</code> that is the bounding
         * 	box of the shape of this <code>QuadCurve2D</code>.
	 */
	public Rectangle2D getBounds2D() {
	    double left   = Math.min(Math.min(x1, x2), ctrlx);
	    double top    = Math.min(Math.min(y1, y2), ctrly);
	    double right  = Math.max(Math.max(x1, x2), ctrlx);
	    double bottom = Math.max(Math.max(y1, y2), ctrly);
	    return new Rectangle2D.Double(left, top,
					  right - left, bottom - top);
	}
    }

    /**
     * This is an abstract class that cannot be instantiated directly.
     * Type-specific implementation subclasses are available for
     * instantiation and provide a number of formats for storing
     * the information necessary to satisfy the various accessor
     * methods below.
     *
     * @see java.awt.geom.QuadCurve2D.Float
     * @see java.awt.geom.QuadCurve2D.Double
     */
    protected QuadCurve2D() {
    }

    /**
     * Returns the x coordinate of the start point in 
     * <code>double</code> in precision.
     * @return the x coordinate of the start point.
     */
    public abstract double getX1();

    /**
     * Returns the y coordinate of the start point in 
     * <code>double</code> precision.
     * @return the y coordinate of the start point.
     */
    public abstract double getY1();

    /**
     * Returns the start point.
     * @return a <code>Point2D</code> that is the start point of this
     * 		<code>QuadCurve2D</code>.
     */
    public abstract Point2D getP1();

    /**
     * Returns the x coordinate of the control point in 
     * <code>double</code> precision.
     * @return x coordinate the control point
     */
    public abstract double getCtrlX();

    /**
     * Returns the y coordinate of the control point in 
     * <code>double</code> precision.
     * @return the y coordinate of the control point.
     */
    public abstract double getCtrlY();

    /**
     * Returns the control point.
     * @return a <code>Point2D</code> that is the control point of this
     * 		<code>Point2D</code>.
     */
    public abstract Point2D getCtrlPt();

    /**
     * Returns the x coordinate of the end point in 
     * <code>double</code> precision.
     * @return the x coordiante of the end point.
     */
    public abstract double getX2();

    /**
     * Returns the y coordinate of the end point in 
     * <code>double</code> precision.
     * @return the y coordinate of the end point.
     */
    public abstract double getY2();

    /**
     * Returns the end point.
     * @return a <code>Point</code> object that is the end point
     * 		of this <code>Point2D</code>.
     */
    public abstract Point2D getP2();

    /**
     * Sets the location of the endpoints and controlpoint of this curve
     * to the specified <code>double</code> coordinates.
     * @param x1, y1 the coordinates of the starting point
     * @param ctrlx, ctrly the coordinates of the control point
     * @param x2, y1 the coordinates of the ending point
     */
    public abstract void setCurve(double x1, double y1,
				  double ctrlx, double ctrly,
				  double x2, double y2);

    /**
     * Sets the location of the endpoints and controlpoints of this 
     * <code>QuadCurve2D</code> to the <code>double</code> coordinates at
     * the specified offset in the specified array.
     * @param coords the array containing coordinate values
     * @param offset the index into the array from which to start
     *		getting the coordinate values and assigning them to this
     *		<code>QuadCurve2D</code>
     */
    public void setCurve(double[] coords, int offset) {
	setCurve(coords[offset + 0], coords[offset + 1],
		 coords[offset + 2], coords[offset + 3],
		 coords[offset + 4], coords[offset + 5]);
    }

    /**
     * Sets the location of the endpoints and controlpoint of this
     * <code>QuadCurve2D</code> to the specified <code>Point2D</code> 
     * coordinates.
     * @param p1 the starting point
     * @param cp the control point
     * @param p2 the ending point
     */
    public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
	setCurve(p1.getX(), p1.getY(),
		 cp.getX(), cp.getY(),
		 p2.getX(), p2.getY());
    }

    /**
     * Sets the location of the endpoints and controlpoints of this
     * <code>QuadCurve2D</code> to the coordinates of the 
     * <code>Point2D</code> objects at the specified offset in
     * the specified array.
     * @param pts an array containing <code>Point2D</code> that define
     *		coordinate values
     * @param offset the index into <code>pts</code> at which to start
     *		getting the coordinate values and assigning them to this
     *		<code>QuadCurve2D</code>
     */
    public void setCurve(Point2D[] pts, int offset) {
	setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
		 pts[offset + 1].getX(), pts[offset + 1].getY(),
		 pts[offset + 2].getX(), pts[offset + 2].getY());
    }

    /**
     * Sets the location of the endpoints and controlpoint of this 
     * <code>QuadCurve2D</code> to the same as those in the specified
     * <code>QuadCurve2D</code>.
     * @param c the specified <code>QuadCurve2D</code>
     */
    public void setCurve(QuadCurve2D c) {
	setCurve(c.getX1(), c.getY1(),
		 c.getCtrlX(), c.getCtrlY(),
		 c.getX2(), c.getY2());
    }

    /**
     * Returns the square of the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the indicated controlpoints.
     * @param x1, y1 the coordinates of the starting point
     * @param ctrlx, ctrly the coordinates of the control point
     * @param x2, y1 the coordinates of the ending point
     * @return the square of the flatness of the quadratic curve
     *		defined by the specified coordinates.
     */
    public static double getFlatnessSq(double x1, double y1,
				       double ctrlx, double ctrly,
				       double x2, double y2) {
	return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
    }

    /**
     * Returns the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the indicated controlpoints.
     * @param x1, y1 the coordinates of the starting point
     * @param ctrlx, ctrly the coordinates of the control point
     * @param x2, y1 the coordinates of the ending point
     * @return the flatness of the quadratic curve defined by the 
     *		specified coordinates. 
     */
    public static double getFlatness(double x1, double y1,
				     double ctrlx, double ctrly,
				     double x2, double y2) {
	return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
    }

    /**
     * Returns the square of the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the controlpoints stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> at which to
     *		to start getting the values from the array and 
     *		assigning them to a quadratic curve
     * @return the flatness of the quadratic curve that is defined by the
     * 		values in the specified array at the specified index.
     */
    public static double getFlatnessSq(double coords[], int offset) {
	return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
				  coords[offset + 4], coords[offset + 5],
				  coords[offset + 2], coords[offset + 3]);
    }

    /**
     * Returns the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the controlpoints stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> at which to
     *		start getting the coordinate values and assigning 
     *		them to a quadratic curve
     * @return the flatness of a quadratic curve defined by the 
     *		specified array at the specified offset.
     */
    public static double getFlatness(double coords[], int offset) {
	return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
				coords[offset + 4], coords[offset + 5],
				coords[offset + 2], coords[offset + 3]);
    }

    /**
     * Returns the square of the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of this 
     * <code>QuadCurve2D</code>.
     * @return the square of the flatness of this
     *		<code>QuadCurve2D</code>.
     */
    public double getFlatnessSq() {
	return Line2D.ptSegDistSq(getX1(), getY1(),
				  getX2(), getY2(),
				  getCtrlX(), getCtrlY());
    }

    /**
     * Returns the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of this
     * <code>QuadCurve2D</code>.
     * @return the flatness of this <code>QuadCurve2D</code>.
     */
    public double getFlatness() {
	return Line2D.ptSegDist(getX1(), getY1(),
				getX2(), getY2(),
				getCtrlX(), getCtrlY());
    }

    /**
     * Subdivides this <code>QuadCurve2D</code> and stores the resulting
     * two subdivided curves into the <code>left</code> and 
     * <code>right</code> curve parameters.
     * Either or both of the <code>left</code> and <code>right</code> 
     * objects can be the same as this <code>QuadCurve2D</code> or
     * <code>null</code>.
     * @param left the <code>QuadCurve2D</code> object for storing the
     * left or first half of the subdivided curve
     * @param right the <code>QuadCurve2D</code> object for storing the
     * right or second half of the subdivided curve
     */
    public void subdivide(QuadCurve2D left, QuadCurve2D right) {
	subdivide(this, left, right);
    }

    /**
     * Subdivides the quadratic curve specified by the <code>src</code> 
     * parameter and stores the resulting two subdivided curves into the
     * <code>left</code> and <code>right</code> curve parameters.
     * Either or both of the <code>left</code> and <code>right</code> 
     * objects can be the same as the <code>src</code> object or 
     * <code>null</code>.
     * @param src the quadratic curve to be subdivided
     * @param left the <code>QuadCurve2D</code> object for storing the
     *		left or first half of the subdivided curve
     * @param right the <code>QuadCurve2D</code> object for storing the
     *		right or second half of the subdivided curve
     */
    public static void subdivide(QuadCurve2D src,
				 QuadCurve2D left,
				 QuadCurve2D right) {
	double x1 = src.getX1();
	double y1 = src.getY1();
	double ctrlx = src.getCtrlX();
	double ctrly = src.getCtrlY();
	double x2 = src.getX2();
	double y2 = src.getY2();
	double ctrlx1 = (x1 + ctrlx) / 2.0;
	double ctrly1 = (y1 + ctrly) / 2.0;
	double ctrlx2 = (x2 + ctrlx) / 2.0;
	double ctrly2 = (y2 + ctrly) / 2.0;
	ctrlx = (ctrlx1 + ctrlx2) / 2.0;
	ctrly = (ctrly1 + ctrly2) / 2.0;
	if (left != null) {
	    left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
	}
	if (right != null) {
	    right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
	}
    }

    /**
     * Subdivides the quadratic curve specified by the coordinates
     * stored in the <code>src</code> array at indices 
     * <code>srcoff</code> through <code>srcoff</code> + 5
     * and stores the resulting two subdivided curves into the two
     * result arrays at the corresponding indices.
     * Either or both of the <code>left</code> and <code>right</code> 
     * arrays can be <code>null</code> or a reference to the same array
     * and offset as the <code>src</code> array.
     * Note that the last point in the first subdivided curve is the
     * same as the first point in the second subdivided curve.  Thus,
     * it is possible to pass the same array for <code>left</code> and
     * <code>right</code> and to use offsets such that 
     * <code>rightoff</code> equals <code>leftoff</code> + 4 in order
     * to avoid allocating extra storage for this common point.
     * @param src the array holding the coordinates for the source curve
     * @param srcoff the offset into the array of the beginning of the
     * the 6 source coordinates
     * @param left the array for storing the coordinates for the first
     * half of the subdivided curve
     * @param leftoff the offset into the array of the beginning of the
     * the 6 left coordinates
     * @param right the array for storing the coordinates for the second
     * half of the subdivided curve
     * @param rightoff the offset into the array of the beginning of the
     * the 6 right coordinates
     */
    public static void subdivide(double src[], int srcoff,
				 double left[], int leftoff,
				 double right[], int rightoff) {
	double x1 = src[srcoff + 0];
	double y1 = src[srcoff + 1];
	double ctrlx = src[srcoff + 2];
	double ctrly = src[srcoff + 3];
	double x2 = src[srcoff + 4];
	double y2 = src[srcoff + 5];
	if (left != null) {
	    left[leftoff + 0] = x1;
	    left[leftoff + 1] = y1;
	}
	if (right != null) {
	    right[rightoff + 4] = x2;
	    right[rightoff + 5] = y2;
	}
	x1 = (x1 + ctrlx) / 2.0;
	y1 = (y1 + ctrly) / 2.0;
	x2 = (x2 + ctrlx) / 2.0;
	y2 = (y2 + ctrly) / 2.0;
	ctrlx = (x1 + x2) / 2.0;
	ctrly = (y1 + y2) / 2.0;
	if (left != null) {
	    left[leftoff + 2] = x1;
	    left[leftoff + 3] = y1;
	    left[leftoff + 4] = ctrlx;
	    left[leftoff + 5] = ctrly;
	}
	if (right != null) {
	    right[rightoff + 0] = ctrlx;
	    right[rightoff + 1] = ctrly;
	    right[rightoff + 2] = x2;
	    right[rightoff + 3] = y2;
	}
    }

    /**
     * Solves the quadratic whose coefficients are in the <code>eqn</code> 
     * array and places the non-complex roots back into the same array,
     * returning the number of roots.  The quadratic solved is represented
     * by the equation:
     * <pre>
     *     eqn = {C, B, A};
     *     ax^2 + bx + c = 0
     * </pre>
     * A return value of <code>-1</code> is used to distinguish a constant
     * equation, which might be always 0 or never 0, from an equation that
     * has no zeroes.
     * @param equ the array that contains the quadratic coefficients
     * @return the number of roots, or <code>-1</code> if the equation is
     *		a constant
     */
    public static int solveQuadratic(double eqn[]) {
	return solveQuadratic(eqn, eqn);
    }

    /**
     * Solves the quadratic whose coefficients are in the <code>eqn</code> 
     * array and places the non-complex roots into the <code>res</code>
     * array, returning the number of roots.
     * The quadratic solved is represented by the equation:
     * <pre>
     *     eqn = {C, B, A};
     *     ax^2 + bx + c = 0
     * </pre>
     * A return value of <code>-1</code> is used to distinguish a constant
     * equation, which might be always 0 or never 0, from an equation that
     * has no zeroes.
     * @return the number of roots, or <code>-1</code> if the equation is
     *	a constant.
     */
    public static int solveQuadratic(double eqn[], double res[]) {
	double a = eqn[2];
	double b = eqn[1];
	double c = eqn[0];
	int roots = 0;
	if (a == 0.0) {
	    // The quadratic parabola has degenerated to a line.
	    if (b == 0.0) {
		// The line has degenerated to a constant.
		return -1;
	    } 
	    res[roots++] = -c / b;
	} else {
	    // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
	    double d = b * b - 4.0 * a * c;
	    if (d < 0.0) {
		// If d < 0.0, then there are no roots
		return 0;
	    }
	    d = Math.sqrt(d);
	    // For accuracy, calculate one root using:
	    //     (-b +/- d) / 2a
	    // and the other using:
	    //     2c / (-b +/- d)
	    // Choose the sign of the +/- so that b+d gets larger in magnitude
	    if (b < 0.0) {
		d = -d;
	    }
	    double q = (b + d) / -2.0;
	    // We already tested a for being 0 above
	    res[roots++] = q / a;
	    if (q != 0.0) {
		res[roots++] = c / q;
	    }
	}
	return roots;
    }

    /**
     * Tests if a specified coordinate is inside the boundary of the
     * shape of this <code>QuadCurve2D</code>.
     * @param x, y the specified coordinates
     * @return <code>true</code> if the specified coordinate is inside
     *		the boundary of the shape of this
     *		<code>QuadCurve2D</code> <code>false</code> otherwise.
     */
    public boolean contains(double x, double y) {
	// We count the "Y" crossings to determine if the point is
	// inside the curve bounded by its closing line.
	int crossings = 0;
	double x1 = getX1();
	double y1 = getY1();
	double x2 = getX2();
	double y2 = getY2();
	// First check for a crossing of the line connecting the endpoints
	double dy = y2 - y1;
	if ((dy > 0.0 && y >= y1 && y <= y2) ||
	    (dy < 0.0 && y <= y1 && y >= y2))
	{
	    if (x <= x1 + (y - y1) * (x2 - x1) / dy) {
		crossings++;
	    }
	}
	// Solve the Y parametric equation for intersections with y
	double ctrlx = getCtrlX();
	double ctrly = getCtrlY();
	boolean include0 = ((y2 - y1) * (ctrly - y1) >= 0);
	boolean include1 = ((y1 - y2) * (ctrly - y2) >= 0);
	double eqn[] = new double[3];
	double res[] = new double[3];
	fillEqn(eqn, y, y1, ctrly, y2);
	int roots = solveQuadratic(eqn, res);
	roots = evalQuadratic(res, roots,
			      include0, include1, eqn,
			      x1, ctrlx, x2);
	while (--roots >= 0) {
	    if (x < res[roots]) {
		crossings++;
	    }
	}
	return ((crossings & 1) == 1);
    }

    /**
     * Tests if a specified <code>Point2D</code> is inside the boundary of
     * the shape of this <code>QuadCurve2D</code>.
     * @param p the specified <code>Point2D</code>
     * @return <code>true</code> if the specified <code>Point2D</code> is
     *		inside the boundary of the shape of this
     *		<code>QuadCurve2D</code>.
     */
    public boolean contains(Point2D p) {
	return contains(p.getX(), p.getY());
    }

    /*
     * Fill an array with the coefficients of the parametric equation
     * in t, ready for solving against val with solveQuadratic.
     * We currently have:
     *     val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
     *                 = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
     *                 = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
     *               0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
     *               0 = C + Bt + At^2
     *     C = C1 - val
     *     B = 2*CP - 2*C1
     *     A = C1 - 2*CP + C2
     */
    private static void fillEqn(double eqn[], double val,
				double c1, double cp, double c2) {
	eqn[0] = c1 - val;
	eqn[1] = cp + cp - c1 - c1;
	eqn[2] = c1 - cp - cp + c2;
	return;
    }

    /*
     * Evaluate the t values in the first num slots of the vals[] array
     * and place the evaluated values back into the same array.  Only
     * evaluate t values that are within the range <0, 1>, including
     * the 0 and 1 ends of the range iff the include0 or include1
     * booleans are true.  If an "inflection" equation is handed in,
     * then any points which represent a point of inflection for that
     * quadratic equation are also ignored.
     */
    private static int evalQuadratic(double vals[], int num,
				     boolean include0,
				     boolean include1,
				     double inflect[],
				     double c1, double ctrl, double c2) {
	int j = 0;
	for (int i = 0; i < num; i++) {
	    double t = vals[i];
	    if ((include0 ? t >= 0 : t > 0) &&
		(include1 ? t <= 1 : t < 1) &&
		(inflect == null ||
		 inflect[1] + 2*inflect[2]*t != 0))
	    {
		double u = 1 - t;
		vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t;
	    }
	}
	return j;
    }

    private static final int BELOW = -2;
    private static final int LOWEDGE = -1;
    private static final int INSIDE = 0;
    private static final int HIGHEDGE = 1;
    private static final int ABOVE = 2;

    /*
     * Determine where coord lies with respect to the range from
     * low to high.  It is assumed that low <= high.  The return
     * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
     * or ABOVE.
     */
    private static int getTag(double coord, double low, double high) {
	if (coord <= low) {
	    return (coord < low ? BELOW : LOWEDGE);
	}
	if (coord >= high) {
	    return (coord > high ? ABOVE : HIGHEDGE);
	}
	return INSIDE;
    }

    /*
     * Determine if the pttag represents a coordinate that is already
     * in its test range, or is on the border with either of the two
     * opttags representing another coordinate that is "towards the
     * inside" of that test range.  In other words, are either of the
     * two "opt" points "drawing the pt inward"?
     */
    private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
	switch (pttag) {
	case BELOW:
	case ABOVE:
	default:
	    return false;
	case LOWEDGE:
	    return (opt1tag >= INSIDE || opt2tag >= INSIDE);
	case INSIDE:
	    return true;
	case HIGHEDGE:
	    return (opt1tag <= INSIDE || opt2tag <= INSIDE);
	}
    }

    /**
     * Tests if the shape of this <code>QuadCurve2D</code> intersects the
     * interior of a specified set of rectangular coordinates.
     * @param x, y the coordinates of the upper-left corner of the
     *		specified rectangular area
     * @param w the width of the specified rectangular area
     * @param h the height of the specified rectangular area
     * @return <code>true</code> if the shape of this
     * 		<code>QuadCurve2D</code> intersects the interior of the
     *		specified set of rectangular coordinates;
     *		<code>false</code> otherwise.
     */
    public boolean intersects(double x, double y, double w, double h) {
	// Trivially reject non-existant rectangles
	if (w < 0 || h < 0) {
	    return false;
	}

	// Trivially accept if either endpoint is inside the rectangle
	// (not on its border since it may end there and not go inside)
	// Record where they lie with respect to the rectangle.
	//     -1 => left, 0 => inside, 1 => right
	double x1 = getX1();
	double y1 = getY1();
	int x1tag = getTag(x1, x, x+w);
	int y1tag = getTag(y1, y, y+h);
	if (x1tag == INSIDE && y1tag == INSIDE) {
	    return true;
	}
	double x2 = getX2();
	double y2 = getY2();
	int x2tag = getTag(x2, x, x+w);
	int y2tag = getTag(y2, y, y+h);
	if (x2tag == INSIDE && y2tag == INSIDE) {
	    return true;
	}
	double ctrlx = getCtrlX();
	double ctrly = getCtrlY();
	int ctrlxtag = getTag(ctrlx, x, x+w);
	int ctrlytag = getTag(ctrly, y, y+h);

	// Trivially reject if all points are entirely to one side of
	// the rectangle.
	if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
	    return false;	// All points left
	}
	if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
	    return false;	// All points above
	}
	if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
	    return false;	// All points right
	}
	if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
	    return false;	// All points below
	}

	// Test for endpoints on the edge where either the segment
	// or the curve is headed "inwards" from them
	// Note: These tests are a superset of the fast endpoint tests
	//       above and thus repeat those tests, but take more time
	//       and cover more cases
	if (inwards(x1tag, x2tag, ctrlxtag) &&
	    inwards(y1tag, y2tag, ctrlytag))
	{
	    // First endpoint on border with either edge moving inside
	    return true;
	}
	if (inwards(x2tag, x1tag, ctrlxtag) &&
	    inwards(y2tag, y1tag, ctrlytag))
	{
	    // Second endpoint on border with either edge moving inside
	    return true;
	}

	// Trivially accept if endpoints span directly across the rectangle
	boolean xoverlap = (x1tag * x2tag <= 0);
	boolean yoverlap = (y1tag * y2tag <= 0);
	if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
	    return true;
	}
	if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
	    return true;
	}

	// We now know that both endpoints are outside the rectangle
	// but the 3 points are not all on one side of the rectangle.
	// Therefore the curve cannot be contained inside the rectangle,
	// but the rectangle might be contained inside the curve, or
	// the curve might intersect the boundary of the rectangle.

	double[] eqn = new double[3];
	double[] res = new double[3];
	if (!yoverlap) {
	    // Both y coordinates for the closing segment are above or
	    // below the rectangle which means that we can only intersect
	    // if the curve crosses the top (or bottom) of the rectangle
	    // in more than one place and if those crossing locations
	    // span the horizontal range of the rectangle.
	    fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2);
	    return (solveQuadratic(eqn, res) == 2 &&
		    evalQuadratic(res, 2, true, true, null,
				  x1, ctrlx, x2) == 2 &&
		    getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
	}

	// Y ranges overlap.  Now we examine the X ranges
	if (!xoverlap) {
	    // Both x coordinates for the closing segment are left of
	    // or right of the rectangle which means that we can only
	    // intersect if the curve crosses the left (or right) edge
	    // of the rectangle in more than one place and if those
	    // crossing locations span the vertical range of the rectangle.
	    fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2);
	    return (solveQuadratic(eqn, res) == 2 &&
		    evalQuadratic(res, 2, true, true, null,
				  y1, ctrly, y2) == 2 &&
		    getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
	}

	// The X and Y ranges of the endpoints overlap the X and Y
	// ranges of the rectangle, now find out how the endpoint
	// line segment intersects the Y range of the rectangle
	double dx = x2 - x1;
	double dy = y2 - y1;
	double k = y2 * x1 - x2 * y1;
	int c1tag, c2tag;
	if (y1tag == INSIDE) {
	    c1tag = x1tag;
	} else {
	    c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
	}
	if (y2tag == INSIDE) {
	    c2tag = x2tag;
	} else {
	    c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
	}
	// If the part of the line segment that intersects the Y range
	// of the rectangle crosses it horizontally - trivially accept
	if (c1tag * c2tag <= 0) {
	    return true;
	}

	// Now we know that both the X and Y ranges intersect and that
	// the endpoint line segment does not directly cross the rectangle.
	//
	// We can almost treat this case like one of the cases above
	// where both endpoints are to one side, except that we will
	// only get one intersection of the curve with the vertical
	// side of the rectangle.  This is because the endpoint segment
	// accounts for the other intersection.
	//
	// (Remember there is overlap in both the X and Y ranges which
	//  means that the segment must cross at least one vertical edge
	//  of the rectangle - in particular, the "near vertical side" -
	//  leaving only one intersection for the curve.)
	//
	// Now we calculate the y tags of the two intersections on the
	// "near vertical side" of the rectangle.  We will have one with
	// the endpoint segment, and one with the curve.  If those two
	// vertical intersections overlap the Y range of the rectangle,
	// we have an intersection.  Otherwise, we don't.

	// c1tag = vertical intersection class of the endpoint segment
	//
	// Choose the y tag of the endpoint that was not on the same
	// side of the rectangle as the subsegment calculated above.
	// Note that we can "steal" the existing Y tag of that endpoint
	// since it will be provably the same as the vertical intersection.
	c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

	// c2tag = vertical intersection class of the curve
	//
	// We have to calculate this one the straightforward way.
	// Note that the c2tag can still tell us which vertical edge
	// to test against.
	fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2);
	int num = solveQuadratic(eqn, res);

	// Note: We should be able to assert(num == 2); since the
	// X range "crosses" (not touches) the vertical boundary,
	// but we pass num to evalQuadratic for completeness.
	evalQuadratic(res, num, true, true, null, y1, ctrly, y2);

	// Note: We can assert(num evals == 1); since one of the
	// 2 crossings will be out of the [0,1] range.
	c2tag = getTag(res[0], y, y+h);

	// Finally, we have an intersection if the two crossings
	// overlap the Y range of the rectangle.
	return (c1tag * c2tag <= 0);
    }

    /**
     * Tests if the shape of this <code>QuadCurve2D</code> intersects the
     * interior of a specified <code>Rectangle2D</code>.
     * @param r the specified <code>Rectangle2D</code>
     * @return <code>true</code> if the shape of this
     * 		<code>QuadCurve2D</code> intersects the interior of 
     *		the specified <code>Rectangle2D</code>
     *		<code>false</code> otherwise.
     */
    public boolean intersects(Rectangle2D r) {
	return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * Tests if the interior of the shape of this
     * <code>QuadCurve2D</code> entirely contains the specified
     * set of rectangular coordinates.
     * @param x, y the coordinates of the upper-left corner of the
     *		specified rectangular area
     * @param w the width of the specified rectangular area
     * @param h the height of the specified rectangular area
     * @return <code>true</code> if the interior of the shape of this
     *		<code>QuadCurve2D</code> entirely contains the specified
     *		rectangluar area; <code>false</code> otherwise.
     */
    public boolean contains(double x, double y, double w, double h) {
	// Assertion: Quadratic curves closed by connecting their
	// endpoints are always convex.
	return (contains(x, y) &&
		contains(x + w, y) &&
		contains(x + w, y + h) &&
		contains(x, y + h));
    }

    /**
     * Tests if the interior of the shape of this
     * <code>QuadCurve2D</code> entirely contains the specified
     * <code>Rectangle2D</code>.
     * @param r the specified <code>Rectangle2D</code>
     * @return <code>true</code> if the interior of the shape of this
     *		<code>QuadCurve2D</code> entirely contains the specified
     *		<code>Rectangle2D</code> <code>false</code> otherwise.
     */
    public boolean contains(Rectangle2D r) {
	return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * Returns the bounding box of this <code>QuadCurve2D</code>.
     * @return a {@link Rectangle} that is the bounding box of the shape
     * 		of this <code>QuadCurve2D</code>.
     */
    public Rectangle getBounds() {
	return getBounds2D().getBounds();
    }

    /**
     * Returns an iteration object that defines the boundary of the
     * shape of this <code>QuadCurve2D</code>.
     * The iterator for this class is not multi-threaded safe,
     * which means that this <code>QuadCurve2D</code> class does not
     * guarantee that modifications to the geometry of this
     * <code>QuadCurve2D</code> object do not affect any iterations of
     * that geometry that are already in process.
     * @param at an optional {@link AffineTransform} to apply to the
     *		shape boundary
     * @return a {@link PathIterator} object that defines the boundary
     *		of the shape.
     */
    public PathIterator getPathIterator(AffineTransform at) {
	return new QuadIterator(this, at);
    }

    /**
     * Returns an iteration object that defines the boundary of the
     * flattened shape of this <code>QuadCurve2D</code>.
     * The iterator for this class is not multi-threaded safe,
     * which means that this <code>QuadCurve2D</code> class does not
     * guarantee that modifications to the geometry of this
     * <code>QuadCurve2D</code> object do not affect any iterations of
     * that geometry that are already in process. 
     * @param at an optional <code>AffineTransform</code> to apply
     *		to the boundary of the shape
     * @param flatness the maximum distance that the control points for a 
     *		subdivided curve can be with respect to a line connecting
     * 		the endpoints of this curve before this curve is
     *		replaced by a straight line connecting the endpoints.
     * @return a <code>PathIterator</code> object that defines the 
     *		flattened boundary of the shape.
     */
    public PathIterator getPathIterator(AffineTransform at, double flatness) {
	return new FlatteningPathIterator(getPathIterator(at), flatness);
    }

    /**
     * Creates a new object of the same class and with the same contents 
     * as this object.
     *
     * @return     a clone of this instance.
     * @exception  OutOfMemoryError            if there is not enough memory.
     * @see        java.lang.Cloneable
     * @since      1.2
     */
    public Object clone() {
	try {
	    return super.clone();
	} catch (CloneNotSupportedException e) {
	    // this shouldn't happen, since we are Cloneable
	    throw new InternalError();
	}
    }
}