/*
 * @(#)Arc2D.java	1.19 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;

/**
 * <CODE>Arc2D</CODE> is the abstract superclass for all objects that 
 * store a 2D arc defined by a bounding rectangle, 
 * start angle, angular extent (length of the arc), and a closure type 
 * (<CODE>OPEN</CODE>, <CODE>CHORD</CODE>, or <CODE>PIE</CODE>).
 * <p>
 * The bounding rectangle defines the outer boundary of the full ellipse
 * of which this arc is a partial section.
 * The angles are specified relative to the non-square extents of the
 * bounding rectangle such that 45 degrees always falls on the line from
 * the center of the ellipse to the upper right corner of the bounding
 * rectangle.
 * As a result, if the bounding rectangle is noticeably longer along one
 * axis than the other, the angles to the start and end of the arc segment
 * will be skewed farther along the longer axis of the bounds.
 * <p>
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @version 10 Feb 1997
 * @author	Jim Graham
 */
public abstract class Arc2D extends RectangularShape {
    /**
     * The closure type for an open arc with no path segments
     * connecting the two ends of the arc segment.
     */
    public final static int OPEN = 0;

    /**
     * The closure type for an arc closed by drawing a straight
     * line segment from the start of the arc segment to the end of the 
     * arc segment.
     */
    public final static int CHORD = 1;

    /**
     * The closure type for an arc closed by drawing straight line
     * segments from the start of the arc segment to the center
     * of the full ellipse and from that point to the end of the arc segment.
     */
    public final static int PIE = 2;

    /**
     * An arc specified in float precision,
     */
    public static class Float extends Arc2D {
 
        /**
         * The x coordinate of the upper left corner of the arc.
         */
	public float x;

        /**
         * The y coordinate of the upper left corner of the arc.
         */
	public float y;

        /**
         * The overall width of the full ellipse of which this arc is 
         * a partial section (not considering the
         * angular extents).
         */
	public float width;

        /**
         * The overall height of the full ellipse of which this arc is 
         * a partial section (not considering the
         * angular extents).
         */
  	public float height;

        /**
         * The starting angle of the arc in degrees.
         */
	public float start;

        /**
         * The angular extent of the arc in degrees.
         */
	public float extent;

        /**
         * Constructs a new OPEN arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0).
         */
	public Float() {
	    super(OPEN);
	}

        /**
         * Constructs a new arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0), and
         * the specified closure type.
         *
         * @param type The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public Float(int type) {
	    super(type);
	}

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param x, y The coordinates of the upper left corner of  
         * the arc. (Specified in float precision.)
         * @param w The overall width of the full ellipse of which  
         * this arc is a partial section. (Specified in float precision.)
         * @param h The overall height of the full ellipse of which this  
         * arc is a partial section. (Specified in float precision.)
         * @param start The starting angle of the arc in degrees.  
         * (Specified in float precision.)
         * @param extent The angular extent of the arc in degrees.  
         * (Specified in float precision.)
         * @param type The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.	 
         */
	public Float(float x, float y, float w, float h,
		     float start, float extent, int type) {
	    super(type);
	    this.x = x;
	    this.y = y;
	    this.width = w;
	    this.height = h;
	    this.start = start;
	    this.extent = extent;
	}

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param ellipseBounds The bounding rectangle that defines the 
         * outer boundary of the full ellipse of which this arc is a 
         * partial section.
         * @param start The starting angle of the arc in degrees. 
         * (Specified in float precision.)
         * @param extent The angular extent of the arc in degrees. 
         * (Specified in float precision.)
         * @param type The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.	  
         */
	public Float(Rectangle2D ellipseBounds,
		     float start, float extent, int type) {
	    super(type);
	    this.x = (float) ellipseBounds.getX();
	    this.y = (float) ellipseBounds.getY();
	    this.width = (float) ellipseBounds.getWidth();
	    this.height = (float) ellipseBounds.getHeight();
	    this.start = start;
	    this.extent = extent;
	}

        /**
         * Returns the x coordinate of the upper left corner of the arc.
         *
         * @return The x coordinate of arc's upper left coordinate in 
         * double precision.
         */
	public double getX() {
	    return (double) x;
	}

        /**
         * Returns the y coordinate of the upper left corner of the arc.
         *
         * @return The y coordinate of arc's upper left coordinate in 
         * double precision.
         */
	public double getY() {
	    return (double) y;
	}

        /**
         * Returns the width of the ellipse of which this arc is 
         * a partial section
         *
         * @return A double value that represents the width of the full 
         * ellipse of which this arc is a partial section.
         */
	public double getWidth() {
	    return (double) width;
	}

        /**
         * Returns the height of the ellipse of which this arc is 
         * a partial section
         *
         * @return A double value that represents the height of the full 
         * ellipse of which this arc is a partial section.	 
         */
	public double getHeight() {
	    return (double) height;
	}

        /**
         * Returns the starting angle of the arc.
         *
         * @return A double value that represents the starting angle of 
         * the arc in degrees.
         */
	public double getAngleStart() {
	    return (double) start;
	}

        /**
         * Returns the angular extent of the arc.
         *
         * @return A double value that represents the angular extent of 
         * the arc in degrees.
         */
	public double getAngleExtent() {
	    return (double) extent;
	}

        /**
         * Determines whether the arc is empty.
         *
         * @return <CODE>true</CODE> if the arc is empty, <CODE>false</CODE> 
         * if it is not.
         */
	public boolean isEmpty() {
	    return (width <= 0.0 || height <= 0.0);
	}

        /**
         * Sets the location, size, angular extents, and closure type of
         * this arc to the specified double values.
         *
         * @param x, y The coordinates of the upper left corner of 
         * the arc.
         * @param w The overall width of the full ellipse of which this  
         * arc is a partial section.
         * @param h The overall height of the full ellipse of which this 
         * arc is a partial section.
         * @param angSt The starting angle of the arc in degrees.
         * @param angExt The angular extent of the arc in degrees.
         * @param closure The closure type for the arc:
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public void setArc(double x, double y, double w, double h,
			   double angSt, double angExt, int closure) {
	    this.setArcType(closure);
	    this.x = (float) x;
	    this.y = (float) y;
	    this.width = (float) w;
	    this.height = (float) h;
	    this.start = (float) angSt;
	    this.extent = (float) angExt;
	}

        /**
         * Sets the starting angle of this arc to the specified double
         * value.
         *
         * @param angSt The starting angle of the arc in degrees.
         */
	public void setAngleStart(double angSt) {
	    this.start = (float) angSt;
	}

        /**
         * Sets the angular extent of this arc to the specified double
         * value.
         *     
         * @param angExt The angular extent of the arc in degrees.
         */
	public void setAngleExtent(double angExt) {
	    this.extent = (float) angExt;
	}

        /**
         * Return the high-precision bounding box of the arc.
         * 
         * @param x, y The coordinates of the upper left corner 
         * of the arc.
         * @param w The overall width of the full ellipse of which 
         * this arc is a partial section.
         * @param h The overall height of the full ellipse of which 
         * this arc is  a partial section.
         *
         * @return The bounding box as a <CODE>Rectangle2D</CODE> object.
         */
	protected Rectangle2D makeBounds(double x, double y,
					 double w, double h) {
	    return new Rectangle2D.Float((float) x, (float) y,
					 (float) w, (float) h);
	}
    }

    /**
     * An arc specified in double precision,
     */
    public static class Double extends Arc2D {
        /**
         * The x coordinate of the upper left corner of the arc.
         */
	public double x;

        /**
         * The y coordinate of the upper left corner of the arc.
         */
	public double y;

        /**
         * The overall width of the full ellipse (not considering the
         * angular extents).
         */
	public double width;

        /**
         * The overall height of the full ellipse (not considering the
         * angular extents).
         */
	public double height;

        /**
         * The starting angle of the arc in degrees.
         */
	public double start;

        /**
         * The angular extent of the arc in degrees.
         */
	public double extent;

        /**
         * Constructs a new OPEN arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0).
         */
	public Double() {
	    super(OPEN);
	}

        /**
         * Constructs a new arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0), and
         * the specified closure type.
         *
         * @param type The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public Double(int type) {
	    super(type);
	}

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param x, y The coordinates of the upper left corner  
         * of the arc. (Specified in double precision.)
         * @param w The overall width of the full ellipse of which this  
         * arc is a partial section. (Specified in double precision.)
         * @param h The overall height of the full ellipse of which this 
         * arc is a partial section. (Specified in double precision.)
         * @param angSt The starting angle of the arc in degrees.  
         * (Specified in double precision.)
         * @param angExt The angular extent of the arc in degrees. 
         * (Specified  in double precision.)
         * @param closure The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public Double(double x, double y, double w, double h,
		      double start, double extent, int type) {
	    super(type);
	    this.x = x;
	    this.y = y;
	    this.width = w;
	    this.height = h;
	    this.start = start;
	    this.extent = extent;
	}

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param ellipseBounds The bounding rectangle that defines the 
         * outer boundary of the full ellipse of which this arc is a 
         * partial section.
         * @param angSt The starting angle of the arc in degrees. 
         * (Specified in double precision.)
         * @param angExt The angular extent of the arc in degrees. 
         * (Specified in double precision.)
         * @param closure The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public Double(Rectangle2D ellipseBounds,
		      double start, double extent, int type) {
	    super(type);
	    this.x = ellipseBounds.getX();
	    this.y = ellipseBounds.getY();
	    this.width = ellipseBounds.getWidth();
	    this.height = ellipseBounds.getHeight();
	    this.start = start;
	    this.extent = extent;
	}

        /**
         * Returns the x coordinate of the upper left corner of the arc.
         *
         * @return The x coordinate of arc's upper left coordinate in 
         * double precision.
         */
	public double getX() {
	    return x;
	}

        /**
         * Returns the y coordinate of the upper left corner of the arc.
         *
         * @return The y coordinate of arc's upper left coordinate in 
         * double precision.
         */
	public double getY() {
	    return y;
	}

        /**
         * Returns the width of the ellipse of which this arc is 
         * a partial section
         *
         * @return A double value that represents the width of the full 
         * ellipse of which this arc is a partial section.
         */
	public double getWidth() {
	    return width;
	}

        /**
         * Returns the height of the ellipse of which this arc is 
         * a partial section
         *
         * @return A double value that represents the height of the full 
         * ellipse of which this arc is a partial section.	 
         */
	public double getHeight() {
	    return height;
	}

        /**
         * Returns the starting angle of the arc.
         *
         * @return A double value that represents the starting angle 
         * of the arc in degrees.
         */
	public double getAngleStart() {
	    return start;
	}

        /**
         * Returns the angular extent of the arc.
         *
         * @return A double value that represents the angular extent of 
         * the arc in degrees.
         */	
	public double getAngleExtent() {
	    return extent;
	}

        /**
         * Determines whether the arc is empty.
         *
         * @return <CODE>true</CODE> if the arc is empty, <CODE>false</CODE> 
         * if it not.
         */
	public boolean isEmpty() {
	    return (width <= 0.0 || height <= 0.0);
	}

        /**
         * Sets the location, size, angular extents, and closure type of
         * this arc to the specified double values.
         *
         * @param x, y The coordinates of the upper left corner 
         * of the arc.
         * @param w The overall width of the full ellipse of which 
         * this arc is a partial section.
         * @param h The overall height of the full ellipse of which 
         * this arc is a partial section.
         * @param angSt The starting angle of the arc in degrees.
         * @param angExt The angular extent of the arc in degrees.
         * @param closure The closure type for the arc: 
         * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
         */
	public void setArc(double x, double y, double w, double h,
			   double angSt, double angExt, int closure) {
	    this.setArcType(closure);
	    this.x = x;
	    this.y = y;
	    this.width = w;
	    this.height = h;
	    this.start = angSt;
	    this.extent = angExt;
	}

        /**
         * Sets the starting angle of this arc to the specified double
         * value.
         *
         * @param angSt The starting angle of the arc in degrees.
         */
	public void setAngleStart(double angSt) {
	    this.start = angSt;
	}

        /**
         * Sets the angular extent of this arc to the specified double
         * value.
         *
         * @param angExt The angular extent of the arc in degrees.
         */
	public void setAngleExtent(double angExt) {
	    this.extent = angExt;
	}

        /**
         * Returns the high-precision bounding box of the arc.
         * 
         * @param x, y The coordinates of the upper left corner 
         * of the arc.
         * @param w The overall width of the full ellipse of which 
         * this arc is a partial section.
         * @param h The overall height of the full ellipse of which 
         * this arc is a partial section.
         *
         * @return The bounding box as a <CODE>Rectangle2D</CODE> object.
         */
	protected Rectangle2D makeBounds(double x, double y,
					 double w, double h) {
	    return new Rectangle2D.Double(x, y, w, h);
	}
    }

    private int type;

    /**
     * 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.
     *
     * @param type The closure type of this arc: 
     * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
     * @see java.awt.geom.Arc2D.Float
     * @see java.awt.geom.Arc2D.Double
     */
    protected Arc2D(int type) {
	setArcType(type);
    }

    /**
     * Returns the starting angle of the arc.
     *
     * @return A double value that represents the starting angle 
     * of the arc in degrees.
     */
    public abstract double getAngleStart();

    /**
     * Returns the angular extent of the arc.
     *
     * @return A double value that represents the angular extent 
     * of the arc in degrees.
     */
    public abstract double getAngleExtent();

    /**
     * Returns the arc closure type of the arc: {@link #OPEN OPEN}, 
     * {@link #CHORD CHORD}, or {@link #PIE PIE}.
     * @return One of the integer constant closure types defined 
     * in this class.
     */
    public int getArcType() {
	return type;
    }

    /**
     * Returns the starting point of the arc.  This point is the
     * intersection of the ray from the center defined by the
     * starting angle and the elliptical boundary of the arc.
     * 
     * @return A <CODE>Point2D</CODE> object representing the 
     * x,y coordinates of the starting point of the arc.
     */
    public Point2D getStartPoint() {
	double angle = Math.toRadians(-getAngleStart());
	double x = getX() + (Math.cos(angle) * 0.5 + 0.5) * getWidth();
	double y = getY() + (Math.sin(angle) * 0.5 + 0.5) * getHeight();
	return new Point2D.Double(x, y);
    }

    /**
     * Returns the ending point of the arc.  This point is the
     * intersection of the ray from the center defined by the
     * starting angle plus the angular extent of the arc and the
     * elliptical boundary of the arc.
     *
     * @return A <CODE>Point2D</CODE> object representing the 
     * x,y coordinates  of the ending point of the arc.
     */
    public Point2D getEndPoint() {
	double angle = Math.toRadians(-getAngleStart() - getAngleExtent());
	double x = getX() + (Math.cos(angle) * 0.5 + 0.5) * getWidth();
	double y = getY() + (Math.sin(angle) * 0.5 + 0.5) * getHeight();
	return new Point2D.Double(x, y);
    }

    /**
     * Sets the location, size, angular extents, and closure type of
     * this arc to the specified double values.
     *
     * @param x, y The coordinates of the upper left corner of 
     * the arc.
     * @param w The overall width of the full ellipse of which 
     * this arc is a partial section.
     * @param h The overall height of the full ellipse of which 
     * this arc is a partial section.
     * @param angSt The starting angle of the arc in degrees.
     * @param angExt The angular extent of the arc in degrees.
     * @param closure The closure type for the arc:
     * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
     */
    public abstract void setArc(double x, double y, double w, double h,
				double angSt, double angExt, int closure);

    /**
     * Sets the location, size, angular extents, and closure type of
     * this arc to the specified values.
     *
     * @param loc The <CODE>Point2D</CODE> representing the coordinates of 
     * the upper left corner of the arc.
     * @param size The <CODE>Dimension2D</CODE> representing the width 
     * and height of the full ellipse of which this arc is 
     * a partial section.
     * @param angSt The starting angle of the arc in degrees. 
     * (Specified in double precision.)
     * @param angExt The angular extent of the arc in degrees. 
     * (Specified in double precision.)
     * @param closure The closure type for the arc:
     * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
     */ 
    public void setArc(Point2D loc, Dimension2D size,
		       double angSt, double angExt, int closure) {
	setArc(loc.getX(), loc.getY(), size.getWidth(), size.getHeight(),
	       angSt, angExt, closure);
    }

    /**
     * Sets the location, size, angular extents, and closure type of
     * this arc to the specified values.
     *
     * @param rect The bounding rectangle that defines the 
     * outer boundary of the full ellipse of which this arc is a 
     * partial section.
     * @param angSt The starting angle of the arc in degrees. 
     * (Specified in double precision.)
     * @param angExt The angular extent of the arc in degrees. 
     * (Specified in double precision.)
     * @param closure The closure type for the arc:
     * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.
     */ 
    public void setArc(Rectangle2D rect, double angSt, double angExt,
		       int closure) {
	setArc(rect.getX(), rect.getY(), rect.getWidth(), rect.getHeight(),
	       angSt, angExt, closure);
    }

    /**
     * Sets this arc to be the same as the specified arc.
     *
     * @param a The <CODE>Arc2D</CODE> to use to set the arc's values.
     */
    public void setArc(Arc2D a) {
	setArc(a.getX(), a.getY(), a.getWidth(), a.getHeight(),
	       a.getAngleStart(), a.getAngleExtent(), a.type);
    }

    /**
     * Sets the position, bounds, angular extents, and closure type of
     * this arc to the specified values. The arc is defined by a center 
     * point and a radius rather than a bounding box for the full ellipse.
     *
     * @param x, y The coordinates of the center of the arc. 
     * (Specified in double precision.)
     * @param r The radius of the arc. (Specified in double precision.)
     * @param angSt The starting angle of the arc in degrees.
     * (Specified in double precision.)
     * @param angExt The angular extent of the arc in degrees. 
     * (Specified in double precision.)
     * @param closure The closure type for the arc:
     * {@link #OPEN OPEN}, {@link #CHORD CHORD}, or {@link #PIE PIE}.     
     */
    public void setArcByCenter(double x, double y, double radius,
			       double angSt, double angExt, int closure) {
	setArc(x - radius, y - radius, radius * 2.0, radius * 2.0,
	       angSt, angExt, closure);
    }

    /**
     * Sets the position, bounds, and angular extents of this arc to the 
     * specified value. The starting angle of the arc is tangent to the 
     * line specified by points (p1, p2), the ending angle is tangent to 
     * the line specified by points (p2, p3), and the arc has the 
     * specified radius.
     *
     * @param p1 The first point that defines the arc. The starting 
     * angle of the arc is tangent to the line specified by points (p1, p2).
     * @param p2 The second point that defines the arc. The starting 
     * angle of the arc is tangent to the line specified by points (p1, p2). 
     * The ending angle of the arc is tangent to the line specified by 
     * points (p2, p3).
     * @param p3 The third point that defines the arc. The ending angle 
     * of the arc is tangent to the line specified by points (p2, p3).
     * @param radius The radius of the arc. (Specified in double precision.)
     */
    public void setArcByTangent(Point2D p1, Point2D p2, Point2D p3,
				double radius) {
	double ang1 = Math.atan2(p1.getY() - p2.getY(),
				 p1.getX() - p2.getX());
	double ang2 = Math.atan2(p3.getY() - p2.getY(),
				 p3.getX() - p2.getX());
	double diff = ang2 - ang1;
	if (diff > Math.PI) {
	    ang2 -= Math.PI * 2.0;
	} else if (diff < -Math.PI) {
	    ang2 += Math.PI * 2.0;
	}
	double bisect = (ang1 + ang2) / 2.0;
	double theta = Math.abs(ang2 - bisect);
	double dist = radius / Math.sin(theta);
	double x = p2.getX() + dist * Math.cos(bisect);
	double y = p2.getY() + dist * Math.sin(bisect);
	// REMIND: This needs some work...
	if (ang1 < ang2) {
	    ang1 -= Math.PI / 2.0;
	    ang2 += Math.PI / 2.0;
	} else {
	    ang1 += Math.PI / 2.0;
	    ang2 -= Math.PI / 2.0;
	}
	ang1 = Math.toDegrees(-ang1);
	ang2 = Math.toDegrees(-ang2);
	diff = ang2 - ang1;
	if (diff < 0) {
	    diff += 360;
	} else {
	    diff -= 360;
	}
	setArcByCenter(x, y, radius, ang1, diff, type);
    }

    /**
     * Sets the starting angle of this arc to the specified double
     * value.
     *
     * @param angSt The starting angle of the arc in degrees.
     */
    public abstract void setAngleStart(double angSt);

    /**
     * Sets the angular extent of this arc to the specified double
     * value.
     *
     * @param angExt The angular extent of the arc in degrees.
     */
    public abstract void setAngleExtent(double angExt);

    /**
     * Sets the starting angle of this arc to the angle that the
     * specified point defines relative to the center of this arc.
     * The angular extent of the arc will remain the same.
     *
     * @param p The <CODE>Point2D</CODE> that defines the starting angle.
     */
    public void setAngleStart(Point2D p) {
	setAngleStart(-Math.toDegrees(Math.atan2(p.getY() - getCenterY(),
						 p.getX() - getCenterX())));
    }

    /**
     * Sets the starting angle and angular extent of this arc using two 
     * sets of coordinates. The first set of coordinates is used to 
     * determine the angle of the starting point relative to the arc's 
     * center. The second set of coordinates is used to determine the 
     * angle of the end point relative to the arc's center. 
     * The arc will always be non-empty and extend counterclockwise
     * from the first point around to the second point.
     *
     * @param x1, y1 The coordinates of the arc's starting point. 
     * @param x2, y2 The coordinates of the arc's ending point.
     */
    public void setAngles(double x1, double y1, double x2, double y2) {
	double x = getCenterX();
	double y = getCenterY();
	// Note: reversing the Y equations negates the angle to adjust
	// for the upside down coordinate system.
	double ang1 = Math.atan2(y - y1, x1 - x);
	double ang2 = Math.atan2(y - y2, x2 - x);
	ang2 -= ang1;
	if (ang2 <= 0.0) {
	    ang2 += Math.PI * 2.0;
	}
	setAngleStart(Math.toDegrees(ang1));
	setAngleExtent(Math.toDegrees(ang2));
    }

    /**
     * Sets the starting angle and angular extent of this arc using  
     * two points. The first point is used to determine the angle of 
     * the starting point relative to the arc's center.
     * The second point is used to determine the angle of the end point
     * relative to the arc's center. 
     * The arc will always be non-empty and extend counterclockwise
     * from the first point around to the second point.
     *
     * @param p1 The <CODE>Point2D</CODE> that defines the arc's 
     * starting point. 
     * @param p2 The <CODE>Point2D</CODE> that defines the arc's 
     * ending point.
     */
    public void setAngles(Point2D p1, Point2D p2) {
	setAngles(p1.getX(), p1.getY(), p2.getX(), p2.getY());
    }

    /**
     * Sets the closure type of this arc to the specified value: 
     * <CODE>OPEN</CODE>, <CODE>CHORD</CODE>, or <CODE>PIE</CODE>.
     *
     * @param type The integer constant that represents the closure 
     * type of this arc: {@link #OPEN}, {@link #CHORD}, or 
     * {@link #PIE}.
     *
     * @throws IllegalArgumentException if <code>type</code> is not
     * 0, 1, or 2.+
     */
    public void setArcType(int type) {
	if (type < OPEN || type > PIE) {
	    throw new IllegalArgumentException("invalid type for Arc: "+type);
	}
	this.type = type;
    }

    /**
     * Sets the location and size of the outer bounds of this arc
     * to the specified values.
     *
     * @param x, y The coordinates of the upper left corner of the 
     * arc's bounding box. (Specified in double precision.)
     * @param w The width of the arc's bounding box. (Specified in 
     * double precision.)
     * @param h The height of the arc's bounding box. (Specified in 
     * double precision.)
     */
    public void setFrame(double x, double y, double w, double h) {
	setArc(x, y, w, h, getAngleStart(), getAngleExtent(), type);
    }

    /**
     * Returns the high-precision bounding box of the arc.  The bounding  
     * box contains only the part of this <code>Arc2D</code> that is 
     * in between the starting and ending angles and contains the pie
     * wedge, if this <code>Arc2D</code> has a <code>PIE</code> closure type.
     * <p>
     * This method differs from the 
     * {@link RectangularShape#getBounds() getBounds} in that the 
     * <code>getBounds</code> method only returns the bounds of the 
     * enclosing ellipse of this <code>Arc2D</code> without considering
     * the starting and ending angles of this <code>Arc2D</code>.
     * 
     * @return the <CODE>Rectangle2D</CODE> that represents the arc's 
     * bounding box.
     */
    public Rectangle2D getBounds2D() {
	if (isEmpty()) {
	    return makeBounds(getX(), getY(), getWidth(), getHeight());
	}
	double x1, y1, x2, y2;
	if (getArcType() == PIE) {
	    x1 = y1 = x2 = y2 = 0.0;
	} else {
	    x1 = y1 = 1.0;
	    x2 = y2 = -1.0;
	}
	double angle = 0.0;
	for (int i = 0; i < 6; i++) {
	    if (i < 4) {
		// 0-3 are the four quadrants
		angle += 90.0;
		if (!containsAngle(angle)) {
		    continue;
		}
	    } else if (i == 4) {
		// 4 is start angle
		angle = getAngleStart();
	    } else {
		// 5 is end angle
		angle += getAngleExtent();
	    }
	    double rads = Math.toRadians(-angle);
	    double xe = Math.cos(rads);
	    double ye = Math.sin(rads);
	    x1 = Math.min(x1, xe);
	    y1 = Math.min(y1, ye);
	    x2 = Math.max(x2, xe);
	    y2 = Math.max(y2, ye);
	}
	double w = getWidth();
	double h = getHeight();
	x2 = (x2 - x1) * 0.5 * w;
	y2 = (y2 - y1) * 0.5 * h;
	x1 = getX() + (x1 * 0.5 + 0.5) * w;
	y1 = getY() + (y1 * 0.5 + 0.5) * h;
	return makeBounds(x1, y1, x2, y2);
    }

    /**
     * Constructs a Rectangle2D of the appropriate precision
     * to hold the parameters calculated to be the bounding box
     * of this arc.
     * 
     * @param x, y The coordinates of the upper left corner of the 
     * bounding box. (Specified in double precision.)
     * @param w The width of the bounding box. (Specified in 
     * double precision.)
     * @param h The height of the bounding box. (Specified in 
     * double precision.)
     */
    protected abstract Rectangle2D makeBounds(double x, double y,
					      double w, double h);

    /*
     * Normalizes the specified angle into the range -180 to 180.
     */
    static double normalizeDegrees(double angle) {
	if (angle > 180.0) {
	    if (angle <= (180.0 + 360.0)) {
		angle = angle - 360.0;
	    } else {
		angle = Math.IEEEremainder(angle, 360.0);
		// IEEEremainder can return -180 here for some input values...
		if (angle == -180.0) {
		    angle = 180.0;
		}
	    }
	} else if (angle <= -180.0) {
	    if (angle > (-180.0 - 360.0)) {
		angle = angle + 360.0;
	    } else {
		angle = Math.IEEEremainder(angle, 360.0);
		// IEEEremainder can return -180 here for some input values...
		if (angle == -180.0) {
		    angle = 180.0;
		}
	    }
	}
	return angle;
    }

    /**
     * Determines whether or not the specified angle is within the  
     * angular extents of the arc.
     *
     * @param angle The angle to test. (Specified in double precision.)
     *
     * @return <CODE>true</CODE> if the arc contains the angle, 
     * <CODE>false</CODE> if the arc doesn't contain the angle.
     */
    public boolean containsAngle(double angle) {
	double angExt = getAngleExtent();
	boolean backwards = (angExt < 0.0);
	if (backwards) {
	    angExt = -angExt;
	}
	if (angExt >= 360.0) {
	    return true;
	}
	angle = normalizeDegrees(angle) - normalizeDegrees(getAngleStart());
	if (backwards) {
	    angle = -angle;
	}
	if (angle < 0.0) {
	    angle += 360.0;
	}

      
	return (angle >= 0.0) && (angle < angExt);
    }

    /**
     * Determines whether or not the specified point is inside the boundary 
     * of the arc.
     *
     * @param x, y The coordinates of the point to test. (Specified in 
     * double precision.)
     *
     * @return <CODE>true</CODE> if the point lies within the bound of 
     * the arc, <CODE>false</CODE> if the point lies outside of the 
     * arc's bounds.
     */
    public boolean contains(double x, double y) {
	// Normalize the coordinates compared to the ellipse
	// having a center at 0,0 and a radius of 0.5.
	double ellw = getWidth();
	if (ellw <= 0.0) {
	    return false;
	}
	double normx = (x - getX()) / ellw - 0.5;
	double ellh = getHeight();
	if (ellh <= 0.0) {
	    return false;
	}
	double normy = (y - getY()) / ellh - 0.5;
	double distSq = (normx * normx + normy * normy);
	if (distSq >= 0.25) {
	    return false;
	}
	double angExt = Math.abs(getAngleExtent());
	if (angExt >= 360.0) {
	    return true;
	}
	boolean inarc = containsAngle(-Math.toDegrees(Math.atan2(normy,
								 normx)));
	if (type == PIE) {
	    return inarc;
	}
	// CHORD and OPEN behave the same way
	if (inarc) {
	    if (angExt >= 180.0) {
		return true;
	    }
	    // point must be outside the "pie triangle"
	} else {
	    if (angExt <= 180.0) {
		return false;
	    }
	    // point must be inside the "pie triangle"
	}
	// The point is inside the pie triangle iff it is on the same
	// side of the line connecting the ends of the arc as the center.
	double angle = Math.toRadians(-getAngleStart());
	double x1 = Math.cos(angle);
	double y1 = Math.sin(angle);
	angle += Math.toRadians(-getAngleExtent());
	double x2 = Math.cos(angle);
	double y2 = Math.sin(angle);
	boolean inside = (Line2D.relativeCCW(x1, y1, x2, y2, x, y) *
			  Line2D.relativeCCW(x1, y1, x2, y2, 0, 0) >= 0);
	return inarc ? !inside : inside;
    }

    /**
     * Determines whether or not the interior of the arc intersects 
     * the interior of the specified rectangle.
     *
     * @param x, y The coordinates of the rectangle's upper left corner. 
     * (Specified in double precision.)
     * @param w The width of the rectangle. (Specified in double precision.)
     * @param h The height of the rectangle. (Specified in double precision.)
     *
     * @return <CODE>true</CODE> if the arc intersects the rectangle, 
     * <CODE>false</CODE> if the arc doesn't intersect the rectangle.
     */

  public boolean intersects(double x, double y, double w, double h) {

      /*
       * REMIND: Verify correct handling of "upside down angles".
       */
      /*
        Change around so that is really works this time
        We check each of the four line segments for intersection with an
        ellipse of the same radius as the imaginary arc.
        We then compute the angle of the intersections and call included
        angle to find out if the intersection is within the arc itself
        - Aaron Muderick
        */

      double intersect_angle;
      double yint, xint; 

      //if there are any points of the rect in the arc then return true;
      if (contains(x, y) || contains(x + w, y) ||
      	  contains(x, y + h) || contains(x + w, y + h)) return true;
      
      //we need to translate the arc and the rect so that we can do
      //quadrant checking
      x = x - (getX() + (getWidth()/2));
      y = (y - (getY() + (getHeight()/2))) * (-1);

      //find out the squash ratio
      double squash = getWidth()/getHeight();

      if (((x*x)/((getWidth()/2)*(getWidth()/2)) < 1)) {
	if ((x == 0) && ((((getHeight()/2) >= (y-h)) && ((getHeight()/2) <= y))
                         || ((((-1) * (getHeight()/2)) >= (y-h)) && (((-1) 
                                    * (getHeight()/2) <= y))))) {
	  if (containsAngle(Math.PI2)) {
              return true;
          }
	  if (containsAngle(Math.PI*(3/2))) {
              return true;
          }
	}
	
	yint = Math.abs(Math.sqrt((1-((x*x)/((getWidth()/2)*(getWidth()/2))))
                                  *((getHeight()/2)*(getHeight()/2))));
	intersect_angle = Math.abs(Math.atan((yint*squash)/x)); 

	if ((x > 0) && (((yint >= (y-h)) && (yint <= y)) 
                        || ((((-1) * yint) >= (y-h)) 
                            && (((-1) * yint) <= y)))) {	  
	  if (containsAngle(intersect_angleMath.PI * 180)) {
              return true;
          }
	  if (containsAngle((((2*Math.PI) - intersect_angle)/Math.PI) 
                            * 180)) {
              return true;
          }
	}

	if ((x < 0) && (((yint >= (y-h)) && (yint <= y)) 
                        || ((((-1) * yint) >= (y-h)) 
                            && (((-1) * yint) <= y)))){
	  
	  if (containsAngle((((Math.PI) - intersect_angle)/Math.PI) * 180)) {
              return true;
          }
	  if (containsAngle(((Math.PI + intersect_angle)/Math.PI) * 180)) {
              return true;
          }
	}
  }

      if ((((x+w)*(x+w))/((getWidth()/2)*(getWidth()/2)) < 1)) {
	if (((x+w) == 0) && ((((getHeight()/2) >= (y-h)) 
                              && ((getHeight()/2) <= y)) 
                             || ((((-1) * (getHeight()/2)) >= (y-h)) 
                                 && (((-1) * (getHeight()/2) <= y))))) {
	  if (containsAngle(Math.PI2)) {
              return true;
          }
	  if (containsAngle(Math.PI*(3/2))) {
              return true;
          }
	}
	
	yint = Math.abs(Math.sqrt((1-(((x+w)*(x+w))
                                      /((getWidth()/2)*(getWidth()/2))))
                                  *((getHeight()/2)*(getHeight()/2))));

	intersect_angle = Math.abs(Math.atan((yint*squash)/(x+w)));

	if (((x+w) > 0) && (((yint >= (y-h)) && (yint <= y)) 
                            || ((((-1) * yint) >= (y-h)) 
                                && (((-1) * yint) <= y)))) {	
	  if (containsAngle((intersect_angleMath.PI) * 180)) {
              return true;
          }
	  if (containsAngle((((2*Math.PI) - intersect_angle)/Math.PI) * 180)) {
              return true;
          }
	}

	if (((x+w) < 0) && (((yint >= (y-h)) && (yint <= y)) 
                            || ((((-1) * yint) >= (y-h)) 
                                && (((-1) * yint) <= y)))) {
            if (containsAngle((((Math.PI) - intersect_angle)/Math.PI) * 180)) {
              return true;
            }
            if (containsAngle(((Math.PI + intersect_angle)/Math.PI) * 180)) {
                return true;
            }
	}
      
      }

      if (((y*y)/((getHeight()/2)*(getHeight()/2)) < 1)) {

	if ((y == 0) && ((((getWidth()/2) >= x) && ((getWidth()/2) <= (x+w))) 
                         || ((((-1) * (getWidth()/2)) >= x)
                             && (((-1) * (getWidth()/2)) <= (x+w))))) {
	  if (containsAngle(Math.PI)) {
              return true;
          }
	  if (containsAngle(Math.PI*2)) {
              return true;
          }
	}
	
	xint = Math.abs(Math.sqrt((1-((y*y)
                                      /((getHeight()/2)
                                        *(getHeight()/2))))
                                  *((getWidth()/2)*(getWidth()/2))));

	intersect_angle = Math.abs(Math.atan(y(xintsquash))); 

	if ((y > 0) && (((xint >= x) && (xint <= (x+w))) 
                        || ((((-1) * xint) >= x) 
                            && (((-1) * xint) <= (x+w))))) {	 
	  if (containsAngle((intersect_angle)/Math.PI * 180)) {
              return true;
          }
	  if (containsAngle(((Math.PI) - intersect_angle)/Math.PI * 180)) {
              return true;
          }
	}

	if ((y < 0) &&  (((xint >= x) && (xint <= (x+w))) 
                         || ((((-1) * xint) >= x) 
                             && (((-1) * xint) <= (x+w))))) {
	  if (containsAngle(((Math.PI*2) - intersect_angle)/Math.PI * 180)) {
              return true;
          }
	  if (containsAngle((Math.PI + intersect_angle)/Math.PI * 180)) {
              return true;
          }
	}
      
      }

      if ((((y-h)*(y-h))/((getHeight()/2)*(getHeight()/2)) < 1)) {
	if (((y-h) == 0) && ((((getWidth()/2) >= x) 
                              && ((getWidth()/2) <= (x+w))) 
                             || ((((-1) * (getWidth()/2)) >= x) 
                                 && (((-1) * (getWidth()/2)) <= (x+w))))) {
	  if (containsAngle(Math.PI)) {
              return true;
          }
	  if (containsAngle(Math.PI*2)) {
              return true;
          }
	}
	
	xint = Math.abs(Math.sqrt((1-(((y-h)*(y-h))
                                      /((getHeight()/2)*(getHeight()/2))))
                                  *((getWidth()/2)*(getWidth()/2))));

	intersect_angle = Math.abs(Math.atan((y-h)/(xintsquash)));   	    

	if (((y-h) > 0) &&  (((xint >= x) && (xint <= (x+w))) 
                             || ((((-1) * xint) >= x) 
                                 && (((-1) * xint) <= (x+w))))) {	  
	  if (containsAngle(intersect_angleMath.PI * 180)) {
              return true;
          }
	  if (containsAngle(((Math.PI) - intersect_angle)/Math.PI * 180)) {
              return true;
          }
	}
	if (((y-h) < 0) && (((xint >= x) && (xint <= (x+w))) 
                            || ((((-1) * xint) >= x) 
                                && (((-1) * xint) <= (x+w))))) {
	  if (containsAngle(((Math.PI*2) - intersect_angle)/Math.PI * 180)) {
              return true;
          }
	  if (containsAngle((Math.PI + intersect_angle)/Math.PI * 180)) {
              return true;
          }
	}
      
      }
      
      return false;

  }
    

    /**
     * Determine whether or not the interior of the arc entirely contains 
     * the specified rectangle.
     *
     * @param x, y The coordinates of the rectangle's upper left corner. 
     * (Specified in double precision.)
     * @param w The width of the rectangle. (Specified in double precision.)
     * @param h The height of the rectangle. (Specified in double precision.)
     *
     * @return <CODE>true</CODE> if the arc contains the rectangle, 
     * <CODE>false</CODE> if the arc doesn't contain the rectangle.
     */
    public boolean contains(double x, double y, double w, double h) {
	return contains(x, y, w, h, null);
    }

    /**
     * Determine whether or not the interior of the arc entirely contains 
     * the specified rectangle.
     *
     * @param r The <CODE>Rectangle2D</CODE> to test.
     *
     * @return <CODE>true</CODE> if the arc contains the rectangle, 
     * <CODE>false</CODE> if the arc doesn't contain the rectangle.
     */  
    public boolean contains(Rectangle2D r) {
	return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight(), r);
    }

    private boolean contains(double x, double y, double w, double h,
			     Rectangle2D origrect) {
	if (!(contains(x, y) &&
	      contains(x + w, y) &&
	      contains(x, y + h) &&
	      contains(x + w, y + h))) {
	    return false;
	}
	// If the shape is convex then we have done all the testing
	// we need.  Only PIE arcs can be concave and then only if
	// the angular extents are greater than 180 degrees.
	if (type != PIE || getAngleExtent() <= 180.0) {
	    return true;
	}
	// For a PIE shape we have an additional test for the case where
	// the angular extents are greater than 180 degrees and all four
	// rectangular corners are inside the shape but one of the
	// rectangle edges spans across the "missing wedge" of the arc.
	// We can test for this case by checking if the rectangle intersects
	// either of the pie angle segments.
	if (origrect == null) {
	    origrect = new Rectangle2D.Double(x, y, w, h);
	}
	double halfW = getWidth() / 2.0;
	double halfH = getHeight() / 2.0;
	double xc = getX() + halfW;
	double yc = getY() + halfH;
	double angle = Math.toRadians(-getAngleStart());
	double xe = xc + halfW * Math.cos(angle);
	double ye = yc + halfH * Math.sin(angle);
	if (origrect.intersectsLine(xc, yc, xe, ye)) {
	    return false;
	}
	angle += Math.toRadians(-getAngleExtent());
	xe = xc + halfW * Math.cos(angle);
	ye = yc + halfH * Math.sin(angle);
	return !origrect.intersectsLine(xc, yc, xe, ye);
    }

    /**
     * Returns an iteration object that defines the boundary of the
     * arc.
     * This iterator is multithread safe.
     * <code>Arc2D</code> guarantees that
     * modifications to the geometry of the arc
     * do not affect any iterations of that geometry that
     * are already in process.
     *
     * @param at an optional <CODE>AffineTransform</CODE> to be applied 
     * to the coordinates as they are returned in the iteration, or null 
     * if the untransformed coordinates are desired.
     *
     * @return A <CODE>PathIterator</CODE> that defines the arc's boundary.
     */
    public PathIterator getPathIterator(AffineTransform at) {
	return new ArcIterator(this, at);
    }
}