/*
 * @(#)Arc2D.java	1.27 03/12/19
 *
 * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
 * SUN PROPRIETARY/CONFIDENTIAL. 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;

    /**
     * This class defines 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.
	 * @see #setAngleStart
         */
	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.
	 * @see #setAngleExtent
         */
	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.
	 * @see #getAngleStart
         */
	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.
	 * @see #getAngleExtent
         */
	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);
	}
    }

    /**
     * This class defines 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 start The starting angle of the arc in degrees.  
         * (Specified in double precision.)
         * @param extent The angular extent of the arc in degrees. 
         * (Specified  in double precision.)
         * @param type 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 start The starting angle of the arc in degrees. 
         * (Specified in double precision.)
         * @param extent The angular extent of the arc in degrees. 
         * (Specified in double precision.)
         * @param type 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.
	 * @see #setAngleStart
         */
	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.
	 * @see #setAngleExtent
         */	
	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.
	 * @see #getAngleStart
         */
	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.
	 * @see #getAngleExtent
         */
	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.
     * @see #setAngleStart
     */
    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.
     * @see #setAngleExtent
     */
    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.
     * @see #setArcType
     */
    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 radius 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.
     * @see #getAngleStart
     */
    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.
     * @see #getAngleExtent
     */
    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.
     * @see #getAngleStart
     */
    public void setAngleStart(Point2D p) {
	// Bias the dx and dy by the height and width of the oval.
	double dx = getHeight() * (p.getX() - getCenterX());
	double dy = getWidth() * (p.getY() - getCenterY());
	setAngleStart(-Math.toDegrees(Math.atan2(dy, dx)));
    }

    /**
     * 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();
	double w = getWidth();
	double h = getHeight();
	// Note: reversing the Y equations negates the angle to adjust
	// for the upside down coordinate system.
	// Also we should bias atans by the height and width of the oval.
	double ang1 = Math.atan2(w * (y - y1), h * (x1 - x));
	double ang2 = Math.atan2(w * (y - y2), h * (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.+
     * @see #getArcType
     */
    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 <code>Rectangle2D</code> 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.)
     * @return a <code>Rectangle2D</code> that is the bounding box
     *     of this arc.
     */
    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, 2*normx, 2*normy) *
			  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) {

	double aw = getWidth();
	double ah = getHeight();

	if ( w <= 0 || h <= 0 || aw <= 0 || ah <= 0 ) {
	    return false;
	}
	double ext = getAngleExtent();
	if (ext == 0) {
	    return false;
	}

	double ax  = getX();
	double ay  = getY();
	double axw = ax + aw;
	double ayh = ay + ah;
	double xw  = x + w;
	double yh  = y + h;

	// check bbox
	if (x >= axw || y >= ayh || xw <= ax || yh <= ay) {
	    return false;
	}

	// extract necessary data
	double axc = getCenterX();
	double ayc = getCenterY();
	Point2D sp = getStartPoint();
	Point2D ep = getEndPoint();
	double sx = sp.getX();
	double sy = sp.getY();
	double ex = ep.getX();
	double ey = ep.getY();

	/*
	 * Try to catch rectangles that intersect arc in areas
	 * outside of rectagle with left top corner coordinates
	 * (min(center x, start point x, end point x),
	 *  min(center y, start point y, end point y))
	 * and rigth bottom corner coordinates
	 * (max(center x, start point x, end point x),
	 *  max(center y, start point y, end point y)).
	 * So we'll check axis segments outside of rectangle above.
	 */
	if (ayc >= y && ayc <= yh) { // 0 and 180
	    if ((sx < xw && ex < xw && axc < xw &&
	         axw > x && containsAngle(0)) ||
	        (sx > x && ex > x && axc > x &&
	         ax < xw && containsAngle(180))) {
		return true;
	    }
	}
	if (axc >= x && axc <= xw) { // 90 and 270
	    if ((sy > y && ey > y && ayc > y &&
	         ay < yh && containsAngle(90)) ||
	        (sy < yh && ey < yh && ayc < yh &&
	         ayh > y && containsAngle(270))) {
		return true;
	    }
	}

	/*
	 * For PIE we should check intersection with pie slices;
	 * also we should do the same for arcs with extent is greater
	 * than 180, because we should cover case of rectangle, which
	 * situated between center of arc and chord, but does not
	 * intersect the chord.
	 */
	Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
	if (type == PIE || Math.abs(ext) > 180) {
	    // for PIE: try to find intersections with pie slices
	    if (rect.intersectsLine(axc, ayc, sx, sy) ||
		rect.intersectsLine(axc, ayc, ex, ey)) {
		return true;
	    }
	} else {
	    // for CHORD and OPEN: try to find intersections with chord
	    if (rect.intersectsLine(sx, sy, ex, ey)) {
		return true;
	    }
	}

	// finally check the rectangle corners inside the arc
	if (contains(x, y) || contains(x + w, y) ||
	    contains(x, y + h) || contains(x + w, y + h)) {
	    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 || Math.abs(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);
    }
}