/*
 * Copyright (c) 1997, 2011, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
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 *
 *
 */

package java.awt.geom;

import java.io.Serializable;

/**
 * <CODE>Arc2D</CODE> is the abstract superclass for all objects that
 * store a 2D arc defined by a framing rectangle,
 * start angle, angular extent (length of the arc), and a closure type
 * (<CODE>OPEN</CODE>, <CODE>CHORD</CODE>, or <CODE>PIE</CODE>).
 * <p>
 * <a name="inscribes">
 * The arc is a partial section of a full ellipse which
 * inscribes the framing rectangle of its parent {@link RectangularShape}.
 * </a>
 * <a name="angles">
 * The angles are specified relative to the non-square
 * framing rectangle such that 45 degrees always falls on the line from
 * the center of the ellipse to the upper right corner of the framing
 * rectangle.
 * As a result, if the framing 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 frame.
 * </a>
 * <p>
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @author      Jim Graham
 * @since 1.2
 */
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.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    public final static int PIE = 2;

    /**
     * This class defines an arc specified in {@code float} precision.
     * @since 1.2
     */
    public static class Float extends Arc2D implements Serializable {
        /**
         * The X coordinate of the upper-left corner of the framing
         * rectangle of the arc.
         * @since 1.2
         * @serial
         */
        public float x;

        /**
         * The Y coordinate of the upper-left corner of the framing
         * rectangle of the arc.
         * @since 1.2
         * @serial
         */
        public float y;

        /**
         * The overall width of the full ellipse of which this arc is
         * a partial section (not considering the
         * angular extents).
         * @since 1.2
         * @serial
         */
        public float width;

        /**
         * The overall height of the full ellipse of which this arc is
         * a partial section (not considering the
         * angular extents).
         * @since 1.2
         * @serial
         */
        public float height;

        /**
         * The starting angle of the arc in degrees.
         * @since 1.2
         * @serial
         */
        public float start;

        /**
         * The angular extent of the arc in degrees.
         * @since 1.2
         * @serial
         */
        public float extent;

        /**
         * Constructs a new OPEN arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0).
         * @since 1.2
         */
        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}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        public Float(int type) {
            super(type);
        }

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param x The X coordinate of the upper-left corner of
         *          the arc's framing rectangle.
         * @param y The Y coordinate of the upper-left corner of
         *          the arc's framing rectangle.
         * @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 start The starting angle of the arc in degrees.
         * @param extent The angular extent of the arc in degrees.
         * @param type The closure type for the arc:
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        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 framing 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.
         * @param extent The angular extent of the arc in degrees.
         * @param type The closure type for the arc:
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        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;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getX() {
            return (double) x;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getY() {
            return (double) y;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getWidth() {
            return (double) width;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getHeight() {
            return (double) height;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getAngleStart() {
            return (double) start;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getAngleExtent() {
            return (double) extent;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public boolean isEmpty() {
            return (width <= 0.0 || height <= 0.0);
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        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;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public void setAngleStart(double angSt) {
            this.start = (float) angSt;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public void setAngleExtent(double angExt) {
            this.extent = (float) angExt;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        protected Rectangle2D makeBounds(double x, double y,
                                         double w, double h) {
            return new Rectangle2D.Float((float) x, (float) y,
                                         (float) w, (float) h);
        }

        /*
         * JDK 1.6 serialVersionUID
         */
        private static final long serialVersionUID = 9130893014586380278L;

        /**
         * Writes the default serializable fields to the
         * <code>ObjectOutputStream</code> followed by a byte
         * indicating the arc type of this <code>Arc2D</code>
         * instance.
         *
         * @serialData
         * <ol>
         * <li>The default serializable fields.
         * <li>
         * followed by a <code>byte</code> indicating the arc type
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * </ol>
         */
        private void writeObject(java.io.ObjectOutputStream s)
            throws java.io.IOException
        {
            s.defaultWriteObject();

            s.writeByte(getArcType());
        }

        /**
         * Reads the default serializable fields from the
         * <code>ObjectInputStream</code> followed by a byte
         * indicating the arc type of this <code>Arc2D</code>
         * instance.
         *
         * @serialData
         * <ol>
         * <li>The default serializable fields.
         * <li>
         * followed by a <code>byte</code> indicating the arc type
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * </ol>
         */
        private void readObject(java.io.ObjectInputStream s)
            throws java.lang.ClassNotFoundException, java.io.IOException
        {
            s.defaultReadObject();

            try {
                setArcType(s.readByte());
            } catch (IllegalArgumentException iae) {
                throw new java.io.InvalidObjectException(iae.getMessage());
            }
        }
    }

    /**
     * This class defines an arc specified in {@code double} precision.
     * @since 1.2
     */
    public static class Double extends Arc2D implements Serializable {
        /**
         * The X coordinate of the upper-left corner of the framing
         * rectangle of the arc.
         * @since 1.2
         * @serial
         */
        public double x;

        /**
         * The Y coordinate of the upper-left corner of the framing
         * rectangle of the arc.
         * @since 1.2
         * @serial
         */
        public double y;

        /**
         * The overall width of the full ellipse of which this arc is
         * a partial section (not considering the angular extents).
         * @since 1.2
         * @serial
         */
        public double width;

        /**
         * The overall height of the full ellipse of which this arc is
         * a partial section (not considering the angular extents).
         * @since 1.2
         * @serial
         */
        public double height;

        /**
         * The starting angle of the arc in degrees.
         * @since 1.2
         * @serial
         */
        public double start;

        /**
         * The angular extent of the arc in degrees.
         * @since 1.2
         * @serial
         */
        public double extent;

        /**
         * Constructs a new OPEN arc, initialized to location (0, 0),
         * size (0, 0), angular extents (start = 0, extent = 0).
         * @since 1.2
         */
        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}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        public Double(int type) {
            super(type);
        }

        /**
         * Constructs a new arc, initialized to the specified location,
         * size, angular extents, and closure type.
         *
         * @param x The X coordinate of the upper-left corner
         *          of the arc's framing rectangle.
         * @param y The Y coordinate of the upper-left corner
         *          of the arc's framing rectangle.
         * @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 start The starting angle of the arc in degrees.
         * @param extent The angular extent of the arc in degrees.
         * @param type The closure type for the arc:
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        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 framing 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.
         * @param extent The angular extent of the arc in degrees.
         * @param type The closure type for the arc:
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * @since 1.2
         */
        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;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getX() {
            return x;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getY() {
            return y;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getWidth() {
            return width;
        }

        /**
         * {@inheritDoc}
         * Note that the arc
         * <a href="Arc2D.html#inscribes">partially inscribes</a>
         * the framing rectangle of this {@code RectangularShape}.
         *
         * @since 1.2
         */
        public double getHeight() {
            return height;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getAngleStart() {
            return start;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public double getAngleExtent() {
            return extent;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public boolean isEmpty() {
            return (width <= 0.0 || height <= 0.0);
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        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;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public void setAngleStart(double angSt) {
            this.start = angSt;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        public void setAngleExtent(double angExt) {
            this.extent = angExt;
        }

        /**
         * {@inheritDoc}
         * @since 1.2
         */
        protected Rectangle2D makeBounds(double x, double y,
                                         double w, double h) {
            return new Rectangle2D.Double(x, y, w, h);
        }

        /*
         * JDK 1.6 serialVersionUID
         */
        private static final long serialVersionUID = 728264085846882001L;

        /**
         * Writes the default serializable fields to the
         * <code>ObjectOutputStream</code> followed by a byte
         * indicating the arc type of this <code>Arc2D</code>
         * instance.
         *
         * @serialData
         * <ol>
         * <li>The default serializable fields.
         * <li>
         * followed by a <code>byte</code> indicating the arc type
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * </ol>
         */
        private void writeObject(java.io.ObjectOutputStream s)
            throws java.io.IOException
        {
            s.defaultWriteObject();

            s.writeByte(getArcType());
        }

        /**
         * Reads the default serializable fields from the
         * <code>ObjectInputStream</code> followed by a byte
         * indicating the arc type of this <code>Arc2D</code>
         * instance.
         *
         * @serialData
         * <ol>
         * <li>The default serializable fields.
         * <li>
         * followed by a <code>byte</code> indicating the arc type
         * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
         * </ol>
         */
        private void readObject(java.io.ObjectInputStream s)
            throws java.lang.ClassNotFoundException, java.io.IOException
        {
            s.defaultReadObject();

            try {
                setArcType(s.readByte());
            } catch (IllegalArgumentException iae) {
                throw new java.io.InvalidObjectException(iae.getMessage());
            }
        }
    }

    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.
     * <p>
     * This constructor creates an object with a default closure
     * type of {@link #OPEN}.  It is provided only to enable
     * serialization of subclasses.
     *
     * @see java.awt.geom.Arc2D.Float
     * @see java.awt.geom.Arc2D.Double
     */
    protected Arc2D() {
        this(OPEN);
    }

    /**
     * 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}, {@link #CHORD}, or {@link #PIE}.
     * @see java.awt.geom.Arc2D.Float
     * @see java.awt.geom.Arc2D.Double
     * @since 1.2
     */
    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
     * @since 1.2
     */
    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
     * @since 1.2
     */
    public abstract double getAngleExtent();

    /**
     * Returns the arc closure type of the arc: {@link #OPEN},
     * {@link #CHORD}, or {@link #PIE}.
     * @return One of the integer constant closure types defined
     * in this class.
     * @see #setArcType
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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 The X coordinate of the upper-left corner of the arc.
     * @param y The Y coordinate 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}, {@link #CHORD}, or {@link #PIE}.
     * @since 1.2
     */
    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.
     * @param angExt The angular extent of the arc in degrees.
     * @param closure The closure type for the arc:
     * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
     * @since 1.2
     */
    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 framing 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.
     * @param angExt The angular extent of the arc in degrees.
     * @param closure The closure type for the arc:
     * {@link #OPEN}, {@link #CHORD}, or {@link #PIE}.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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 framing rectangle for the full ellipse.
     *
     * @param x The X coordinate of the center of the arc.
     * @param y The Y coordinate of the center of the arc.
     * @param radius The radius of the arc.
     * @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}, {@link #CHORD}, or {@link #PIE}.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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
     * @since 1.2
     */
    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
     * @since 1.2
     */
    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
     * @since 1.2
     */
    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 The X coordinate of the arc's starting point.
     * @param y1 The Y coordinate of the arc's starting point.
     * @param x2 The X coordinate of the arc's ending point.
     * @param y2 The Y coordinate of the arc's ending point.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    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
     * @since 1.2
     */
    public void setArcType(int type) {
        if (type < OPEN || type > PIE) {
            throw new IllegalArgumentException("invalid type for Arc: "+type);
        }
        this.type = type;
    }

    /**
     * {@inheritDoc}
     * Note that the arc
     * <a href="Arc2D.html#inscribes">partially inscribes</a>
     * the framing rectangle of this {@code RectangularShape}.
     *
     * @since 1.2
     */
    public void setFrame(double x, double y, double w, double h) {
        setArc(x, y, w, h, getAngleStart(), getAngleExtent(), type);
    }

    /**
     * Returns the high-precision framing rectangle of the arc.  The framing
     * rectangle 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
     * framing rectangle.
     * @since 1.2
     */
    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 framing rectangle
     * of this arc.
     *
     * @param x The X coordinate of the upper-left corner of the
     * framing rectangle.
     * @param y The Y coordinate of the upper-left corner of the
     * framing rectangle.
     * @param w The width of the framing rectangle.
     * @param h The height of the framing rectangle.
     * @return a <code>Rectangle2D</code> that is the framing rectangle
     *     of this arc.
     * @since 1.2
     */
    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.
     *
     * @return <CODE>true</CODE> if the arc contains the angle,
     * <CODE>false</CODE> if the arc doesn't contain the angle.
     * @since 1.2
     */
    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 The X coordinate of the point to test.
     * @param y The Y coordinate of the point to test.
     *
     * @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.
     * @since 1.2
     */
    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 The X coordinate of the rectangle's upper-left corner.
     * @param y The Y coordinate of the rectangle's upper-left corner.
     * @param w The width of the rectangle.
     * @param h The height of the rectangle.
     *
     * @return <CODE>true</CODE> if the arc intersects the rectangle,
     * <CODE>false</CODE> if the arc doesn't intersect the rectangle.
     * @since 1.2
     */
    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;
    }

    /**
     * Determines whether or not the interior of the arc entirely contains
     * the specified rectangle.
     *
     * @param x The X coordinate of the rectangle's upper-left corner.
     * @param y The Y coordinate of the rectangle's upper-left corner.
     * @param w The width of the rectangle.
     * @param h The height of the rectangle.
     *
     * @return <CODE>true</CODE> if the arc contains the rectangle,
     * <CODE>false</CODE> if the arc doesn't contain the rectangle.
     * @since 1.2
     */
    public boolean contains(double x, double y, double w, double h) {
        return contains(x, y, w, h, null);
    }

    /**
     * Determines 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.
     * @since 1.2
     */
    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.
     * @since 1.2
     */
    public PathIterator getPathIterator(AffineTransform at) {
        return new ArcIterator(this, at);
    }

    /**
     * Returns the hashcode for this <code>Arc2D</code>.
     * @return the hashcode for this <code>Arc2D</code>.
     * @since 1.6
     */
    public int hashCode() {
        long bits = java.lang.Double.doubleToLongBits(getX());
        bits += java.lang.Double.doubleToLongBits(getY()) * 37;
        bits += java.lang.Double.doubleToLongBits(getWidth()) * 43;
        bits += java.lang.Double.doubleToLongBits(getHeight()) * 47;
        bits += java.lang.Double.doubleToLongBits(getAngleStart()) * 53;
        bits += java.lang.Double.doubleToLongBits(getAngleExtent()) * 59;
        bits += getArcType() * 61;
        return (((int) bits) ^ ((int) (bits >> 32)));
    }

    /**
     * Determines whether or not the specified <code>Object</code> is
     * equal to this <code>Arc2D</code>.  The specified
     * <code>Object</code> is equal to this <code>Arc2D</code>
     * if it is an instance of <code>Arc2D</code> and if its
     * location, size, arc extents and type are the same as this
     * <code>Arc2D</code>.
     * @param obj  an <code>Object</code> to be compared with this
     *             <code>Arc2D</code>.
     * @return  <code>true</code> if <code>obj</code> is an instance
     *          of <code>Arc2D</code> and has the same values;
     *          <code>false</code> otherwise.
     * @since 1.6
     */
    public boolean equals(Object obj) {
        if (obj == this) {
            return true;
        }
        if (obj instanceof Arc2D) {
            Arc2D a2d = (Arc2D) obj;
            return ((getX() == a2d.getX()) &&
                    (getY() == a2d.getY()) &&
                    (getWidth() == a2d.getWidth()) &&
                    (getHeight() == a2d.getHeight()) &&
                    (getAngleStart() == a2d.getAngleStart()) &&
                    (getAngleExtent() == a2d.getAngleExtent()) &&
                    (getArcType() == a2d.getArcType()));
        }
        return false;
    }
}
