/*
 * Copyright (c) 2006, 2015, 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.awt.Shape;
import java.awt.Rectangle;
import sun.awt.geom.Curve;
import java.io.Serializable;
import java.io.StreamCorruptedException;
import java.util.Arrays;

/**
 * The {@code Path2D} class provides a simple, yet flexible
 * shape which represents an arbitrary geometric path.
 * It can fully represent any path which can be iterated by the
 * {@link PathIterator} interface including all of its segment
 * types and winding rules and it implements all of the
 * basic hit testing methods of the {@link Shape} interface.
 * <p>
 * Use {@link Float} when dealing with data that can be represented
 * and used with floating point precision.  Use {@link Double}
 * for data that requires the accuracy or range of double precision.
 * <p>
 * {@code Path2D} provides exactly those facilities required for
 * basic construction and management of a geometric path and
 * implementation of the above interfaces with little added
 * interpretation.
 * If it is useful to manipulate the interiors of closed
 * geometric shapes beyond simple hit testing then the
 * {@link Area} class provides additional capabilities
 * specifically targeted at closed figures.
 * While both classes nominally implement the {@code Shape}
 * interface, they differ in purpose and together they provide
 * two useful views of a geometric shape where {@code Path2D}
 * deals primarily with a trajectory formed by path segments
 * and {@code Area} deals more with interpretation and manipulation
 * of enclosed regions of 2D geometric space.
 * <p>
 * The {@link PathIterator} interface has more detailed descriptions
 * of the types of segments that make up a path and the winding rules
 * that control how to determine which regions are inside or outside
 * the path.
 *
 * @author Jim Graham
 * @since 1.6
 */
public abstract class Path2D implements Shape, Cloneable {
    /**
     * An even-odd winding rule for determining the interior of
     * a path.
     *
     * @see PathIterator#WIND_EVEN_ODD
     * @since 1.6
     */
    public static final int WIND_EVEN_ODD = PathIterator.WIND_EVEN_ODD;

    /**
     * A non-zero winding rule for determining the interior of a
     * path.
     *
     * @see PathIterator#WIND_NON_ZERO
     * @since 1.6
     */
    public static final int WIND_NON_ZERO = PathIterator.WIND_NON_ZERO;

    // For code simplicity, copy these constants to our namespace
    // and cast them to byte constants for easy storage.
    private static final byte SEG_MOVETO  = (byte) PathIterator.SEG_MOVETO;
    private static final byte SEG_LINETO  = (byte) PathIterator.SEG_LINETO;
    private static final byte SEG_QUADTO  = (byte) PathIterator.SEG_QUADTO;
    private static final byte SEG_CUBICTO = (byte) PathIterator.SEG_CUBICTO;
    private static final byte SEG_CLOSE   = (byte) PathIterator.SEG_CLOSE;

    transient byte[] pointTypes;
    transient int numTypes;
    transient int numCoords;
    transient int windingRule;

    static final int INIT_SIZE = 20;
    static final int EXPAND_MAX = 500;
    static final int EXPAND_MAX_COORDS = EXPAND_MAX * 2;
    static final int EXPAND_MIN = 10; // ensure > 6 (cubics)

    /**
     * Constructs a new empty {@code Path2D} object.
     * It is assumed that the package sibling subclass that is
     * defaulting to this constructor will fill in all values.
     *
     * @since 1.6
     */
    /* private protected */
    Path2D() {
    }

    /**
     * Constructs a new {@code Path2D} object from the given
     * specified initial values.
     * This method is only intended for internal use and should
     * not be made public if the other constructors for this class
     * are ever exposed.
     *
     * @param rule the winding rule
     * @param initialTypes the size to make the initial array to
     *                     store the path segment types
     * @since 1.6
     */
    /* private protected */
    Path2D(int rule, int initialTypes) {
        setWindingRule(rule);
        this.pointTypes = new byte[initialTypes];
    }

    abstract float[] cloneCoordsFloat(AffineTransform at);
    abstract double[] cloneCoordsDouble(AffineTransform at);
    abstract void append(float x, float y);
    abstract void append(double x, double y);
    abstract Point2D getPoint(int coordindex);
    abstract void needRoom(boolean needMove, int newCoords);
    abstract int pointCrossings(double px, double py);
    abstract int rectCrossings(double rxmin, double rymin,
                               double rxmax, double rymax);

    static byte[] expandPointTypes(byte[] oldPointTypes, int needed) {
        final int oldSize = oldPointTypes.length;
        final int newSizeMin = oldSize + needed;
        if (newSizeMin < oldSize) {
            // hard overflow failure - we can't even accommodate
            // new items without overflowing
            throw new ArrayIndexOutOfBoundsException(
                          "pointTypes exceeds maximum capacity !");
        }
        // growth algorithm computation
        int grow = oldSize;
        if (grow > EXPAND_MAX) {
            grow = Math.max(EXPAND_MAX, oldSize >> 3); // 1/8th min
        } else if (grow < EXPAND_MIN) {
            grow = EXPAND_MIN;
        }
        assert grow > 0;

        int newSize = oldSize + grow;
        if (newSize < newSizeMin) {
            // overflow in growth algorithm computation
            newSize = Integer.MAX_VALUE;
        }
        while (true) {
            try {
                // try allocating the larger array
                return Arrays.copyOf(oldPointTypes, newSize);
            } catch (OutOfMemoryError oome) {
                if (newSize == newSizeMin) {
                    throw oome;
                }
            }
            newSize = newSizeMin + (newSize - newSizeMin) / 2;
        }
    }

    /**
     * The {@code Float} class defines a geometric path with
     * coordinates stored in single precision floating point.
     *
     * @since 1.6
     */
    public static class Float extends Path2D implements Serializable {
        transient float floatCoords[];

        /**
         * Constructs a new empty single precision {@code Path2D} object
         * with a default winding rule of {@link #WIND_NON_ZERO}.
         *
         * @since 1.6
         */
        public Float() {
            this(WIND_NON_ZERO, INIT_SIZE);
        }

        /**
         * Constructs a new empty single precision {@code Path2D} object
         * with the specified winding rule to control operations that
         * require the interior of the path to be defined.
         *
         * @param rule the winding rule
         * @see #WIND_EVEN_ODD
         * @see #WIND_NON_ZERO
         * @since 1.6
         */
        public Float(int rule) {
            this(rule, INIT_SIZE);
        }

        /**
         * Constructs a new empty single precision {@code Path2D} object
         * with the specified winding rule and the specified initial
         * capacity to store path segments.
         * This number is an initial guess as to how many path segments
         * will be added to the path, but the storage is expanded as
         * needed to store whatever path segments are added.
         *
         * @param rule the winding rule
         * @param initialCapacity the estimate for the number of path segments
         *                        in the path
         * @see #WIND_EVEN_ODD
         * @see #WIND_NON_ZERO
         * @since 1.6
         */
        public Float(int rule, int initialCapacity) {
            super(rule, initialCapacity);
            floatCoords = new float[initialCapacity * 2];
        }

        /**
         * Constructs a new single precision {@code Path2D} object
         * from an arbitrary {@link Shape} object.
         * All of the initial geometry and the winding rule for this path are
         * taken from the specified {@code Shape} object.
         *
         * @param s the specified {@code Shape} object
         * @since 1.6
         */
        public Float(Shape s) {
            this(s, null);
        }

        /**
         * Constructs a new single precision {@code Path2D} object
         * from an arbitrary {@link Shape} object, transformed by an
         * {@link AffineTransform} object.
         * All of the initial geometry and the winding rule for this path are
         * taken from the specified {@code Shape} object and transformed
         * by the specified {@code AffineTransform} object.
         *
         * @param s the specified {@code Shape} object
         * @param at the specified {@code AffineTransform} object
         * @since 1.6
         */
        public Float(Shape s, AffineTransform at) {
            if (s instanceof Path2D) {
                Path2D p2d = (Path2D) s;
                setWindingRule(p2d.windingRule);
                this.numTypes = p2d.numTypes;
                // trim arrays:
                this.pointTypes = Arrays.copyOf(p2d.pointTypes, p2d.numTypes);
                this.numCoords = p2d.numCoords;
                this.floatCoords = p2d.cloneCoordsFloat(at);
            } else {
                PathIterator pi = s.getPathIterator(at);
                setWindingRule(pi.getWindingRule());
                this.pointTypes = new byte[INIT_SIZE];
                this.floatCoords = new float[INIT_SIZE * 2];
                append(pi, false);
            }
        }

        @Override
        float[] cloneCoordsFloat(AffineTransform at) {
            // trim arrays:
            float ret[];
            if (at == null) {
                ret = Arrays.copyOf(floatCoords, numCoords);
            } else {
                ret = new float[numCoords];
                at.transform(floatCoords, 0, ret, 0, numCoords / 2);
            }
            return ret;
        }

        @Override
        double[] cloneCoordsDouble(AffineTransform at) {
            // trim arrays:
            double ret[] = new double[numCoords];
            if (at == null) {
                for (int i = 0; i < numCoords; i++) {
                    ret[i] = floatCoords[i];
                }
            } else {
                at.transform(floatCoords, 0, ret, 0, numCoords / 2);
            }
            return ret;
        }

        void append(float x, float y) {
            floatCoords[numCoords++] = x;
            floatCoords[numCoords++] = y;
        }

        void append(double x, double y) {
            floatCoords[numCoords++] = (float) x;
            floatCoords[numCoords++] = (float) y;
        }

        Point2D getPoint(int coordindex) {
            return new Point2D.Float(floatCoords[coordindex],
                                     floatCoords[coordindex+1]);
        }

        @Override
        void needRoom(boolean needMove, int newCoords) {
            if ((numTypes == 0) && needMove) {
                throw new IllegalPathStateException("missing initial moveto "+
                                                    "in path definition");
            }
            if (numTypes >= pointTypes.length) {
                pointTypes = expandPointTypes(pointTypes, 1);
            }
            if (numCoords > (floatCoords.length - newCoords)) {
                floatCoords = expandCoords(floatCoords, newCoords);
            }
        }

        static float[] expandCoords(float[] oldCoords, int needed) {
            final int oldSize = oldCoords.length;
            final int newSizeMin = oldSize + needed;
            if (newSizeMin < oldSize) {
                // hard overflow failure - we can't even accommodate
                // new items without overflowing
                throw new ArrayIndexOutOfBoundsException(
                              "coords exceeds maximum capacity !");
            }
            // growth algorithm computation
            int grow = oldSize;
            if (grow > EXPAND_MAX_COORDS) {
                grow = Math.max(EXPAND_MAX_COORDS, oldSize >> 3); // 1/8th min
            } else if (grow < EXPAND_MIN) {
                grow = EXPAND_MIN;
            }
            assert grow > needed;

            int newSize = oldSize + grow;
            if (newSize < newSizeMin) {
                // overflow in growth algorithm computation
                newSize = Integer.MAX_VALUE;
            }
            while (true) {
                try {
                    // try allocating the larger array
                    return Arrays.copyOf(oldCoords, newSize);
                } catch (OutOfMemoryError oome) {
                    if (newSize == newSizeMin) {
                        throw oome;
                    }
                }
                newSize = newSizeMin + (newSize - newSizeMin) / 2;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void moveTo(double x, double y) {
            if (numTypes > 0 && pointTypes[numTypes - 1] == SEG_MOVETO) {
                floatCoords[numCoords-2] = (float) x;
                floatCoords[numCoords-1] = (float) y;
            } else {
                needRoom(false, 2);
                pointTypes[numTypes++] = SEG_MOVETO;
                floatCoords[numCoords++] = (float) x;
                floatCoords[numCoords++] = (float) y;
            }
        }

        /**
         * Adds a point to the path by moving to the specified
         * coordinates specified in float precision.
         * <p>
         * This method provides a single precision variant of
         * the double precision {@code moveTo()} method on the
         * base {@code Path2D} class.
         *
         * @param x the specified X coordinate
         * @param y the specified Y coordinate
         * @see Path2D#moveTo
         * @since 1.6
         */
        public final synchronized void moveTo(float x, float y) {
            if (numTypes > 0 && pointTypes[numTypes - 1] == SEG_MOVETO) {
                floatCoords[numCoords-2] = x;
                floatCoords[numCoords-1] = y;
            } else {
                needRoom(false, 2);
                pointTypes[numTypes++] = SEG_MOVETO;
                floatCoords[numCoords++] = x;
                floatCoords[numCoords++] = y;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void lineTo(double x, double y) {
            needRoom(true, 2);
            pointTypes[numTypes++] = SEG_LINETO;
            floatCoords[numCoords++] = (float) x;
            floatCoords[numCoords++] = (float) y;
        }

        /**
         * Adds a point to the path by drawing a straight line from the
         * current coordinates to the new specified coordinates
         * specified in float precision.
         * <p>
         * This method provides a single precision variant of
         * the double precision {@code lineTo()} method on the
         * base {@code Path2D} class.
         *
         * @param x the specified X coordinate
         * @param y the specified Y coordinate
         * @see Path2D#lineTo
         * @since 1.6
         */
        public final synchronized void lineTo(float x, float y) {
            needRoom(true, 2);
            pointTypes[numTypes++] = SEG_LINETO;
            floatCoords[numCoords++] = x;
            floatCoords[numCoords++] = y;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void quadTo(double x1, double y1,
                                              double x2, double y2)
        {
            needRoom(true, 4);
            pointTypes[numTypes++] = SEG_QUADTO;
            floatCoords[numCoords++] = (float) x1;
            floatCoords[numCoords++] = (float) y1;
            floatCoords[numCoords++] = (float) x2;
            floatCoords[numCoords++] = (float) y2;
        }

        /**
         * Adds a curved segment, defined by two new points, to the path by
         * drawing a Quadratic curve that intersects both the current
         * coordinates and the specified coordinates {@code (x2,y2)},
         * using the specified point {@code (x1,y1)} as a quadratic
         * parametric control point.
         * All coordinates are specified in float precision.
         * <p>
         * This method provides a single precision variant of
         * the double precision {@code quadTo()} method on the
         * base {@code Path2D} class.
         *
         * @param x1 the X coordinate of the quadratic control point
         * @param y1 the Y coordinate of the quadratic control point
         * @param x2 the X coordinate of the final end point
         * @param y2 the Y coordinate of the final end point
         * @see Path2D#quadTo
         * @since 1.6
         */
        public final synchronized void quadTo(float x1, float y1,
                                              float x2, float y2)
        {
            needRoom(true, 4);
            pointTypes[numTypes++] = SEG_QUADTO;
            floatCoords[numCoords++] = x1;
            floatCoords[numCoords++] = y1;
            floatCoords[numCoords++] = x2;
            floatCoords[numCoords++] = y2;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void curveTo(double x1, double y1,
                                               double x2, double y2,
                                               double x3, double y3)
        {
            needRoom(true, 6);
            pointTypes[numTypes++] = SEG_CUBICTO;
            floatCoords[numCoords++] = (float) x1;
            floatCoords[numCoords++] = (float) y1;
            floatCoords[numCoords++] = (float) x2;
            floatCoords[numCoords++] = (float) y2;
            floatCoords[numCoords++] = (float) x3;
            floatCoords[numCoords++] = (float) y3;
        }

        /**
         * Adds a curved segment, defined by three new points, to the path by
         * drawing a B&eacute;zier curve that intersects both the current
         * coordinates and the specified coordinates {@code (x3,y3)},
         * using the specified points {@code (x1,y1)} and {@code (x2,y2)} as
         * B&eacute;zier control points.
         * All coordinates are specified in float precision.
         * <p>
         * This method provides a single precision variant of
         * the double precision {@code curveTo()} method on the
         * base {@code Path2D} class.
         *
         * @param x1 the X coordinate of the first B&eacute;zier control point
         * @param y1 the Y coordinate of the first B&eacute;zier control point
         * @param x2 the X coordinate of the second B&eacute;zier control point
         * @param y2 the Y coordinate of the second B&eacute;zier control point
         * @param x3 the X coordinate of the final end point
         * @param y3 the Y coordinate of the final end point
         * @see Path2D#curveTo
         * @since 1.6
         */
        public final synchronized void curveTo(float x1, float y1,
                                               float x2, float y2,
                                               float x3, float y3)
        {
            needRoom(true, 6);
            pointTypes[numTypes++] = SEG_CUBICTO;
            floatCoords[numCoords++] = x1;
            floatCoords[numCoords++] = y1;
            floatCoords[numCoords++] = x2;
            floatCoords[numCoords++] = y2;
            floatCoords[numCoords++] = x3;
            floatCoords[numCoords++] = y3;
        }

        int pointCrossings(double px, double py) {
            if (numTypes == 0) {
                return 0;
            }
            double movx, movy, curx, cury, endx, endy;
            float coords[] = floatCoords;
            curx = movx = coords[0];
            cury = movy = coords[1];
            int crossings = 0;
            int ci = 2;
            for (int i = 1; i < numTypes; i++) {
                switch (pointTypes[i]) {
                case PathIterator.SEG_MOVETO:
                    if (cury != movy) {
                        crossings +=
                            Curve.pointCrossingsForLine(px, py,
                                                        curx, cury,
                                                        movx, movy);
                    }
                    movx = curx = coords[ci++];
                    movy = cury = coords[ci++];
                    break;
                case PathIterator.SEG_LINETO:
                    crossings +=
                        Curve.pointCrossingsForLine(px, py,
                                                    curx, cury,
                                                    endx = coords[ci++],
                                                    endy = coords[ci++]);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_QUADTO:
                    crossings +=
                        Curve.pointCrossingsForQuad(px, py,
                                                    curx, cury,
                                                    coords[ci++],
                                                    coords[ci++],
                                                    endx = coords[ci++],
                                                    endy = coords[ci++],
                                                    0);
                    curx = endx;
                    cury = endy;
                    break;
            case PathIterator.SEG_CUBICTO:
                    crossings +=
                        Curve.pointCrossingsForCubic(px, py,
                                                     curx, cury,
                                                     coords[ci++],
                                                     coords[ci++],
                                                     coords[ci++],
                                                     coords[ci++],
                                                     endx = coords[ci++],
                                                     endy = coords[ci++],
                                                     0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CLOSE:
                    if (cury != movy) {
                        crossings +=
                            Curve.pointCrossingsForLine(px, py,
                                                        curx, cury,
                                                        movx, movy);
                    }
                    curx = movx;
                    cury = movy;
                    break;
                }
            }
            if (cury != movy) {
                crossings +=
                    Curve.pointCrossingsForLine(px, py,
                                                curx, cury,
                                                movx, movy);
            }
            return crossings;
        }

        int rectCrossings(double rxmin, double rymin,
                          double rxmax, double rymax)
        {
            if (numTypes == 0) {
                return 0;
            }
            float coords[] = floatCoords;
            double curx, cury, movx, movy, endx, endy;
            curx = movx = coords[0];
            cury = movy = coords[1];
            int crossings = 0;
            int ci = 2;
            for (int i = 1;
                 crossings != Curve.RECT_INTERSECTS && i < numTypes;
                 i++)
            {
                switch (pointTypes[i]) {
                case PathIterator.SEG_MOVETO:
                    if (curx != movx || cury != movy) {
                        crossings =
                            Curve.rectCrossingsForLine(crossings,
                                                       rxmin, rymin,
                                                       rxmax, rymax,
                                                       curx, cury,
                                                       movx, movy);
                    }
                    // Count should always be a multiple of 2 here.
                    // assert((crossings & 1) != 0);
                    movx = curx = coords[ci++];
                    movy = cury = coords[ci++];
                    break;
                case PathIterator.SEG_LINETO:
                    crossings =
                        Curve.rectCrossingsForLine(crossings,
                                                   rxmin, rymin,
                                                   rxmax, rymax,
                                                   curx, cury,
                                                   endx = coords[ci++],
                                                   endy = coords[ci++]);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_QUADTO:
                    crossings =
                        Curve.rectCrossingsForQuad(crossings,
                                                   rxmin, rymin,
                                                   rxmax, rymax,
                                                   curx, cury,
                                                   coords[ci++],
                                                   coords[ci++],
                                                   endx = coords[ci++],
                                                   endy = coords[ci++],
                                                   0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CUBICTO:
                    crossings =
                        Curve.rectCrossingsForCubic(crossings,
                                                    rxmin, rymin,
                                                    rxmax, rymax,
                                                    curx, cury,
                                                    coords[ci++],
                                                    coords[ci++],
                                                    coords[ci++],
                                                    coords[ci++],
                                                    endx = coords[ci++],
                                                    endy = coords[ci++],
                                                    0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CLOSE:
                    if (curx != movx || cury != movy) {
                        crossings =
                            Curve.rectCrossingsForLine(crossings,
                                                       rxmin, rymin,
                                                       rxmax, rymax,
                                                       curx, cury,
                                                       movx, movy);
                    }
                    curx = movx;
                    cury = movy;
                    // Count should always be a multiple of 2 here.
                    // assert((crossings & 1) != 0);
                    break;
                }
            }
            if (crossings != Curve.RECT_INTERSECTS &&
                (curx != movx || cury != movy))
            {
                crossings =
                    Curve.rectCrossingsForLine(crossings,
                                               rxmin, rymin,
                                               rxmax, rymax,
                                               curx, cury,
                                               movx, movy);
            }
            // Count should always be a multiple of 2 here.
            // assert((crossings & 1) != 0);
            return crossings;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final void append(PathIterator pi, boolean connect) {
            float coords[] = new float[6];
            while (!pi.isDone()) {
                switch (pi.currentSegment(coords)) {
                case SEG_MOVETO:
                    if (!connect || numTypes < 1 || numCoords < 1) {
                        moveTo(coords[0], coords[1]);
                        break;
                    }
                    if (pointTypes[numTypes - 1] != SEG_CLOSE &&
                        floatCoords[numCoords-2] == coords[0] &&
                        floatCoords[numCoords-1] == coords[1])
                    {
                        // Collapse out initial moveto/lineto
                        break;
                    }
                    lineTo(coords[0], coords[1]);
                    break;
                case SEG_LINETO:
                    lineTo(coords[0], coords[1]);
                    break;
                case SEG_QUADTO:
                    quadTo(coords[0], coords[1],
                           coords[2], coords[3]);
                    break;
                case SEG_CUBICTO:
                    curveTo(coords[0], coords[1],
                            coords[2], coords[3],
                            coords[4], coords[5]);
                    break;
                case SEG_CLOSE:
                    closePath();
                    break;
                }
                pi.next();
                connect = false;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final void transform(AffineTransform at) {
            at.transform(floatCoords, 0, floatCoords, 0, numCoords / 2);
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized Rectangle2D getBounds2D() {
            float x1, y1, x2, y2;
            int i = numCoords;
            if (i > 0) {
                y1 = y2 = floatCoords[--i];
                x1 = x2 = floatCoords[--i];
                while (i > 0) {
                    float y = floatCoords[--i];
                    float x = floatCoords[--i];
                    if (x < x1) x1 = x;
                    if (y < y1) y1 = y;
                    if (x > x2) x2 = x;
                    if (y > y2) y2 = y;
                }
            } else {
                x1 = y1 = x2 = y2 = 0.0f;
            }
            return new Rectangle2D.Float(x1, y1, x2 - x1, y2 - y1);
        }

        /**
         * {@inheritDoc}
         * <p>
         * The iterator for this class is not multi-threaded safe,
         * which means that the {@code Path2D} class does not
         * guarantee that modifications to the geometry of this
         * {@code Path2D} object do not affect any iterations of
         * that geometry that are already in process.
         *
         * @since 1.6
         */
        public final PathIterator getPathIterator(AffineTransform at) {
            if (at == null) {
                return new CopyIterator(this);
            } else {
                return new TxIterator(this, at);
            }
        }

        /**
         * Creates a new object of the same class as this object.
         *
         * @return     a clone of this instance.
         * @exception  OutOfMemoryError    if there is not enough memory.
         * @see        Cloneable
         * @since      1.6
         */
        public final Object clone() {
            // Note: It would be nice to have this return Path2D
            // but one of our subclasses (GeneralPath) needs to
            // offer "public Object clone()" for backwards
            // compatibility so we cannot restrict it further.
            // REMIND: Can we do both somehow?
            if (this instanceof GeneralPath) {
                return new GeneralPath(this);
            } else {
                return new Float(this);
            }
        }

        /*
         * JDK 1.6 serialVersionUID
         */
        private static final long serialVersionUID = 6990832515060788886L;

        /**
         * Writes the default serializable fields to the
         * {@code ObjectOutputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         *
         * @serialData
         * <a name="Path2DSerialData"><!-- --></a>
         * <ol>
         * <li>The default serializable fields.
         * There are no default serializable fields as of 1.6.
         * <li>followed by
         * a byte indicating the storage type of the original object
         * as a hint (SERIAL_STORAGE_FLT_ARRAY)
         * <li>followed by
         * an integer indicating the number of path segments to follow (NP)
         * or -1 to indicate an unknown number of path segments follows
         * <li>followed by
         * an integer indicating the total number of coordinates to follow (NC)
         * or -1 to indicate an unknown number of coordinates follows
         * (NC should always be even since coordinates always appear in pairs
         *  representing an x,y pair)
         * <li>followed by
         * a byte indicating the winding rule
         * ({@link #WIND_EVEN_ODD WIND_EVEN_ODD} or
         *  {@link #WIND_NON_ZERO WIND_NON_ZERO})
         * <li>followed by
         * {@code NP} (or unlimited if {@code NP < 0}) sets of values consisting of
         * a single byte indicating a path segment type
         * followed by one or more pairs of float or double
         * values representing the coordinates of the path segment
         * <li>followed by
         * a byte indicating the end of the path (SERIAL_PATH_END).
         * </ol>
         * <p>
         * The following byte value constants are used in the serialized form
         * of {@code Path2D} objects:
         * <table>
         * <tr>
         * <th>Constant Name</th>
         * <th>Byte Value</th>
         * <th>Followed by</th>
         * <th>Description</th>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_STORAGE_FLT_ARRAY}</td>
         * <td>0x30</td>
         * <td></td>
         * <td>A hint that the original {@code Path2D} object stored
         * the coordinates in a Java array of floats.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_STORAGE_DBL_ARRAY}</td>
         * <td>0x31</td>
         * <td></td>
         * <td>A hint that the original {@code Path2D} object stored
         * the coordinates in a Java array of doubles.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_MOVETO}</td>
         * <td>0x40</td>
         * <td>2 floats</td>
         * <td>A {@link #moveTo moveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_LINETO}</td>
         * <td>0x41</td>
         * <td>2 floats</td>
         * <td>A {@link #lineTo lineTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_QUADTO}</td>
         * <td>0x42</td>
         * <td>4 floats</td>
         * <td>A {@link #quadTo quadTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_CUBICTO}</td>
         * <td>0x43</td>
         * <td>6 floats</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_MOVETO}</td>
         * <td>0x50</td>
         * <td>2 doubles</td>
         * <td>A {@link #moveTo moveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_LINETO}</td>
         * <td>0x51</td>
         * <td>2 doubles</td>
         * <td>A {@link #lineTo lineTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_QUADTO}</td>
         * <td>0x52</td>
         * <td>4 doubles</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_CUBICTO}</td>
         * <td>0x53</td>
         * <td>6 doubles</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_CLOSE}</td>
         * <td>0x60</td>
         * <td></td>
         * <td>A {@link #closePath closePath} path segment.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_PATH_END}</td>
         * <td>0x61</td>
         * <td></td>
         * <td>There are no more path segments following.</td>
         * </table>
         *
         * @since 1.6
         */
        private void writeObject(java.io.ObjectOutputStream s)
            throws java.io.IOException
        {
            super.writeObject(s, false);
        }

        /**
         * Reads the default serializable fields from the
         * {@code ObjectInputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         * <p>
         * There are no default serializable fields as of 1.6.
         * <p>
         * The serial data for this object is described in the
         * writeObject method.
         *
         * @since 1.6
         */
        private void readObject(java.io.ObjectInputStream s)
            throws ClassNotFoundException, java.io.IOException
        {
            super.readObject(s, false);
        }

        static class CopyIterator extends Iterator {
            float floatCoords[];

            CopyIterator(Float p2df) {
                super(p2df);
                this.floatCoords = p2df.floatCoords;
            }

            public int currentSegment(float[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    System.arraycopy(floatCoords, pointIdx,
                                     coords, 0, numCoords);
                }
                return type;
            }

            public int currentSegment(double[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    for (int i = 0; i < numCoords; i++) {
                        coords[i] = floatCoords[pointIdx + i];
                    }
                }
                return type;
            }
        }

        static class TxIterator extends Iterator {
            float floatCoords[];
            AffineTransform affine;

            TxIterator(Float p2df, AffineTransform at) {
                super(p2df);
                this.floatCoords = p2df.floatCoords;
                this.affine = at;
            }

            public int currentSegment(float[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    affine.transform(floatCoords, pointIdx,
                                     coords, 0, numCoords / 2);
                }
                return type;
            }

            public int currentSegment(double[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    affine.transform(floatCoords, pointIdx,
                                     coords, 0, numCoords / 2);
                }
                return type;
            }
        }

    }

    /**
     * The {@code Double} class defines a geometric path with
     * coordinates stored in double precision floating point.
     *
     * @since 1.6
     */
    public static class Double extends Path2D implements Serializable {
        transient double doubleCoords[];

        /**
         * Constructs a new empty double precision {@code Path2D} object
         * with a default winding rule of {@link #WIND_NON_ZERO}.
         *
         * @since 1.6
         */
        public Double() {
            this(WIND_NON_ZERO, INIT_SIZE);
        }

        /**
         * Constructs a new empty double precision {@code Path2D} object
         * with the specified winding rule to control operations that
         * require the interior of the path to be defined.
         *
         * @param rule the winding rule
         * @see #WIND_EVEN_ODD
         * @see #WIND_NON_ZERO
         * @since 1.6
         */
        public Double(int rule) {
            this(rule, INIT_SIZE);
        }

        /**
         * Constructs a new empty double precision {@code Path2D} object
         * with the specified winding rule and the specified initial
         * capacity to store path segments.
         * This number is an initial guess as to how many path segments
         * are in the path, but the storage is expanded as needed to store
         * whatever path segments are added to this path.
         *
         * @param rule the winding rule
         * @param initialCapacity the estimate for the number of path segments
         *                        in the path
         * @see #WIND_EVEN_ODD
         * @see #WIND_NON_ZERO
         * @since 1.6
         */
        public Double(int rule, int initialCapacity) {
            super(rule, initialCapacity);
            doubleCoords = new double[initialCapacity * 2];
        }

        /**
         * Constructs a new double precision {@code Path2D} object
         * from an arbitrary {@link Shape} object.
         * All of the initial geometry and the winding rule for this path are
         * taken from the specified {@code Shape} object.
         *
         * @param s the specified {@code Shape} object
         * @since 1.6
         */
        public Double(Shape s) {
            this(s, null);
        }

        /**
         * Constructs a new double precision {@code Path2D} object
         * from an arbitrary {@link Shape} object, transformed by an
         * {@link AffineTransform} object.
         * All of the initial geometry and the winding rule for this path are
         * taken from the specified {@code Shape} object and transformed
         * by the specified {@code AffineTransform} object.
         *
         * @param s the specified {@code Shape} object
         * @param at the specified {@code AffineTransform} object
         * @since 1.6
         */
        public Double(Shape s, AffineTransform at) {
            if (s instanceof Path2D) {
                Path2D p2d = (Path2D) s;
                setWindingRule(p2d.windingRule);
                this.numTypes = p2d.numTypes;
                // trim arrays:
                this.pointTypes = Arrays.copyOf(p2d.pointTypes, p2d.numTypes);
                this.numCoords = p2d.numCoords;
                this.doubleCoords = p2d.cloneCoordsDouble(at);
            } else {
                PathIterator pi = s.getPathIterator(at);
                setWindingRule(pi.getWindingRule());
                this.pointTypes = new byte[INIT_SIZE];
                this.doubleCoords = new double[INIT_SIZE * 2];
                append(pi, false);
            }
        }

        @Override
        float[] cloneCoordsFloat(AffineTransform at) {
            // trim arrays:
            float ret[] = new float[numCoords];
            if (at == null) {
                for (int i = 0; i < numCoords; i++) {
                    ret[i] = (float) doubleCoords[i];
                }
            } else {
                at.transform(doubleCoords, 0, ret, 0, numCoords / 2);
            }
            return ret;
        }

        @Override
        double[] cloneCoordsDouble(AffineTransform at) {
            // trim arrays:
            double ret[];
            if (at == null) {
                ret = Arrays.copyOf(doubleCoords, numCoords);
            } else {
                ret = new double[numCoords];
                at.transform(doubleCoords, 0, ret, 0, numCoords / 2);
            }
            return ret;
        }

        void append(float x, float y) {
            doubleCoords[numCoords++] = x;
            doubleCoords[numCoords++] = y;
        }

        void append(double x, double y) {
            doubleCoords[numCoords++] = x;
            doubleCoords[numCoords++] = y;
        }

        Point2D getPoint(int coordindex) {
            return new Point2D.Double(doubleCoords[coordindex],
                                      doubleCoords[coordindex+1]);
        }

        @Override
        void needRoom(boolean needMove, int newCoords) {
            if ((numTypes == 0) && needMove) {
                throw new IllegalPathStateException("missing initial moveto "+
                                                    "in path definition");
            }
            if (numTypes >= pointTypes.length) {
                pointTypes = expandPointTypes(pointTypes, 1);
            }
            if (numCoords > (doubleCoords.length - newCoords)) {
                doubleCoords = expandCoords(doubleCoords, newCoords);
            }
        }

        static double[] expandCoords(double[] oldCoords, int needed) {
            final int oldSize = oldCoords.length;
            final int newSizeMin = oldSize + needed;
            if (newSizeMin < oldSize) {
                // hard overflow failure - we can't even accommodate
                // new items without overflowing
                throw new ArrayIndexOutOfBoundsException(
                              "coords exceeds maximum capacity !");
            }
            // growth algorithm computation
            int grow = oldSize;
            if (grow > EXPAND_MAX_COORDS) {
                grow = Math.max(EXPAND_MAX_COORDS, oldSize >> 3); // 1/8th min
            } else if (grow < EXPAND_MIN) {
                grow = EXPAND_MIN;
            }
            assert grow > needed;

            int newSize = oldSize + grow;
            if (newSize < newSizeMin) {
                // overflow in growth algorithm computation
                newSize = Integer.MAX_VALUE;
            }
            while (true) {
                try {
                    // try allocating the larger array
                    return Arrays.copyOf(oldCoords, newSize);
                } catch (OutOfMemoryError oome) {
                    if (newSize == newSizeMin) {
                        throw oome;
                    }
                }
                newSize = newSizeMin + (newSize - newSizeMin) / 2;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void moveTo(double x, double y) {
            if (numTypes > 0 && pointTypes[numTypes - 1] == SEG_MOVETO) {
                doubleCoords[numCoords-2] = x;
                doubleCoords[numCoords-1] = y;
            } else {
                needRoom(false, 2);
                pointTypes[numTypes++] = SEG_MOVETO;
                doubleCoords[numCoords++] = x;
                doubleCoords[numCoords++] = y;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void lineTo(double x, double y) {
            needRoom(true, 2);
            pointTypes[numTypes++] = SEG_LINETO;
            doubleCoords[numCoords++] = x;
            doubleCoords[numCoords++] = y;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void quadTo(double x1, double y1,
                                              double x2, double y2)
        {
            needRoom(true, 4);
            pointTypes[numTypes++] = SEG_QUADTO;
            doubleCoords[numCoords++] = x1;
            doubleCoords[numCoords++] = y1;
            doubleCoords[numCoords++] = x2;
            doubleCoords[numCoords++] = y2;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized void curveTo(double x1, double y1,
                                               double x2, double y2,
                                               double x3, double y3)
        {
            needRoom(true, 6);
            pointTypes[numTypes++] = SEG_CUBICTO;
            doubleCoords[numCoords++] = x1;
            doubleCoords[numCoords++] = y1;
            doubleCoords[numCoords++] = x2;
            doubleCoords[numCoords++] = y2;
            doubleCoords[numCoords++] = x3;
            doubleCoords[numCoords++] = y3;
        }

        int pointCrossings(double px, double py) {
            if (numTypes == 0) {
                return 0;
            }
            double movx, movy, curx, cury, endx, endy;
            double coords[] = doubleCoords;
            curx = movx = coords[0];
            cury = movy = coords[1];
            int crossings = 0;
            int ci = 2;
            for (int i = 1; i < numTypes; i++) {
                switch (pointTypes[i]) {
                case PathIterator.SEG_MOVETO:
                    if (cury != movy) {
                        crossings +=
                            Curve.pointCrossingsForLine(px, py,
                                                        curx, cury,
                                                        movx, movy);
                    }
                    movx = curx = coords[ci++];
                    movy = cury = coords[ci++];
                    break;
                case PathIterator.SEG_LINETO:
                    crossings +=
                        Curve.pointCrossingsForLine(px, py,
                                                    curx, cury,
                                                    endx = coords[ci++],
                                                    endy = coords[ci++]);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_QUADTO:
                    crossings +=
                        Curve.pointCrossingsForQuad(px, py,
                                                    curx, cury,
                                                    coords[ci++],
                                                    coords[ci++],
                                                    endx = coords[ci++],
                                                    endy = coords[ci++],
                                                    0);
                    curx = endx;
                    cury = endy;
                    break;
            case PathIterator.SEG_CUBICTO:
                    crossings +=
                        Curve.pointCrossingsForCubic(px, py,
                                                     curx, cury,
                                                     coords[ci++],
                                                     coords[ci++],
                                                     coords[ci++],
                                                     coords[ci++],
                                                     endx = coords[ci++],
                                                     endy = coords[ci++],
                                                     0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CLOSE:
                    if (cury != movy) {
                        crossings +=
                            Curve.pointCrossingsForLine(px, py,
                                                        curx, cury,
                                                        movx, movy);
                    }
                    curx = movx;
                    cury = movy;
                    break;
                }
            }
            if (cury != movy) {
                crossings +=
                    Curve.pointCrossingsForLine(px, py,
                                                curx, cury,
                                                movx, movy);
            }
            return crossings;
        }

        int rectCrossings(double rxmin, double rymin,
                          double rxmax, double rymax)
        {
            if (numTypes == 0) {
                return 0;
            }
            double coords[] = doubleCoords;
            double curx, cury, movx, movy, endx, endy;
            curx = movx = coords[0];
            cury = movy = coords[1];
            int crossings = 0;
            int ci = 2;
            for (int i = 1;
                 crossings != Curve.RECT_INTERSECTS && i < numTypes;
                 i++)
            {
                switch (pointTypes[i]) {
                case PathIterator.SEG_MOVETO:
                    if (curx != movx || cury != movy) {
                        crossings =
                            Curve.rectCrossingsForLine(crossings,
                                                       rxmin, rymin,
                                                       rxmax, rymax,
                                                       curx, cury,
                                                       movx, movy);
                    }
                    // Count should always be a multiple of 2 here.
                    // assert((crossings & 1) != 0);
                    movx = curx = coords[ci++];
                    movy = cury = coords[ci++];
                    break;
                case PathIterator.SEG_LINETO:
                    endx = coords[ci++];
                    endy = coords[ci++];
                    crossings =
                        Curve.rectCrossingsForLine(crossings,
                                                   rxmin, rymin,
                                                   rxmax, rymax,
                                                   curx, cury,
                                                   endx, endy);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_QUADTO:
                    crossings =
                        Curve.rectCrossingsForQuad(crossings,
                                                   rxmin, rymin,
                                                   rxmax, rymax,
                                                   curx, cury,
                                                   coords[ci++],
                                                   coords[ci++],
                                                   endx = coords[ci++],
                                                   endy = coords[ci++],
                                                   0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CUBICTO:
                    crossings =
                        Curve.rectCrossingsForCubic(crossings,
                                                    rxmin, rymin,
                                                    rxmax, rymax,
                                                    curx, cury,
                                                    coords[ci++],
                                                    coords[ci++],
                                                    coords[ci++],
                                                    coords[ci++],
                                                    endx = coords[ci++],
                                                    endy = coords[ci++],
                                                    0);
                    curx = endx;
                    cury = endy;
                    break;
                case PathIterator.SEG_CLOSE:
                    if (curx != movx || cury != movy) {
                        crossings =
                            Curve.rectCrossingsForLine(crossings,
                                                       rxmin, rymin,
                                                       rxmax, rymax,
                                                       curx, cury,
                                                       movx, movy);
                    }
                    curx = movx;
                    cury = movy;
                    // Count should always be a multiple of 2 here.
                    // assert((crossings & 1) != 0);
                    break;
                }
            }
            if (crossings != Curve.RECT_INTERSECTS &&
                (curx != movx || cury != movy))
            {
                crossings =
                    Curve.rectCrossingsForLine(crossings,
                                               rxmin, rymin,
                                               rxmax, rymax,
                                               curx, cury,
                                               movx, movy);
            }
            // Count should always be a multiple of 2 here.
            // assert((crossings & 1) != 0);
            return crossings;
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final void append(PathIterator pi, boolean connect) {
            double coords[] = new double[6];
            while (!pi.isDone()) {
                switch (pi.currentSegment(coords)) {
                case SEG_MOVETO:
                    if (!connect || numTypes < 1 || numCoords < 1) {
                        moveTo(coords[0], coords[1]);
                        break;
                    }
                    if (pointTypes[numTypes - 1] != SEG_CLOSE &&
                        doubleCoords[numCoords-2] == coords[0] &&
                        doubleCoords[numCoords-1] == coords[1])
                    {
                        // Collapse out initial moveto/lineto
                        break;
                    }
                    lineTo(coords[0], coords[1]);
                    break;
                case SEG_LINETO:
                    lineTo(coords[0], coords[1]);
                    break;
                case SEG_QUADTO:
                    quadTo(coords[0], coords[1],
                           coords[2], coords[3]);
                    break;
                case SEG_CUBICTO:
                    curveTo(coords[0], coords[1],
                            coords[2], coords[3],
                            coords[4], coords[5]);
                    break;
                case SEG_CLOSE:
                    closePath();
                    break;
                }
                pi.next();
                connect = false;
            }
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final void transform(AffineTransform at) {
            at.transform(doubleCoords, 0, doubleCoords, 0, numCoords / 2);
        }

        /**
         * {@inheritDoc}
         * @since 1.6
         */
        public final synchronized Rectangle2D getBounds2D() {
            double x1, y1, x2, y2;
            int i = numCoords;
            if (i > 0) {
                y1 = y2 = doubleCoords[--i];
                x1 = x2 = doubleCoords[--i];
                while (i > 0) {
                    double y = doubleCoords[--i];
                    double x = doubleCoords[--i];
                    if (x < x1) x1 = x;
                    if (y < y1) y1 = y;
                    if (x > x2) x2 = x;
                    if (y > y2) y2 = y;
                }
            } else {
                x1 = y1 = x2 = y2 = 0.0;
            }
            return new Rectangle2D.Double(x1, y1, x2 - x1, y2 - y1);
        }

        /**
         * {@inheritDoc}
         * <p>
         * The iterator for this class is not multi-threaded safe,
         * which means that the {@code Path2D} class does not
         * guarantee that modifications to the geometry of this
         * {@code Path2D} object do not affect any iterations of
         * that geometry that are already in process.
         *
         * @param at an {@code AffineTransform}
         * @return a new {@code PathIterator} that iterates along the boundary
         *         of this {@code Shape} and provides access to the geometry
         *         of this {@code Shape}'s outline
         * @since 1.6
         */
        public final PathIterator getPathIterator(AffineTransform at) {
            if (at == null) {
                return new CopyIterator(this);
            } else {
                return new TxIterator(this, at);
            }
        }

        /**
         * Creates a new object of the same class as this object.
         *
         * @return     a clone of this instance.
         * @exception  OutOfMemoryError    if there is not enough memory.
         * @see        Cloneable
         * @since      1.6
         */
        public final Object clone() {
            // Note: It would be nice to have this return Path2D
            // but one of our subclasses (GeneralPath) needs to
            // offer "public Object clone()" for backwards
            // compatibility so we cannot restrict it further.
            // REMIND: Can we do both somehow?
            return new Double(this);
        }

        /*
         * JDK 1.6 serialVersionUID
         */
        private static final long serialVersionUID = 1826762518450014216L;

        /**
         * Writes the default serializable fields to the
         * {@code ObjectOutputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         *
         * @serialData
         * <a name="Path2DSerialData"><!-- --></a>
         * <ol>
         * <li>The default serializable fields.
         * There are no default serializable fields as of 1.6.
         * <li>followed by
         * a byte indicating the storage type of the original object
         * as a hint (SERIAL_STORAGE_DBL_ARRAY)
         * <li>followed by
         * an integer indicating the number of path segments to follow (NP)
         * or -1 to indicate an unknown number of path segments follows
         * <li>followed by
         * an integer indicating the total number of coordinates to follow (NC)
         * or -1 to indicate an unknown number of coordinates follows
         * (NC should always be even since coordinates always appear in pairs
         *  representing an x,y pair)
         * <li>followed by
         * a byte indicating the winding rule
         * ({@link #WIND_EVEN_ODD WIND_EVEN_ODD} or
         *  {@link #WIND_NON_ZERO WIND_NON_ZERO})
         * <li>followed by
         * {@code NP} (or unlimited if {@code NP < 0}) sets of values consisting of
         * a single byte indicating a path segment type
         * followed by one or more pairs of float or double
         * values representing the coordinates of the path segment
         * <li>followed by
         * a byte indicating the end of the path (SERIAL_PATH_END).
         * </ol>
         * <p>
         * The following byte value constants are used in the serialized form
         * of {@code Path2D} objects:
         * <table>
         * <tr>
         * <th>Constant Name</th>
         * <th>Byte Value</th>
         * <th>Followed by</th>
         * <th>Description</th>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_STORAGE_FLT_ARRAY}</td>
         * <td>0x30</td>
         * <td></td>
         * <td>A hint that the original {@code Path2D} object stored
         * the coordinates in a Java array of floats.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_STORAGE_DBL_ARRAY}</td>
         * <td>0x31</td>
         * <td></td>
         * <td>A hint that the original {@code Path2D} object stored
         * the coordinates in a Java array of doubles.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_MOVETO}</td>
         * <td>0x40</td>
         * <td>2 floats</td>
         * <td>A {@link #moveTo moveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_LINETO}</td>
         * <td>0x41</td>
         * <td>2 floats</td>
         * <td>A {@link #lineTo lineTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_QUADTO}</td>
         * <td>0x42</td>
         * <td>4 floats</td>
         * <td>A {@link #quadTo quadTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_FLT_CUBICTO}</td>
         * <td>0x43</td>
         * <td>6 floats</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_MOVETO}</td>
         * <td>0x50</td>
         * <td>2 doubles</td>
         * <td>A {@link #moveTo moveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_LINETO}</td>
         * <td>0x51</td>
         * <td>2 doubles</td>
         * <td>A {@link #lineTo lineTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_QUADTO}</td>
         * <td>0x52</td>
         * <td>4 doubles</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_DBL_CUBICTO}</td>
         * <td>0x53</td>
         * <td>6 doubles</td>
         * <td>A {@link #curveTo curveTo} path segment follows.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_SEG_CLOSE}</td>
         * <td>0x60</td>
         * <td></td>
         * <td>A {@link #closePath closePath} path segment.</td>
         * </tr>
         * <tr>
         * <td>{@code SERIAL_PATH_END}</td>
         * <td>0x61</td>
         * <td></td>
         * <td>There are no more path segments following.</td>
         * </table>
         *
         * @since 1.6
         */
        private void writeObject(java.io.ObjectOutputStream s)
            throws java.io.IOException
        {
            super.writeObject(s, true);
        }

        /**
         * Reads the default serializable fields from the
         * {@code ObjectInputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         * <p>
         * There are no default serializable fields as of 1.6.
         * <p>
         * The serial data for this object is described in the
         * writeObject method.
         *
         * @since 1.6
         */
        private void readObject(java.io.ObjectInputStream s)
            throws ClassNotFoundException, java.io.IOException
        {
            super.readObject(s, true);
        }

        static class CopyIterator extends Iterator {
            double doubleCoords[];

            CopyIterator(Double p2dd) {
                super(p2dd);
                this.doubleCoords = p2dd.doubleCoords;
            }

            public int currentSegment(float[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    for (int i = 0; i < numCoords; i++) {
                        coords[i] = (float) doubleCoords[pointIdx + i];
                    }
                }
                return type;
            }

            public int currentSegment(double[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    System.arraycopy(doubleCoords, pointIdx,
                                     coords, 0, numCoords);
                }
                return type;
            }
        }

        static class TxIterator extends Iterator {
            double doubleCoords[];
            AffineTransform affine;

            TxIterator(Double p2dd, AffineTransform at) {
                super(p2dd);
                this.doubleCoords = p2dd.doubleCoords;
                this.affine = at;
            }

            public int currentSegment(float[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    affine.transform(doubleCoords, pointIdx,
                                     coords, 0, numCoords / 2);
                }
                return type;
            }

            public int currentSegment(double[] coords) {
                int type = path.pointTypes[typeIdx];
                int numCoords = curvecoords[type];
                if (numCoords > 0) {
                    affine.transform(doubleCoords, pointIdx,
                                     coords, 0, numCoords / 2);
                }
                return type;
            }
        }
    }

    /**
     * Adds a point to the path by moving to the specified
     * coordinates specified in double precision.
     *
     * @param x the specified X coordinate
     * @param y the specified Y coordinate
     * @since 1.6
     */
    public abstract void moveTo(double x, double y);

    /**
     * Adds a point to the path by drawing a straight line from the
     * current coordinates to the new specified coordinates
     * specified in double precision.
     *
     * @param x the specified X coordinate
     * @param y the specified Y coordinate
     * @since 1.6
     */
    public abstract void lineTo(double x, double y);

    /**
     * Adds a curved segment, defined by two new points, to the path by
     * drawing a Quadratic curve that intersects both the current
     * coordinates and the specified coordinates {@code (x2,y2)},
     * using the specified point {@code (x1,y1)} as a quadratic
     * parametric control point.
     * All coordinates are specified in double precision.
     *
     * @param x1 the X coordinate of the quadratic control point
     * @param y1 the Y coordinate of the quadratic control point
     * @param x2 the X coordinate of the final end point
     * @param y2 the Y coordinate of the final end point
     * @since 1.6
     */
    public abstract void quadTo(double x1, double y1,
                                double x2, double y2);

    /**
     * Adds a curved segment, defined by three new points, to the path by
     * drawing a B&eacute;zier curve that intersects both the current
     * coordinates and the specified coordinates {@code (x3,y3)},
     * using the specified points {@code (x1,y1)} and {@code (x2,y2)} as
     * B&eacute;zier control points.
     * All coordinates are specified in double precision.
     *
     * @param x1 the X coordinate of the first B&eacute;zier control point
     * @param y1 the Y coordinate of the first B&eacute;zier control point
     * @param x2 the X coordinate of the second B&eacute;zier control point
     * @param y2 the Y coordinate of the second B&eacute;zier control point
     * @param x3 the X coordinate of the final end point
     * @param y3 the Y coordinate of the final end point
     * @since 1.6
     */
    public abstract void curveTo(double x1, double y1,
                                 double x2, double y2,
                                 double x3, double y3);

    /**
     * Closes the current subpath by drawing a straight line back to
     * the coordinates of the last {@code moveTo}.  If the path is already
     * closed then this method has no effect.
     *
     * @since 1.6
     */
    public final synchronized void closePath() {
        if (numTypes == 0 || pointTypes[numTypes - 1] != SEG_CLOSE) {
            needRoom(true, 0);
            pointTypes[numTypes++] = SEG_CLOSE;
        }
    }

    /**
     * Appends the geometry of the specified {@code Shape} object to the
     * path, possibly connecting the new geometry to the existing path
     * segments with a line segment.
     * If the {@code connect} parameter is {@code true} and the
     * path is not empty then any initial {@code moveTo} in the
     * geometry of the appended {@code Shape}
     * is turned into a {@code lineTo} segment.
     * If the destination coordinates of such a connecting {@code lineTo}
     * segment match the ending coordinates of a currently open
     * subpath then the segment is omitted as superfluous.
     * The winding rule of the specified {@code Shape} is ignored
     * and the appended geometry is governed by the winding
     * rule specified for this path.
     *
     * @param s the {@code Shape} whose geometry is appended
     *          to this path
     * @param connect a boolean to control whether or not to turn an initial
     *                {@code moveTo} segment into a {@code lineTo} segment
     *                to connect the new geometry to the existing path
     * @since 1.6
     */
    public final void append(Shape s, boolean connect) {
        append(s.getPathIterator(null), connect);
    }

    /**
     * Appends the geometry of the specified
     * {@link PathIterator} object
     * to the path, possibly connecting the new geometry to the existing
     * path segments with a line segment.
     * If the {@code connect} parameter is {@code true} and the
     * path is not empty then any initial {@code moveTo} in the
     * geometry of the appended {@code Shape} is turned into a
     * {@code lineTo} segment.
     * If the destination coordinates of such a connecting {@code lineTo}
     * segment match the ending coordinates of a currently open
     * subpath then the segment is omitted as superfluous.
     * The winding rule of the specified {@code Shape} is ignored
     * and the appended geometry is governed by the winding
     * rule specified for this path.
     *
     * @param pi the {@code PathIterator} whose geometry is appended to
     *           this path
     * @param connect a boolean to control whether or not to turn an initial
     *                {@code moveTo} segment into a {@code lineTo} segment
     *                to connect the new geometry to the existing path
     * @since 1.6
     */
    public abstract void append(PathIterator pi, boolean connect);

    /**
     * Returns the fill style winding rule.
     *
     * @return an integer representing the current winding rule.
     * @see #WIND_EVEN_ODD
     * @see #WIND_NON_ZERO
     * @see #setWindingRule
     * @since 1.6
     */
    public final synchronized int getWindingRule() {
        return windingRule;
    }

    /**
     * Sets the winding rule for this path to the specified value.
     *
     * @param rule an integer representing the specified
     *             winding rule
     * @exception IllegalArgumentException if
     *          {@code rule} is not either
     *          {@link #WIND_EVEN_ODD} or
     *          {@link #WIND_NON_ZERO}
     * @see #getWindingRule
     * @since 1.6
     */
    public final void setWindingRule(int rule) {
        if (rule != WIND_EVEN_ODD && rule != WIND_NON_ZERO) {
            throw new IllegalArgumentException("winding rule must be "+
                                               "WIND_EVEN_ODD or "+
                                               "WIND_NON_ZERO");
        }
        windingRule = rule;
    }

    /**
     * Returns the coordinates most recently added to the end of the path
     * as a {@link Point2D} object.
     *
     * @return a {@code Point2D} object containing the ending coordinates of
     *         the path or {@code null} if there are no points in the path.
     * @since 1.6
     */
    public final synchronized Point2D getCurrentPoint() {
        int index = numCoords;
        if (numTypes < 1 || index < 1) {
            return null;
        }
        if (pointTypes[numTypes - 1] == SEG_CLOSE) {
        loop:
            for (int i = numTypes - 2; i > 0; i--) {
                switch (pointTypes[i]) {
                case SEG_MOVETO:
                    break loop;
                case SEG_LINETO:
                    index -= 2;
                    break;
                case SEG_QUADTO:
                    index -= 4;
                    break;
                case SEG_CUBICTO:
                    index -= 6;
                    break;
                case SEG_CLOSE:
                    break;
                }
            }
        }
        return getPoint(index - 2);
    }

    /**
     * Resets the path to empty.  The append position is set back to the
     * beginning of the path and all coordinates and point types are
     * forgotten.
     *
     * @since 1.6
     */
    public final synchronized void reset() {
        numTypes = numCoords = 0;
    }

    /**
     * Transforms the geometry of this path using the specified
     * {@link AffineTransform}.
     * The geometry is transformed in place, which permanently changes the
     * boundary defined by this object.
     *
     * @param at the {@code AffineTransform} used to transform the area
     * @since 1.6
     */
    public abstract void transform(AffineTransform at);

    /**
     * Returns a new {@code Shape} representing a transformed version
     * of this {@code Path2D}.
     * Note that the exact type and coordinate precision of the return
     * value is not specified for this method.
     * The method will return a Shape that contains no less precision
     * for the transformed geometry than this {@code Path2D} currently
     * maintains, but it may contain no more precision either.
     * If the tradeoff of precision vs. storage size in the result is
     * important then the convenience constructors in the
     * {@link Float#Path2D.Float(Shape, AffineTransform) Path2D.Float}
     * and
     * {@link Double#Path2D.Double(Shape, AffineTransform) Path2D.Double}
     * subclasses should be used to make the choice explicit.
     *
     * @param at the {@code AffineTransform} used to transform a
     *           new {@code Shape}.
     * @return a new {@code Shape}, transformed with the specified
     *         {@code AffineTransform}.
     * @since 1.6
     */
    public final synchronized Shape createTransformedShape(AffineTransform at) {
        Path2D p2d = (Path2D) clone();
        if (at != null) {
            p2d.transform(at);
        }
        return p2d;
    }

    /**
     * {@inheritDoc}
     * @since 1.6
     */
    public final Rectangle getBounds() {
        return getBounds2D().getBounds();
    }

    /**
     * Tests if the specified coordinates are inside the closed
     * boundary of the specified {@link PathIterator}.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#contains(double, double)} method.
     *
     * @param pi the specified {@code PathIterator}
     * @param x the specified X coordinate
     * @param y the specified Y coordinate
     * @return {@code true} if the specified coordinates are inside the
     *         specified {@code PathIterator}; {@code false} otherwise
     * @since 1.6
     */
    public static boolean contains(PathIterator pi, double x, double y) {
        if (x * 0.0 + y * 0.0 == 0.0) {
            /* N * 0.0 is 0.0 only if N is finite.
             * Here we know that both x and y are finite.
             */
            int mask = (pi.getWindingRule() == WIND_NON_ZERO ? -1 : 1);
            int cross = Curve.pointCrossingsForPath(pi, x, y);
            return ((cross & mask) != 0);
        } else {
            /* Either x or y was infinite or NaN.
             * A NaN always produces a negative response to any test
             * and Infinity values cannot be "inside" any path so
             * they should return false as well.
             */
            return false;
        }
    }

    /**
     * Tests if the specified {@link Point2D} is inside the closed
     * boundary of the specified {@link PathIterator}.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#contains(Point2D)} method.
     *
     * @param pi the specified {@code PathIterator}
     * @param p the specified {@code Point2D}
     * @return {@code true} if the specified coordinates are inside the
     *         specified {@code PathIterator}; {@code false} otherwise
     * @since 1.6
     */
    public static boolean contains(PathIterator pi, Point2D p) {
        return contains(pi, p.getX(), p.getY());
    }

    /**
     * {@inheritDoc}
     * @since 1.6
     */
    public final boolean contains(double x, double y) {
        if (x * 0.0 + y * 0.0 == 0.0) {
            /* N * 0.0 is 0.0 only if N is finite.
             * Here we know that both x and y are finite.
             */
            if (numTypes < 2) {
                return false;
            }
            int mask = (windingRule == WIND_NON_ZERO ? -1 : 1);
            return ((pointCrossings(x, y) & mask) != 0);
        } else {
            /* Either x or y was infinite or NaN.
             * A NaN always produces a negative response to any test
             * and Infinity values cannot be "inside" any path so
             * they should return false as well.
             */
            return false;
        }
    }

    /**
     * {@inheritDoc}
     * @since 1.6
     */
    public final boolean contains(Point2D p) {
        return contains(p.getX(), p.getY());
    }

    /**
     * Tests if the specified rectangular area is entirely inside the
     * closed boundary of the specified {@link PathIterator}.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#contains(double, double, double, double)} method.
     * <p>
     * This method object may conservatively return false in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such segments could lie entirely within the interior of the
     * path if they are part of a path with a {@link #WIND_NON_ZERO}
     * winding rule or if the segments are retraced in the reverse
     * direction such that the two sets of segments cancel each
     * other out without any exterior area falling between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @param pi the specified {@code PathIterator}
     * @param x the specified X coordinate
     * @param y the specified Y coordinate
     * @param w the width of the specified rectangular area
     * @param h the height of the specified rectangular area
     * @return {@code true} if the specified {@code PathIterator} contains
     *         the specified rectangular area; {@code false} otherwise.
     * @since 1.6
     */
    public static boolean contains(PathIterator pi,
                                   double x, double y, double w, double h)
    {
        if (java.lang.Double.isNaN(x+w) || java.lang.Double.isNaN(y+h)) {
            /* [xy]+[wh] is NaN if any of those values are NaN,
             * or if adding the two together would produce NaN
             * by virtue of adding opposing Infinte values.
             * Since we need to add them below, their sum must
             * not be NaN.
             * We return false because NaN always produces a
             * negative response to tests
             */
            return false;
        }
        if (w <= 0 || h <= 0) {
            return false;
        }
        int mask = (pi.getWindingRule() == WIND_NON_ZERO ? -1 : 2);
        int crossings = Curve.rectCrossingsForPath(pi, x, y, x+w, y+h);
        return (crossings != Curve.RECT_INTERSECTS &&
                (crossings & mask) != 0);
    }

    /**
     * Tests if the specified {@link Rectangle2D} is entirely inside the
     * closed boundary of the specified {@link PathIterator}.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#contains(Rectangle2D)} method.
     * <p>
     * This method object may conservatively return false in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such segments could lie entirely within the interior of the
     * path if they are part of a path with a {@link #WIND_NON_ZERO}
     * winding rule or if the segments are retraced in the reverse
     * direction such that the two sets of segments cancel each
     * other out without any exterior area falling between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @param pi the specified {@code PathIterator}
     * @param r a specified {@code Rectangle2D}
     * @return {@code true} if the specified {@code PathIterator} contains
     *         the specified {@code Rectangle2D}; {@code false} otherwise.
     * @since 1.6
     */
    public static boolean contains(PathIterator pi, Rectangle2D r) {
        return contains(pi, r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * {@inheritDoc}
     * <p>
     * This method object may conservatively return false in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such segments could lie entirely within the interior of the
     * path if they are part of a path with a {@link #WIND_NON_ZERO}
     * winding rule or if the segments are retraced in the reverse
     * direction such that the two sets of segments cancel each
     * other out without any exterior area falling between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @since 1.6
     */
    public final boolean contains(double x, double y, double w, double h) {
        if (java.lang.Double.isNaN(x+w) || java.lang.Double.isNaN(y+h)) {
            /* [xy]+[wh] is NaN if any of those values are NaN,
             * or if adding the two together would produce NaN
             * by virtue of adding opposing Infinte values.
             * Since we need to add them below, their sum must
             * not be NaN.
             * We return false because NaN always produces a
             * negative response to tests
             */
            return false;
        }
        if (w <= 0 || h <= 0) {
            return false;
        }
        int mask = (windingRule == WIND_NON_ZERO ? -1 : 2);
        int crossings = rectCrossings(x, y, x+w, y+h);
        return (crossings != Curve.RECT_INTERSECTS &&
                (crossings & mask) != 0);
    }

    /**
     * {@inheritDoc}
     * <p>
     * This method object may conservatively return false in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such segments could lie entirely within the interior of the
     * path if they are part of a path with a {@link #WIND_NON_ZERO}
     * winding rule or if the segments are retraced in the reverse
     * direction such that the two sets of segments cancel each
     * other out without any exterior area falling between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @since 1.6
     */
    public final boolean contains(Rectangle2D r) {
        return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * Tests if the interior of the specified {@link PathIterator}
     * intersects the interior of a specified set of rectangular
     * coordinates.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#intersects(double, double, double, double)} method.
     * <p>
     * This method object may conservatively return true in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such a case may occur if some set of segments of the
     * path are retraced in the reverse direction such that the
     * two sets of segments cancel each other out without any
     * interior area between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @param pi the specified {@code PathIterator}
     * @param x the specified X coordinate
     * @param y the specified Y coordinate
     * @param w the width of the specified rectangular coordinates
     * @param h the height of the specified rectangular coordinates
     * @return {@code true} if the specified {@code PathIterator} and
     *         the interior of the specified set of rectangular
     *         coordinates intersect each other; {@code false} otherwise.
     * @since 1.6
     */
    public static boolean intersects(PathIterator pi,
                                     double x, double y, double w, double h)
    {
        if (java.lang.Double.isNaN(x+w) || java.lang.Double.isNaN(y+h)) {
            /* [xy]+[wh] is NaN if any of those values are NaN,
             * or if adding the two together would produce NaN
             * by virtue of adding opposing Infinte values.
             * Since we need to add them below, their sum must
             * not be NaN.
             * We return false because NaN always produces a
             * negative response to tests
             */
            return false;
        }
        if (w <= 0 || h <= 0) {
            return false;
        }
        int mask = (pi.getWindingRule() == WIND_NON_ZERO ? -1 : 2);
        int crossings = Curve.rectCrossingsForPath(pi, x, y, x+w, y+h);
        return (crossings == Curve.RECT_INTERSECTS ||
                (crossings & mask) != 0);
    }

    /**
     * Tests if the interior of the specified {@link PathIterator}
     * intersects the interior of a specified {@link Rectangle2D}.
     * <p>
     * This method provides a basic facility for implementors of
     * the {@link Shape} interface to implement support for the
     * {@link Shape#intersects(Rectangle2D)} method.
     * <p>
     * This method object may conservatively return true in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such a case may occur if some set of segments of the
     * path are retraced in the reverse direction such that the
     * two sets of segments cancel each other out without any
     * interior area between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @param pi the specified {@code PathIterator}
     * @param r the specified {@code Rectangle2D}
     * @return {@code true} if the specified {@code PathIterator} and
     *         the interior of the specified {@code Rectangle2D}
     *         intersect each other; {@code false} otherwise.
     * @since 1.6
     */
    public static boolean intersects(PathIterator pi, Rectangle2D r) {
        return intersects(pi, r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * {@inheritDoc}
     * <p>
     * This method object may conservatively return true in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such a case may occur if some set of segments of the
     * path are retraced in the reverse direction such that the
     * two sets of segments cancel each other out without any
     * interior area between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @since 1.6
     */
    public final boolean intersects(double x, double y, double w, double h) {
        if (java.lang.Double.isNaN(x+w) || java.lang.Double.isNaN(y+h)) {
            /* [xy]+[wh] is NaN if any of those values are NaN,
             * or if adding the two together would produce NaN
             * by virtue of adding opposing Infinte values.
             * Since we need to add them below, their sum must
             * not be NaN.
             * We return false because NaN always produces a
             * negative response to tests
             */
            return false;
        }
        if (w <= 0 || h <= 0) {
            return false;
        }
        int mask = (windingRule == WIND_NON_ZERO ? -1 : 2);
        int crossings = rectCrossings(x, y, x+w, y+h);
        return (crossings == Curve.RECT_INTERSECTS ||
                (crossings & mask) != 0);
    }

    /**
     * {@inheritDoc}
     * <p>
     * This method object may conservatively return true in
     * cases where the specified rectangular area intersects a
     * segment of the path, but that segment does not represent a
     * boundary between the interior and exterior of the path.
     * Such a case may occur if some set of segments of the
     * path are retraced in the reverse direction such that the
     * two sets of segments cancel each other out without any
     * interior area between them.
     * To determine whether segments represent true boundaries of
     * the interior of the path would require extensive calculations
     * involving all of the segments of the path and the winding
     * rule and are thus beyond the scope of this implementation.
     *
     * @since 1.6
     */
    public final boolean intersects(Rectangle2D r) {
        return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
    }

    /**
     * {@inheritDoc}
     * <p>
     * The iterator for this class is not multi-threaded safe,
     * which means that this {@code Path2D} class does not
     * guarantee that modifications to the geometry of this
     * {@code Path2D} object do not affect any iterations of
     * that geometry that are already in process.
     *
     * @since 1.6
     */
    public final PathIterator getPathIterator(AffineTransform at,
                                              double flatness)
    {
        return new FlatteningPathIterator(getPathIterator(at), flatness);
    }

    /**
     * Creates a new object of the same class as this object.
     *
     * @return     a clone of this instance.
     * @exception  OutOfMemoryError            if there is not enough memory.
     * @see        Cloneable
     * @since      1.6
     */
    public abstract Object clone();
        // Note: It would be nice to have this return Path2D
        // but one of our subclasses (GeneralPath) needs to
        // offer "public Object clone()" for backwards
        // compatibility so we cannot restrict it further.
        // REMIND: Can we do both somehow?

    /*
     * Support fields and methods for serializing the subclasses.
     */
    private static final byte SERIAL_STORAGE_FLT_ARRAY = 0x30;
    private static final byte SERIAL_STORAGE_DBL_ARRAY = 0x31;

    private static final byte SERIAL_SEG_FLT_MOVETO    = 0x40;
    private static final byte SERIAL_SEG_FLT_LINETO    = 0x41;
    private static final byte SERIAL_SEG_FLT_QUADTO    = 0x42;
    private static final byte SERIAL_SEG_FLT_CUBICTO   = 0x43;

    private static final byte SERIAL_SEG_DBL_MOVETO    = 0x50;
    private static final byte SERIAL_SEG_DBL_LINETO    = 0x51;
    private static final byte SERIAL_SEG_DBL_QUADTO    = 0x52;
    private static final byte SERIAL_SEG_DBL_CUBICTO   = 0x53;

    private static final byte SERIAL_SEG_CLOSE         = 0x60;
    private static final byte SERIAL_PATH_END          = 0x61;

    final void writeObject(java.io.ObjectOutputStream s, boolean isdbl)
        throws java.io.IOException
    {
        s.defaultWriteObject();

        float fCoords[];
        double dCoords[];

        if (isdbl) {
            dCoords = ((Double) this).doubleCoords;
            fCoords = null;
        } else {
            fCoords = ((Float) this).floatCoords;
            dCoords = null;
        }

        int numTypes = this.numTypes;

        s.writeByte(isdbl
                    ? SERIAL_STORAGE_DBL_ARRAY
                    : SERIAL_STORAGE_FLT_ARRAY);
        s.writeInt(numTypes);
        s.writeInt(numCoords);
        s.writeByte((byte) windingRule);

        int cindex = 0;
        for (int i = 0; i < numTypes; i++) {
            int npoints;
            byte serialtype;
            switch (pointTypes[i]) {
            case SEG_MOVETO:
                npoints = 1;
                serialtype = (isdbl
                              ? SERIAL_SEG_DBL_MOVETO
                              : SERIAL_SEG_FLT_MOVETO);
                break;
            case SEG_LINETO:
                npoints = 1;
                serialtype = (isdbl
                              ? SERIAL_SEG_DBL_LINETO
                              : SERIAL_SEG_FLT_LINETO);
                break;
            case SEG_QUADTO:
                npoints = 2;
                serialtype = (isdbl
                              ? SERIAL_SEG_DBL_QUADTO
                              : SERIAL_SEG_FLT_QUADTO);
                break;
            case SEG_CUBICTO:
                npoints = 3;
                serialtype = (isdbl
                              ? SERIAL_SEG_DBL_CUBICTO
                              : SERIAL_SEG_FLT_CUBICTO);
                break;
            case SEG_CLOSE:
                npoints = 0;
                serialtype = SERIAL_SEG_CLOSE;
                break;

            default:
                // Should never happen
                throw new InternalError("unrecognized path type");
            }
            s.writeByte(serialtype);
            while (--npoints >= 0) {
                if (isdbl) {
                    s.writeDouble(dCoords[cindex++]);
                    s.writeDouble(dCoords[cindex++]);
                } else {
                    s.writeFloat(fCoords[cindex++]);
                    s.writeFloat(fCoords[cindex++]);
                }
            }
        }
        s.writeByte(SERIAL_PATH_END);
    }

    final void readObject(java.io.ObjectInputStream s, boolean storedbl)
        throws ClassNotFoundException, java.io.IOException
    {
        s.defaultReadObject();

        // The subclass calls this method with the storage type that
        // they want us to use (storedbl) so we ignore the storage
        // method hint from the stream.
        s.readByte();
        int nT = s.readInt();
        int nC = s.readInt();
        try {
            setWindingRule(s.readByte());
        } catch (IllegalArgumentException iae) {
            throw new java.io.InvalidObjectException(iae.getMessage());
        }

        pointTypes = new byte[(nT < 0) ? INIT_SIZE : nT];
        if (nC < 0) {
            nC = INIT_SIZE * 2;
        }
        if (storedbl) {
            ((Double) this).doubleCoords = new double[nC];
        } else {
            ((Float) this).floatCoords = new float[nC];
        }

    PATHDONE:
        for (int i = 0; nT < 0 || i < nT; i++) {
            boolean isdbl;
            int npoints;
            byte segtype;

            byte serialtype = s.readByte();
            switch (serialtype) {
            case SERIAL_SEG_FLT_MOVETO:
                isdbl = false;
                npoints = 1;
                segtype = SEG_MOVETO;
                break;
            case SERIAL_SEG_FLT_LINETO:
                isdbl = false;
                npoints = 1;
                segtype = SEG_LINETO;
                break;
            case SERIAL_SEG_FLT_QUADTO:
                isdbl = false;
                npoints = 2;
                segtype = SEG_QUADTO;
                break;
            case SERIAL_SEG_FLT_CUBICTO:
                isdbl = false;
                npoints = 3;
                segtype = SEG_CUBICTO;
                break;

            case SERIAL_SEG_DBL_MOVETO:
                isdbl = true;
                npoints = 1;
                segtype = SEG_MOVETO;
                break;
            case SERIAL_SEG_DBL_LINETO:
                isdbl = true;
                npoints = 1;
                segtype = SEG_LINETO;
                break;
            case SERIAL_SEG_DBL_QUADTO:
                isdbl = true;
                npoints = 2;
                segtype = SEG_QUADTO;
                break;
            case SERIAL_SEG_DBL_CUBICTO:
                isdbl = true;
                npoints = 3;
                segtype = SEG_CUBICTO;
                break;

            case SERIAL_SEG_CLOSE:
                isdbl = false;
                npoints = 0;
                segtype = SEG_CLOSE;
                break;

            case SERIAL_PATH_END:
                if (nT < 0) {
                    break PATHDONE;
                }
                throw new StreamCorruptedException("unexpected PATH_END");

            default:
                throw new StreamCorruptedException("unrecognized path type");
            }
            needRoom(segtype != SEG_MOVETO, npoints * 2);
            if (isdbl) {
                while (--npoints >= 0) {
                    append(s.readDouble(), s.readDouble());
                }
            } else {
                while (--npoints >= 0) {
                    append(s.readFloat(), s.readFloat());
                }
            }
            pointTypes[numTypes++] = segtype;
        }
        if (nT >= 0 && s.readByte() != SERIAL_PATH_END) {
            throw new StreamCorruptedException("missing PATH_END");
        }
    }

    static abstract class Iterator implements PathIterator {
        int typeIdx;
        int pointIdx;
        Path2D path;

        static final int curvecoords[] = {2, 2, 4, 6, 0};

        Iterator(Path2D path) {
            this.path = path;
        }

        public int getWindingRule() {
            return path.getWindingRule();
        }

        public boolean isDone() {
            return (typeIdx >= path.numTypes);
        }

        public void next() {
            int type = path.pointTypes[typeIdx++];
            pointIdx += curvecoords[type];
        }
    }
}
