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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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package java.awt.geom;

import java.awt.Rectangle;
import java.awt.Shape;
import java.io.Serializable;
import java.io.StreamCorruptedException;
import java.util.Arrays;

import sun.awt.geom.Curve;

The 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 PathIterator interface including all of its segment types and winding rules and it implements all of the basic hit testing methods of the Shape interface. 
 Use Float when dealing with data that can be represented and used with floating point precision. Use Double for data that requires the accuracy or range of double precision. 
 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 Area class provides additional capabilities specifically targeted at closed figures. While both classes nominally implement the Shape interface, they differ in purpose and together they provide two useful views of a geometric shape where Path2D deals primarily with a trajectory formed by path segments and Area deals more with interpretation and manipulation of enclosed regions of 2D geometric space. 
 The 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/**
 * 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 Path2D.Float} when dealing with data that can be represented
 * and used with floating point precision.  Use {@link Path2D.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 Also:
WIND_EVEN_ODD.WIND_EVEN_ODD
Since:
1.6/**
     * 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 Also:
WIND_NON_ZERO.WIND_NON_ZERO
Since:
1.6/**
     * 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 Path2D object. It is assumed that the package sibling subclass that is defaulting to this constructor will fill in all values. 
Since:
1.6/**
     * 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 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. 
Params:
rule – the winding rule
initialTypes – the size to make the initial array to
                    store the path segment types
Since:
1.6/**
     * 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 Float class defines a geometric path with coordinates stored in single precision floating point. 
Since:
1.6/**
     * 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 Path2D object with a default winding rule of Path2D.WIND_NON_ZERO. 
Since:
1.6/**
         * 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 Path2D object with the specified winding rule to control operations that require the interior of the path to be defined. 
Params:
rule – the winding rule
See Also:
Path2D.WIND_EVEN_ODD
Path2D.WIND_NON_ZERO
Since:
1.6/**
         * 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 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. 
Params:
rule – the winding rule
initialCapacity – the estimate for the number of path segments
                       in the path
See Also:
Path2D.WIND_EVEN_ODD
Path2D.WIND_NON_ZERO
Since:
1.6/**
         * 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 Path2D object from an arbitrary Shape object. All of the initial geometry and the winding rule for this path are taken from the specified Shape object. 
Params:
s – the specified Shape object
Since:
1.6/**
         * 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 Path2D object from an arbitrary Shape object, transformed by an AffineTransform object. All of the initial geometry and the winding rule for this path are taken from the specified Shape object and transformed by the specified AffineTransform object. 
Params:
s – the specified Shape object
at – the specified AffineTransform object
Since:
1.6/**
         * 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
        public final void trimToSize() {
            // trim arrays:
            if (numTypes < pointTypes.length) {
                this.pointTypes = Arrays.copyOf(pointTypes, numTypes);
            }
            if (numCoords < floatCoords.length) {
                this.floatCoords = Arrays.copyOf(floatCoords, numCoords);
            }
        }

        @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/**
         * {@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.
 This method provides a single precision variant of the double precision moveTo() method on the base Path2D class. 
Params:
x – the specified X coordinate
y – the specified Y coordinate
See Also:
Path2D.moveTo
Since:
1.6/**
         * 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/**
         * {@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.
 This method provides a single precision variant of the double precision lineTo() method on the base Path2D class. 
Params:
x – the specified X coordinate
y – the specified Y coordinate
See Also:
Path2D.lineTo
Since:
1.6/**
         * 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/**
         * {@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 (x2,y2), using the specified point (x1,y1) as a quadratic parametric control point. All coordinates are specified in float precision. 
 This method provides a single precision variant of the double precision quadTo() method on the base Path2D class. 
Params:
x1 – the X coordinate of the quadratic control point
y1 – the Y coordinate of the quadratic control point
x2 – the X coordinate of the final end point
y2 – the Y coordinate of the final end point
See Also:
Path2D.quadTo
Since:
1.6/**
         * 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/**
         * {@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 Bézier curve that intersects both the current coordinates and the specified coordinates (x3,y3), using the specified points (x1,y1) and (x2,y2) as Bézier control points. All coordinates are specified in float precision. 
 This method provides a single precision variant of the double precision curveTo() method on the base Path2D class. 
Params:
x1 – the X coordinate of the first Bézier control point
y1 – the Y coordinate of the first Bézier control point
x2 – the X coordinate of the second Bézier control point
y2 – the Y coordinate of the second Bézier control point
x3 – the X coordinate of the final end point
y3 – the Y coordinate of the final end point
See Also:
Path2D.curveTo
Since:
1.6/**
         * 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/**
         * {@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/**
         * {@inheritDoc}
         * @since 1.6
         */
        public final void transform(AffineTransform at) {
            at.transform(floatCoords, 0, floatCoords, 0, numCoords / 2);
        }

        
{@inheritDoc}
Since:
1.6/**
         * {@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}
 The iterator for this class is not multi-threaded safe, which means that the Path2D class does not guarantee that modifications to the geometry of this Path2D object do not affect any iterations of that geometry that are already in process. 
Since:
1.6/**
         * {@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.
Throws:
OutOfMemoryError –    if there is not enough memory.
See Also:
Cloneable
Returns:
    a clone of this instance.
Since:
     1.6/**
         * 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        java.lang.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 Path2D.Float(this);
            }
        }

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

        
Writes the default serializable fields to the ObjectOutputStream followed by an explicit serialization of the path segments stored in this path. 
@serialData



The default serializable fields.
There are no default serializable fields as of 1.6.
followed by
a byte indicating the storage type of the original object
as a hint (SERIAL_STORAGE_FLT_ARRAY)
followed by
an integer indicating the number of path segments to follow (NP)
or -1 to indicate an unknown number of path segments follows
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)
followed by a byte indicating the winding rule (WIND_EVEN_ODD or WIND_NON_ZERO) 
followed by NP (or unlimited if 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 
followed by
a byte indicating the end of the path (SERIAL_PATH_END).

 The following byte value constants are used in the serialized form of Path2D objects: 

Constants


Constant Name
Byte Value
Followed by
Description




SERIAL_STORAGE_FLT_ARRAY
0x30

A hint that the original Path2D object stored the coordinates in a Java array of floats.


SERIAL_STORAGE_DBL_ARRAY
0x31

A hint that the original Path2D object stored the coordinates in a Java array of doubles.


SERIAL_SEG_FLT_MOVETO
0x40
2 floats
A moveTo path segment follows.


SERIAL_SEG_FLT_LINETO
0x41
2 floats
A lineTo path segment follows.


SERIAL_SEG_FLT_QUADTO
0x42
4 floats
A quadTo path segment follows.


SERIAL_SEG_FLT_CUBICTO
0x43
6 floats
A curveTo path segment follows.


SERIAL_SEG_DBL_MOVETO
0x50
2 doubles
A moveTo path segment follows.


SERIAL_SEG_DBL_LINETO
0x51
2 doubles
A lineTo path segment follows.


SERIAL_SEG_DBL_QUADTO
0x52
4 doubles
A curveTo path segment follows.


SERIAL_SEG_DBL_CUBICTO
0x53
6 doubles
A curveTo path segment follows.


SERIAL_SEG_CLOSE
0x60

A closePath path segment.


SERIAL_PATH_END
0x61

There are no more path segments following.

Since:
1.6/**
         * Writes the default serializable fields to the
         * {@code ObjectOutputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         *
         * @serialData
         * <a id="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 class="striped">
         * <caption>Constants</caption>
         * <thead>
         * <tr>
         * <th>Constant Name</th>
         * <th>Byte Value</th>
         * <th>Followed by</th>
         * <th>Description</th>
         * </tr>
         * </thead>
         * <tbody>
         * <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>
         * </tbody>
         * </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 ObjectInputStream followed by an explicit serialization of the path segments stored in this path. 

There are no default serializable fields as of 1.6.

The serial data for this object is described in the
writeObject method.
Since:
1.6/**
         * 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 java.lang.ClassNotFoundException, java.io.IOException
        {
            super.readObject(s, false);
        }

        static class CopyIterator extends Path2D.Iterator {
            float floatCoords[];

            CopyIterator(Path2D.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 Path2D.Iterator {
            float floatCoords[];
            AffineTransform affine;

            TxIterator(Path2D.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 Double class defines a geometric path with coordinates stored in double precision floating point. 
Since:
1.6/**
     * 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 Path2D object with a default winding rule of Path2D.WIND_NON_ZERO. 
Since:
1.6/**
         * 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 Path2D object with the specified winding rule to control operations that require the interior of the path to be defined. 
Params:
rule – the winding rule
See Also:
Path2D.WIND_EVEN_ODD
Path2D.WIND_NON_ZERO
Since:
1.6/**
         * 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 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. 
Params:
rule – the winding rule
initialCapacity – the estimate for the number of path segments
                       in the path
See Also:
Path2D.WIND_EVEN_ODD
Path2D.WIND_NON_ZERO
Since:
1.6/**
         * 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 Path2D object from an arbitrary Shape object. All of the initial geometry and the winding rule for this path are taken from the specified Shape object. 
Params:
s – the specified Shape object
Since:
1.6/**
         * 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 Path2D object from an arbitrary Shape object, transformed by an AffineTransform object. All of the initial geometry and the winding rule for this path are taken from the specified Shape object and transformed by the specified AffineTransform object. 
Params:
s – the specified Shape object
at – the specified AffineTransform object
Since:
1.6/**
         * 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
        public final void trimToSize() {
            // trim arrays:
            if (numTypes < pointTypes.length) {
                this.pointTypes = Arrays.copyOf(pointTypes, numTypes);
            }
            if (numCoords < doubleCoords.length) {
                this.doubleCoords = Arrays.copyOf(doubleCoords, numCoords);
            }
        }

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

        
{@inheritDoc}
Since:
1.6/**
         * {@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}
 The iterator for this class is not multi-threaded safe, which means that the Path2D class does not guarantee that modifications to the geometry of this Path2D object do not affect any iterations of that geometry that are already in process. 
Params:
at – an AffineTransform
Returns:
a new PathIterator that iterates along the boundary of this Shape and provides access to the geometry of this Shape's outline
Since:
1.6/**
         * {@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.
Throws:
OutOfMemoryError –    if there is not enough memory.
See Also:
Cloneable
Returns:
    a clone of this instance.
Since:
     1.6/**
         * 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        java.lang.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 Path2D.Double(this);
        }

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

        
Writes the default serializable fields to the ObjectOutputStream followed by an explicit serialization of the path segments stored in this path. 
@serialData



The default serializable fields.
There are no default serializable fields as of 1.6.
followed by
a byte indicating the storage type of the original object
as a hint (SERIAL_STORAGE_DBL_ARRAY)
followed by
an integer indicating the number of path segments to follow (NP)
or -1 to indicate an unknown number of path segments follows
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)
followed by a byte indicating the winding rule (WIND_EVEN_ODD or WIND_NON_ZERO) 
followed by NP (or unlimited if 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 
followed by
a byte indicating the end of the path (SERIAL_PATH_END).

 The following byte value constants are used in the serialized form of Path2D objects: 

Constants


Constant Name
Byte Value
Followed by
Description




SERIAL_STORAGE_FLT_ARRAY
0x30

A hint that the original Path2D object stored the coordinates in a Java array of floats.


SERIAL_STORAGE_DBL_ARRAY
0x31

A hint that the original Path2D object stored the coordinates in a Java array of doubles.


SERIAL_SEG_FLT_MOVETO
0x40
2 floats
A moveTo path segment follows.


SERIAL_SEG_FLT_LINETO
0x41
2 floats
A lineTo path segment follows.


SERIAL_SEG_FLT_QUADTO
0x42
4 floats
A quadTo path segment follows.


SERIAL_SEG_FLT_CUBICTO
0x43
6 floats
A curveTo path segment follows.


SERIAL_SEG_DBL_MOVETO
0x50
2 doubles
A moveTo path segment follows.


SERIAL_SEG_DBL_LINETO
0x51
2 doubles
A lineTo path segment follows.


SERIAL_SEG_DBL_QUADTO
0x52
4 doubles
A curveTo path segment follows.


SERIAL_SEG_DBL_CUBICTO
0x53
6 doubles
A curveTo path segment follows.


SERIAL_SEG_CLOSE
0x60

A closePath path segment.


SERIAL_PATH_END
0x61

There are no more path segments following.

Since:
1.6/**
         * Writes the default serializable fields to the
         * {@code ObjectOutputStream} followed by an explicit
         * serialization of the path segments stored in this
         * path.
         *
         * @serialData
         * <a id="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 class="striped">
         * <caption>Constants</caption>
         * <thead>
         * <tr>
         * <th>Constant Name</th>
         * <th>Byte Value</th>
         * <th>Followed by</th>
         * <th>Description</th>
         * </tr>
         * </thead>
         * <tbody>
         * <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>
         * </tbody>
         * </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 ObjectInputStream followed by an explicit serialization of the path segments stored in this path. 

There are no default serializable fields as of 1.6.

The serial data for this object is described in the
writeObject method.
Since:
1.6/**
         * 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 java.lang.ClassNotFoundException, java.io.IOException
        {
            super.readObject(s, true);
        }

        static class CopyIterator extends Path2D.Iterator {
            double doubleCoords[];

            CopyIterator(Path2D.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 Path2D.Iterator {
            double doubleCoords[];
            AffineTransform affine;

            TxIterator(Path2D.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.
Params:
x – the specified X coordinate
y – the specified Y coordinate
Since:
1.6/**
     * 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.
Params:
x – the specified X coordinate
y – the specified Y coordinate
Since:
1.6/**
     * 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 (x2,y2), using the specified point (x1,y1) as a quadratic parametric control point. All coordinates are specified in double precision. 
Params:
x1 – the X coordinate of the quadratic control point
y1 – the Y coordinate of the quadratic control point
x2 – the X coordinate of the final end point
y2 – the Y coordinate of the final end point
Since:
1.6/**
     * 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 Bézier curve that intersects both the current coordinates and the specified coordinates (x3,y3), using the specified points (x1,y1) and (x2,y2) as Bézier control points. All coordinates are specified in double precision. 
Params:
x1 – the X coordinate of the first Bézier control point
y1 – the Y coordinate of the first Bézier control point
x2 – the X coordinate of the second Bézier control point
y2 – the Y coordinate of the second Bézier control point
x3 – the X coordinate of the final end point
y3 – the Y coordinate of the final end point
Since:
1.6/**
     * 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 moveTo. If the path is already closed then this method has no effect. 
Since:
1.6/**
     * 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 Shape object to the path, possibly connecting the new geometry to the existing path segments with a line segment. If the connect parameter is true and the path is not empty then any initial moveTo in the geometry of the appended Shape is turned into a lineTo segment. If the destination coordinates of such a connecting lineTo segment match the ending coordinates of a currently open subpath then the segment is omitted as superfluous. The winding rule of the specified Shape is ignored and the appended geometry is governed by the winding rule specified for this path. 
Params:
s – the Shape whose geometry is appended to this path
connect – a boolean to control whether or not to turn an initial moveTo segment into a lineTo segment to connect the new geometry to the existing path
Since:
1.6/**
     * 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 PathIterator object to the path, possibly connecting the new geometry to the existing path segments with a line segment. If the connect parameter is true and the path is not empty then any initial moveTo in the geometry of the appended Shape is turned into a lineTo segment. If the destination coordinates of such a connecting lineTo segment match the ending coordinates of a currently open subpath then the segment is omitted as superfluous. The winding rule of the specified Shape is ignored and the appended geometry is governed by the winding rule specified for this path. 
Params:
pi – the PathIterator whose geometry is appended to this path
connect – a boolean to control whether or not to turn an initial moveTo segment into a lineTo segment to connect the new geometry to the existing path
Since:
1.6/**
     * 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.
See Also:
WIND_EVEN_ODD
WIND_NON_ZERO
setWindingRule
Returns:
an integer representing the current winding rule.
Since:
1.6/**
     * 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.
Params:
rule – an integer representing the specified
            winding rule
Throws:
IllegalArgumentException – if rule is not either WIND_EVEN_ODD or WIND_NON_ZERO
See Also:
getWindingRule
Since:
1.6/**
     * 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 Point2D object. 
Returns:
a Point2D object containing the ending coordinates of the path or null if there are no points in the path.
Since:
1.6/**
     * 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/**
     * 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 AffineTransform. The geometry is transformed in place, which permanently changes the boundary defined by this object. 
Params:
at – the AffineTransform used to transform the area
Since:
1.6/**
     * 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 Shape representing a transformed version of this 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 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 Path2D.Float and Path2D.Double subclasses should be used to make the choice explicit. 
Params:
at – the AffineTransform used to transform a new Shape.
Returns:
a new Shape, transformed with the specified AffineTransform.
Since:
1.6/**
     * 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 Path2D.Float#Float(Shape, AffineTransform) Path2D.Float}
     * and
     * {@link Path2D.Double#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/**
     * {@inheritDoc}
     * @since 1.6
     */
    public final Rectangle getBounds() {
        return getBounds2D().getBounds();
    }

    
Tests if the specified coordinates are inside the closed boundary of the specified PathIterator. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.contains(double, double) method. 
Params:
pi – the specified PathIterator
x – the specified X coordinate
y – the specified Y coordinate
Returns:
true if the specified coordinates are inside the specified PathIterator; false otherwise
Since:
1.6/**
     * 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 Point2D is inside the closed boundary of the specified PathIterator. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.contains(Point2D) method. 
Params:
pi – the specified PathIterator
p – the specified Point2D
Returns:
true if the specified coordinates are inside the specified PathIterator; false otherwise
Since:
1.6/**
     * 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/**
     * {@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/**
     * {@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 PathIterator. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.contains(double, double, double, double) method. 
 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 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. 
Params:
pi – the specified PathIterator
x – the specified X coordinate
y – the specified Y coordinate
w – the width of the specified rectangular area
h – the height of the specified rectangular area
Returns:
true if the specified PathIterator contains the specified rectangular area; false otherwise.
Since:
1.6/**
     * 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 Rectangle2D is entirely inside the closed boundary of the specified PathIterator. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.contains(Rectangle2D) method. 
 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 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. 
Params:
pi – the specified PathIterator
r – a specified Rectangle2D
Returns:
true if the specified PathIterator contains the specified Rectangle2D; false otherwise.
Since:
1.6/**
     * 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}
 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 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/**
     * {@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}
 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 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/**
     * {@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 PathIterator intersects the interior of a specified set of rectangular coordinates. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.intersects(double, double, double, double) method. 

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.
Params:
pi – the specified PathIterator
x – the specified X coordinate
y – the specified Y coordinate
w – the width of the specified rectangular coordinates
h – the height of the specified rectangular coordinates
Returns:
true if the specified PathIterator and the interior of the specified set of rectangular coordinates intersect each other; false otherwise.
Since:
1.6/**
     * 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 PathIterator intersects the interior of a specified Rectangle2D. 
 This method provides a basic facility for implementors of the Shape interface to implement support for the Shape.intersects(Rectangle2D) method. 

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.
Params:
pi – the specified PathIterator
r – the specified Rectangle2D
Returns:
true if the specified PathIterator and the interior of the specified Rectangle2D intersect each other; false otherwise.
Since:
1.6/**
     * 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}

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/**
     * {@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}

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/**
     * {@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}
 The iterator for this class is not multi-threaded safe, which means that this Path2D class does not guarantee that modifications to the geometry of this Path2D object do not affect any iterations of that geometry that are already in process. 
Since:
1.6/**
     * {@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.
Throws:
OutOfMemoryError –            if there is not enough memory.
See Also:
Cloneable
Returns:
    a clone of this instance.
Since:
     1.6/**
     * 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        java.lang.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?

    
Trims the capacity of this Path2D instance to its current
size. An application can use this operation to minimize the
storage of a path.
Since:
10/**
     * Trims the capacity of this Path2D instance to its current
     * size. An application can use this operation to minimize the
     * storage of a path.
     *
     * @since 10
     */
    public abstract void trimToSize();

    /*
     * 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 = ((Path2D.Double) this).doubleCoords;
            fCoords = null;
        } else {
            fCoords = ((Path2D.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 java.lang.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());
        }

        // Accept the size from the stream only if it is less than INIT_SIZE
        // otherwise the size will be based on the real data in the stream
        pointTypes = new byte[(nT < 0 || nT > INIT_SIZE) ? INIT_SIZE : nT];
        final int initX2 = INIT_SIZE * 2;
        if (nC < 0 || nC > initX2) {
            nC = initX2;
        }
        if (storedbl) {
            ((Path2D.Double) this).doubleCoords = new double[nC];
        } else {
            ((Path2D.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");
        }
    }

    abstract static 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];
        }
    }
}