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	/*
	* Copyright (c) 1997, 2006, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	package java.awt.geom;

	import java.io.Serializable;

	/**
	* The <code>Rectangle2D</code> class describes a rectangle
	* defined by a location {@code (x,y)} and dimension
	* {@code (w x h)}.
	* <p>
	* This class is only the abstract superclass for all objects that
	* store a 2D rectangle.
	* The actual storage representation of the coordinates is left to
	* the subclass.
	*
	* @author Jim Graham
	* @since 1.2
	*/
	public abstract class Rectangle2D extends RectangularShape {
	/**
	* The bitmask that indicates that a point lies to the left of
	* this <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public static final int OUT_LEFT = 1;

	/**
	* The bitmask that indicates that a point lies above
	* this <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public static final int OUT_TOP = 2;

	/**
	* The bitmask that indicates that a point lies to the right of
	* this <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public static final int OUT_RIGHT = 4;

	/**
	* The bitmask that indicates that a point lies below
	* this <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public static final int OUT_BOTTOM = 8;

	/**
	* The <code>Float</code> class defines a rectangle specified in float
	* coordinates.
	* @since 1.2
	*/
	public static class Float extends Rectangle2D implements Serializable {
	/**
	* The X coordinate of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public float x;

	/**
	* The Y coordinate of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public float y;

	/**
	* The width of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public float width;

	/**
	* The height of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public float height;

	/**
	* Constructs a new <code>Rectangle2D</code>, initialized to
	* location (0.0, 0.0) and size (0.0, 0.0).
	* @since 1.2
	*/
	public Float() {
	}

	/**
	* Constructs and initializes a <code>Rectangle2D</code>
	* from the specified <code>float</code> coordinates.
	*
	* @param x the X coordinate of the upper-left corner
	* of the newly constructed <code>Rectangle2D</code>
	* @param y the Y coordinate of the upper-left corner
	* of the newly constructed <code>Rectangle2D</code>
	* @param w the width of the newly constructed
	* <code>Rectangle2D</code>
	* @param h the height of the newly constructed
	* <code>Rectangle2D</code>
	* @since 1.2
	*/
	public Float(float x, float y, float w, float h) {
	setRect(x, y, w, h);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX() {
	return (double) x;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY() {
	return (double) y;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getWidth() {
	return (double) width;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getHeight() {
	return (double) height;
	}

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

	/**
	* Sets the location and size of this <code>Rectangle2D</code>
	* to the specified <code>float</code> values.
	*
	* @param x the X coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param y the Y coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param w the width of this <code>Rectangle2D</code>
	* @param h the height of this <code>Rectangle2D</code>
	* @since 1.2
	*/
	public void setRect(float x, float y, float w, float h) {
	this.x = x;
	this.y = y;
	this.width = w;
	this.height = h;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setRect(double x, double y, double w, double h) {
	this.x = (float) x;
	this.y = (float) y;
	this.width = (float) w;
	this.height = (float) h;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setRect(Rectangle2D r) {
	this.x = (float) r.getX();
	this.y = (float) r.getY();
	this.width = (float) r.getWidth();
	this.height = (float) r.getHeight();
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public int outcode(double x, double y) {
	/*
	* Note on casts to double below. If the arithmetic of
	* x+w or y+h is done in float, then some bits may be
	* lost if the binary exponents of x/y and w/h are not
	* similar. By converting to double before the addition
	* we force the addition to be carried out in double to
	* avoid rounding error in the comparison.
	*
	* See bug 4320890 for problems that this inaccuracy causes.
	*/
	int out = 0;
	if (this.width <= 0) {
	out \|= OUT_LEFT \| OUT_RIGHT;
	} else if (x < this.x) {
	out \|= OUT_LEFT;
	} else if (x > this.x + (double) this.width) {
	out \|= OUT_RIGHT;
	}
	if (this.height <= 0) {
	out \|= OUT_TOP \| OUT_BOTTOM;
	} else if (y < this.y) {
	out \|= OUT_TOP;
	} else if (y > this.y + (double) this.height) {
	out \|= OUT_BOTTOM;
	}
	return out;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D getBounds2D() {
	return new Float(x, y, width, height);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D createIntersection(Rectangle2D r) {
	Rectangle2D dest;
	if (r instanceof Float) {
	dest = new Rectangle2D.Float();
	} else {
	dest = new Rectangle2D.Double();
	}
	Rectangle2D.intersect(this, r, dest);
	return dest;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D createUnion(Rectangle2D r) {
	Rectangle2D dest;
	if (r instanceof Float) {
	dest = new Rectangle2D.Float();
	} else {
	dest = new Rectangle2D.Double();
	}
	Rectangle2D.union(this, r, dest);
	return dest;
	}

	/**
	* Returns the <code>String</code> representation of this
	* <code>Rectangle2D</code>.
	* @return a <code>String</code> representing this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public String toString() {
	return getClass().getName()
	+ "[x=" + x +
	",y=" + y +
	",w=" + width +
	",h=" + height + "]";
	}

	/*
	* JDK 1.6 serialVersionUID
	*/
	private static final long serialVersionUID = 3798716824173675777L;
	}

	/**
	* The <code>Double</code> class defines a rectangle specified in
	* double coordinates.
	* @since 1.2
	*/
	public static class Double extends Rectangle2D implements Serializable {
	/**
	* The X coordinate of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public double x;

	/**
	* The Y coordinate of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public double y;

	/**
	* The width of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public double width;

	/**
	* The height of this <code>Rectangle2D</code>.
	* @since 1.2
	* @serial
	*/
	public double height;

	/**
	* Constructs a new <code>Rectangle2D</code>, initialized to
	* location (0, 0) and size (0, 0).
	* @since 1.2
	*/
	public Double() {
	}

	/**
	* Constructs and initializes a <code>Rectangle2D</code>
	* from the specified <code>double</code> coordinates.
	*
	* @param x the X coordinate of the upper-left corner
	* of the newly constructed <code>Rectangle2D</code>
	* @param y the Y coordinate of the upper-left corner
	* of the newly constructed <code>Rectangle2D</code>
	* @param w the width of the newly constructed
	* <code>Rectangle2D</code>
	* @param h the height of the newly constructed
	* <code>Rectangle2D</code>
	* @since 1.2
	*/
	public Double(double x, double y, double w, double h) {
	setRect(x, y, w, h);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX() {
	return x;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY() {
	return y;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getWidth() {
	return width;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getHeight() {
	return height;
	}

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

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setRect(double x, double y, double w, double h) {
	this.x = x;
	this.y = y;
	this.width = w;
	this.height = h;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setRect(Rectangle2D r) {
	this.x = r.getX();
	this.y = r.getY();
	this.width = r.getWidth();
	this.height = r.getHeight();
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public int outcode(double x, double y) {
	int out = 0;
	if (this.width <= 0) {
	out \|= OUT_LEFT \| OUT_RIGHT;
	} else if (x < this.x) {
	out \|= OUT_LEFT;
	} else if (x > this.x + this.width) {
	out \|= OUT_RIGHT;
	}
	if (this.height <= 0) {
	out \|= OUT_TOP \| OUT_BOTTOM;
	} else if (y < this.y) {
	out \|= OUT_TOP;
	} else if (y > this.y + this.height) {
	out \|= OUT_BOTTOM;
	}
	return out;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D getBounds2D() {
	return new Double(x, y, width, height);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D createIntersection(Rectangle2D r) {
	Rectangle2D dest = new Rectangle2D.Double();
	Rectangle2D.intersect(this, r, dest);
	return dest;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D createUnion(Rectangle2D r) {
	Rectangle2D dest = new Rectangle2D.Double();
	Rectangle2D.union(this, r, dest);
	return dest;
	}

	/**
	* Returns the <code>String</code> representation of this
	* <code>Rectangle2D</code>.
	* @return a <code>String</code> representing this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public String toString() {
	return getClass().getName()
	+ "[x=" + x +
	",y=" + y +
	",w=" + width +
	",h=" + height + "]";
	}

	/*
	* JDK 1.6 serialVersionUID
	*/
	private static final long serialVersionUID = 7771313791441850493L;
	}

	/**
	* This is an abstract class that cannot be instantiated directly.
	* Type-specific implementation subclasses are available for
	* instantiation and provide a number of formats for storing
	* the information necessary to satisfy the various accessor
	* methods below.
	*
	* @see java.awt.geom.Rectangle2D.Float
	* @see java.awt.geom.Rectangle2D.Double
	* @see java.awt.Rectangle
	* @since 1.2
	*/
	protected Rectangle2D() {
	}

	/**
	* Sets the location and size of this <code>Rectangle2D</code>
	* to the specified <code>double</code> values.
	*
	* @param x the X coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param y the Y coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param w the width of this <code>Rectangle2D</code>
	* @param h the height of this <code>Rectangle2D</code>
	* @since 1.2
	*/
	public abstract void setRect(double x, double y, double w, double h);

	/**
	* Sets this <code>Rectangle2D</code> to be the same as the specified
	* <code>Rectangle2D</code>.
	* @param r the specified <code>Rectangle2D</code>
	* @since 1.2
	*/
	public void setRect(Rectangle2D r) {
	setRect(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	* Tests if the specified line segment intersects the interior of this
	* <code>Rectangle2D</code>.
	*
	* @param x1 the X coordinate of the start point of the specified
	* line segment
	* @param y1 the Y coordinate of the start point of the specified
	* line segment
	* @param x2 the X coordinate of the end point of the specified
	* line segment
	* @param y2 the Y coordinate of the end point of the specified
	* line segment
	* @return <code>true</code> if the specified line segment intersects
	* the interior of this <code>Rectangle2D</code>; <code>false</code>
	* otherwise.
	* @since 1.2
	*/
	public boolean intersectsLine(double x1, double y1, double x2, double y2) {
	int out1, out2;
	if ((out2 = outcode(x2, y2)) == 0) {
	return true;
	}
	while ((out1 = outcode(x1, y1)) != 0) {
	if ((out1 & out2) != 0) {
	return false;
	}
	if ((out1 & (OUT_LEFT \| OUT_RIGHT)) != 0) {
	double x = getX();
	if ((out1 & OUT_RIGHT) != 0) {
	x += getWidth();
	}
	y1 = y1 + (x - x1) * (y2 - y1) / (x2 - x1);
	x1 = x;
	} else {
	double y = getY();
	if ((out1 & OUT_BOTTOM) != 0) {
	y += getHeight();
	}
	x1 = x1 + (y - y1) * (x2 - x1) / (y2 - y1);
	y1 = y;
	}
	}
	return true;
	}

	/**
	* Tests if the specified line segment intersects the interior of this
	* <code>Rectangle2D</code>.
	* @param l the specified {@link Line2D} to test for intersection
	* with the interior of this <code>Rectangle2D</code>
	* @return <code>true</code> if the specified <code>Line2D</code>
	* intersects the interior of this <code>Rectangle2D</code>;
	* <code>false</code> otherwise.
	* @since 1.2
	*/
	public boolean intersectsLine(Line2D l) {
	return intersectsLine(l.getX1(), l.getY1(), l.getX2(), l.getY2());
	}

	/**
	* Determines where the specified coordinates lie with respect
	* to this <code>Rectangle2D</code>.
	* This method computes a binary OR of the appropriate mask values
	* indicating, for each side of this <code>Rectangle2D</code>,
	* whether or not the specified coordinates are on the same side
	* of the edge as the rest of this <code>Rectangle2D</code>.
	* @param x the specified X coordinate
	* @param y the specified Y coordinate
	* @return the logical OR of all appropriate out codes.
	* @see #OUT_LEFT
	* @see #OUT_TOP
	* @see #OUT_RIGHT
	* @see #OUT_BOTTOM
	* @since 1.2
	*/
	public abstract int outcode(double x, double y);

	/**
	* Determines where the specified {@link Point2D} lies with
	* respect to this <code>Rectangle2D</code>.
	* This method computes a binary OR of the appropriate mask values
	* indicating, for each side of this <code>Rectangle2D</code>,
	* whether or not the specified <code>Point2D</code> is on the same
	* side of the edge as the rest of this <code>Rectangle2D</code>.
	* @param p the specified <code>Point2D</code>
	* @return the logical OR of all appropriate out codes.
	* @see #OUT_LEFT
	* @see #OUT_TOP
	* @see #OUT_RIGHT
	* @see #OUT_BOTTOM
	* @since 1.2
	*/
	public int outcode(Point2D p) {
	return outcode(p.getX(), p.getY());
	}

	/**
	* Sets the location and size of the outer bounds of this
	* <code>Rectangle2D</code> to the specified rectangular values.
	*
	* @param x the X coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param y the Y coordinate of the upper-left corner
	* of this <code>Rectangle2D</code>
	* @param w the width of this <code>Rectangle2D</code>
	* @param h the height of this <code>Rectangle2D</code>
	* @since 1.2
	*/
	public void setFrame(double x, double y, double w, double h) {
	setRect(x, y, w, h);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D getBounds2D() {
	return (Rectangle2D) clone();
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(double x, double y) {
	double x0 = getX();
	double y0 = getY();
	return (x >= x0 &&
	y >= y0 &&
	x < x0 + getWidth() &&
	y < y0 + getHeight());
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean intersects(double x, double y, double w, double h) {
	if (isEmpty() \|\| w <= 0 \|\| h <= 0) {
	return false;
	}
	double x0 = getX();
	double y0 = getY();
	return (x + w > x0 &&
	y + h > y0 &&
	x < x0 + getWidth() &&
	y < y0 + getHeight());
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(double x, double y, double w, double h) {
	if (isEmpty() \|\| w <= 0 \|\| h <= 0) {
	return false;
	}
	double x0 = getX();
	double y0 = getY();
	return (x >= x0 &&
	y >= y0 &&
	(x + w) <= x0 + getWidth() &&
	(y + h) <= y0 + getHeight());
	}

	/**
	* Returns a new <code>Rectangle2D</code> object representing the
	* intersection of this <code>Rectangle2D</code> with the specified
	* <code>Rectangle2D</code>.
	* @param r the <code>Rectangle2D</code> to be intersected with
	* this <code>Rectangle2D</code>
	* @return the largest <code>Rectangle2D</code> contained in both
	* the specified <code>Rectangle2D</code> and in this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public abstract Rectangle2D createIntersection(Rectangle2D r);

	/**
	* Intersects the pair of specified source <code>Rectangle2D</code>
	* objects and puts the result into the specified destination
	* <code>Rectangle2D</code> object. One of the source rectangles
	* can also be the destination to avoid creating a third Rectangle2D
	* object, but in this case the original points of this source
	* rectangle will be overwritten by this method.
	* @param src1 the first of a pair of <code>Rectangle2D</code>
	* objects to be intersected with each other
	* @param src2 the second of a pair of <code>Rectangle2D</code>
	* objects to be intersected with each other
	* @param dest the <code>Rectangle2D</code> that holds the
	* results of the intersection of <code>src1</code> and
	* <code>src2</code>
	* @since 1.2
	*/
	public static void intersect(Rectangle2D src1,
	Rectangle2D src2,
	Rectangle2D dest) {
	double x1 = Math.max(src1.getMinX(), src2.getMinX());
	double y1 = Math.max(src1.getMinY(), src2.getMinY());
	double x2 = Math.min(src1.getMaxX(), src2.getMaxX());
	double y2 = Math.min(src1.getMaxY(), src2.getMaxY());
	dest.setFrame(x1, y1, x2-x1, y2-y1);
	}

	/**
	* Returns a new <code>Rectangle2D</code> object representing the
	* union of this <code>Rectangle2D</code> with the specified
	* <code>Rectangle2D</code>.
	* @param r the <code>Rectangle2D</code> to be combined with
	* this <code>Rectangle2D</code>
	* @return the smallest <code>Rectangle2D</code> containing both
	* the specified <code>Rectangle2D</code> and this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public abstract Rectangle2D createUnion(Rectangle2D r);

	/**
	* Unions the pair of source <code>Rectangle2D</code> objects
	* and puts the result into the specified destination
	* <code>Rectangle2D</code> object. One of the source rectangles
	* can also be the destination to avoid creating a third Rectangle2D
	* object, but in this case the original points of this source
	* rectangle will be overwritten by this method.
	* @param src1 the first of a pair of <code>Rectangle2D</code>
	* objects to be combined with each other
	* @param src2 the second of a pair of <code>Rectangle2D</code>
	* objects to be combined with each other
	* @param dest the <code>Rectangle2D</code> that holds the
	* results of the union of <code>src1</code> and
	* <code>src2</code>
	* @since 1.2
	*/
	public static void union(Rectangle2D src1,
	Rectangle2D src2,
	Rectangle2D dest) {
	double x1 = Math.min(src1.getMinX(), src2.getMinX());
	double y1 = Math.min(src1.getMinY(), src2.getMinY());
	double x2 = Math.max(src1.getMaxX(), src2.getMaxX());
	double y2 = Math.max(src1.getMaxY(), src2.getMaxY());
	dest.setFrameFromDiagonal(x1, y1, x2, y2);
	}

	/**
	* Adds a point, specified by the double precision arguments
	* <code>newx</code> and <code>newy</code>, to this
	* <code>Rectangle2D</code>. The resulting <code>Rectangle2D</code>
	* is the smallest <code>Rectangle2D</code> that
	* contains both the original <code>Rectangle2D</code> and the
	* specified point.
	* <p>
	* After adding a point, a call to <code>contains</code> with the
	* added point as an argument does not necessarily return
	* <code>true</code>. The <code>contains</code> method does not
	* return <code>true</code> for points on the right or bottom
	* edges of a rectangle. Therefore, if the added point falls on
	* the left or bottom edge of the enlarged rectangle,
	* <code>contains</code> returns <code>false</code> for that point.
	* @param newx the X coordinate of the new point
	* @param newy the Y coordinate of the new point
	* @since 1.2
	*/
	public void add(double newx, double newy) {
	double x1 = Math.min(getMinX(), newx);
	double x2 = Math.max(getMaxX(), newx);
	double y1 = Math.min(getMinY(), newy);
	double y2 = Math.max(getMaxY(), newy);
	setRect(x1, y1, x2 - x1, y2 - y1);
	}

	/**
	* Adds the <code>Point2D</code> object <code>pt</code> to this
	* <code>Rectangle2D</code>.
	* The resulting <code>Rectangle2D</code> is the smallest
	* <code>Rectangle2D</code> that contains both the original
	* <code>Rectangle2D</code> and the specified <code>Point2D</code>.
	* <p>
	* After adding a point, a call to <code>contains</code> with the
	* added point as an argument does not necessarily return
	* <code>true</code>. The <code>contains</code>
	* method does not return <code>true</code> for points on the right
	* or bottom edges of a rectangle. Therefore, if the added point falls
	* on the left or bottom edge of the enlarged rectangle,
	* <code>contains</code> returns <code>false</code> for that point.
	* @param pt the new <code>Point2D</code> to add to this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public void add(Point2D pt) {
	add(pt.getX(), pt.getY());
	}

	/**
	* Adds a <code>Rectangle2D</code> object to this
	* <code>Rectangle2D</code>. The resulting <code>Rectangle2D</code>
	* is the union of the two <code>Rectangle2D</code> objects.
	* @param r the <code>Rectangle2D</code> to add to this
	* <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public void add(Rectangle2D r) {
	double x1 = Math.min(getMinX(), r.getMinX());
	double x2 = Math.max(getMaxX(), r.getMaxX());
	double y1 = Math.min(getMinY(), r.getMinY());
	double y2 = Math.max(getMaxY(), r.getMaxY());
	setRect(x1, y1, x2 - x1, y2 - y1);
	}

	/**
	* Returns an iteration object that defines the boundary of this
	* <code>Rectangle2D</code>.
	* The iterator for this class is multi-threaded safe, which means
	* that this <code>Rectangle2D</code> class guarantees that
	* modifications to the geometry of this <code>Rectangle2D</code>
	* object do not affect any iterations of that geometry that
	* are already in process.
	* @param at an optional <code>AffineTransform</code> to be applied to
	* the coordinates as they are returned in the iteration, or
	* <code>null</code> if untransformed coordinates are desired
	* @return the <code>PathIterator</code> object that returns the
	* geometry of the outline of this
	* <code>Rectangle2D</code>, one segment at a time.
	* @since 1.2
	*/
	public PathIterator getPathIterator(AffineTransform at) {
	return new RectIterator(this, at);
	}

	/**
	* Returns an iteration object that defines the boundary of the
	* flattened <code>Rectangle2D</code>. Since rectangles are already
	* flat, the <code>flatness</code> parameter is ignored.
	* The iterator for this class is multi-threaded safe, which means
	* that this <code>Rectangle2D</code> class guarantees that
	* modifications to the geometry of this <code>Rectangle2D</code>
	* object do not affect any iterations of that geometry that
	* are already in process.
	* @param at an optional <code>AffineTransform</code> to be applied to
	* the coordinates as they are returned in the iteration, or
	* <code>null</code> if untransformed coordinates are desired
	* @param flatness the maximum distance that the line segments used to
	* approximate the curved segments are allowed to deviate from any
	* point on the original curve. Since rectangles are already flat,
	* the <code>flatness</code> parameter is ignored.
	* @return the <code>PathIterator</code> object that returns the
	* geometry of the outline of this
	* <code>Rectangle2D</code>, one segment at a time.
	* @since 1.2
	*/
	public PathIterator getPathIterator(AffineTransform at, double flatness) {
	return new RectIterator(this, at);
	}

	/**
	* Returns the hashcode for this <code>Rectangle2D</code>.
	* @return the hashcode for this <code>Rectangle2D</code>.
	* @since 1.2
	*/
	public int hashCode() {
	long bits = java.lang.Double.doubleToLongBits(getX());
	bits += java.lang.Double.doubleToLongBits(getY()) * 37;
	bits += java.lang.Double.doubleToLongBits(getWidth()) * 43;
	bits += java.lang.Double.doubleToLongBits(getHeight()) * 47;
	return (((int) bits) ^ ((int) (bits >> 32)));
	}

	/**
	* Determines whether or not the specified <code>Object</code> is
	* equal to this <code>Rectangle2D</code>. The specified
	* <code>Object</code> is equal to this <code>Rectangle2D</code>
	* if it is an instance of <code>Rectangle2D</code> and if its
	* location and size are the same as this <code>Rectangle2D</code>.
	* @param obj an <code>Object</code> to be compared with this
	* <code>Rectangle2D</code>.
	* @return <code>true</code> if <code>obj</code> is an instance
	* of <code>Rectangle2D</code> and has
	* the same values; <code>false</code> otherwise.
	* @since 1.2
	*/
	public boolean equals(Object obj) {
	if (obj == this) {
	return true;
	}
	if (obj instanceof Rectangle2D) {
	Rectangle2D r2d = (Rectangle2D) obj;
	return ((getX() == r2d.getX()) &&
	(getY() == r2d.getY()) &&
	(getWidth() == r2d.getWidth()) &&
	(getHeight() == r2d.getHeight()));
	}
	return false;
	}
	}

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