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	/*
	* Copyright (c) 1997, 2013, 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.awt.Shape;
	import java.awt.Rectangle;
	import java.io.Serializable;
	import sun.awt.geom.Curve;

	/**
	* The <code>QuadCurve2D</code> class defines a quadratic parametric curve
	* segment in {@code (x,y)} coordinate space.
	* <p>
	* This class is only the abstract superclass for all objects that
	* store a 2D quadratic curve segment.
	* The actual storage representation of the coordinates is left to
	* the subclass.
	*
	* @author Jim Graham
	* @since 1.2
	*/
	public abstract class QuadCurve2D implements Shape, Cloneable {

	/**
	* A quadratic parametric curve segment specified with
	* {@code float} coordinates.
	*
	* @since 1.2
	*/
	public static class Float extends QuadCurve2D implements Serializable {
	/**
	* The X coordinate of the start point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float x1;

	/**
	* The Y coordinate of the start point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float y1;

	/**
	* The X coordinate of the control point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float ctrlx;

	/**
	* The Y coordinate of the control point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float ctrly;

	/**
	* The X coordinate of the end point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float x2;

	/**
	* The Y coordinate of the end point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public float y2;

	/**
	* Constructs and initializes a <code>QuadCurve2D</code> with
	* coordinates (0, 0, 0, 0, 0, 0).
	* @since 1.2
	*/
	public Float() {
	}

	/**
	* Constructs and initializes a <code>QuadCurve2D</code> from the
	* specified {@code float} coordinates.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @since 1.2
	*/
	public Float(float x1, float y1,
	float ctrlx, float ctrly,
	float x2, float y2)
	{
	setCurve(x1, y1, ctrlx, ctrly, x2, y2);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX1() {
	return (double) x1;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY1() {
	return (double) y1;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getP1() {
	return new Point2D.Float(x1, y1);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getCtrlX() {
	return (double) ctrlx;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getCtrlY() {
	return (double) ctrly;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getCtrlPt() {
	return new Point2D.Float(ctrlx, ctrly);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX2() {
	return (double) x2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY2() {
	return (double) y2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getP2() {
	return new Point2D.Float(x2, y2);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setCurve(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2)
	{
	this.x1 = (float) x1;
	this.y1 = (float) y1;
	this.ctrlx = (float) ctrlx;
	this.ctrly = (float) ctrly;
	this.x2 = (float) x2;
	this.y2 = (float) y2;
	}

	/**
	* Sets the location of the end points and control point of this curve
	* to the specified {@code float} coordinates.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @since 1.2
	*/
	public void setCurve(float x1, float y1,
	float ctrlx, float ctrly,
	float x2, float y2)
	{
	this.x1 = x1;
	this.y1 = y1;
	this.ctrlx = ctrlx;
	this.ctrly = ctrly;
	this.x2 = x2;
	this.y2 = y2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D getBounds2D() {
	float left = Math.min(Math.min(x1, x2), ctrlx);
	float top = Math.min(Math.min(y1, y2), ctrly);
	float right = Math.max(Math.max(x1, x2), ctrlx);
	float bottom = Math.max(Math.max(y1, y2), ctrly);
	return new Rectangle2D.Float(left, top,
	right - left, bottom - top);
	}

	/*
	* JDK 1.6 serialVersionUID
	*/
	private static final long serialVersionUID = -8511188402130719609L;
	}

	/**
	* A quadratic parametric curve segment specified with
	* {@code double} coordinates.
	*
	* @since 1.2
	*/
	public static class Double extends QuadCurve2D implements Serializable {
	/**
	* The X coordinate of the start point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double x1;

	/**
	* The Y coordinate of the start point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double y1;

	/**
	* The X coordinate of the control point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double ctrlx;

	/**
	* The Y coordinate of the control point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double ctrly;

	/**
	* The X coordinate of the end point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double x2;

	/**
	* The Y coordinate of the end point of the quadratic curve
	* segment.
	* @since 1.2
	* @serial
	*/
	public double y2;

	/**
	* Constructs and initializes a <code>QuadCurve2D</code> with
	* coordinates (0, 0, 0, 0, 0, 0).
	* @since 1.2
	*/
	public Double() {
	}

	/**
	* Constructs and initializes a <code>QuadCurve2D</code> from the
	* specified {@code double} coordinates.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @since 1.2
	*/
	public Double(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2)
	{
	setCurve(x1, y1, ctrlx, ctrly, x2, y2);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX1() {
	return x1;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY1() {
	return y1;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getP1() {
	return new Point2D.Double(x1, y1);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getCtrlX() {
	return ctrlx;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getCtrlY() {
	return ctrly;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getCtrlPt() {
	return new Point2D.Double(ctrlx, ctrly);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getX2() {
	return x2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public double getY2() {
	return y2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Point2D getP2() {
	return new Point2D.Double(x2, y2);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public void setCurve(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2)
	{
	this.x1 = x1;
	this.y1 = y1;
	this.ctrlx = ctrlx;
	this.ctrly = ctrly;
	this.x2 = x2;
	this.y2 = y2;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle2D getBounds2D() {
	double left = Math.min(Math.min(x1, x2), ctrlx);
	double top = Math.min(Math.min(y1, y2), ctrly);
	double right = Math.max(Math.max(x1, x2), ctrlx);
	double bottom = Math.max(Math.max(y1, y2), ctrly);
	return new Rectangle2D.Double(left, top,
	right - left, bottom - top);
	}

	/*
	* JDK 1.6 serialVersionUID
	*/
	private static final long serialVersionUID = 4217149928428559721L;
	}

	/**
	* 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.QuadCurve2D.Float
	* @see java.awt.geom.QuadCurve2D.Double
	* @since 1.2
	*/
	protected QuadCurve2D() {
	}

	/**
	* Returns the X coordinate of the start point in
	* <code>double</code> in precision.
	* @return the X coordinate of the start point.
	* @since 1.2
	*/
	public abstract double getX1();

	/**
	* Returns the Y coordinate of the start point in
	* <code>double</code> precision.
	* @return the Y coordinate of the start point.
	* @since 1.2
	*/
	public abstract double getY1();

	/**
	* Returns the start point.
	* @return a <code>Point2D</code> that is the start point of this
	* <code>QuadCurve2D</code>.
	* @since 1.2
	*/
	public abstract Point2D getP1();

	/**
	* Returns the X coordinate of the control point in
	* <code>double</code> precision.
	* @return X coordinate the control point
	* @since 1.2
	*/
	public abstract double getCtrlX();

	/**
	* Returns the Y coordinate of the control point in
	* <code>double</code> precision.
	* @return the Y coordinate of the control point.
	* @since 1.2
	*/
	public abstract double getCtrlY();

	/**
	* Returns the control point.
	* @return a <code>Point2D</code> that is the control point of this
	* <code>Point2D</code>.
	* @since 1.2
	*/
	public abstract Point2D getCtrlPt();

	/**
	* Returns the X coordinate of the end point in
	* <code>double</code> precision.
	* @return the x coordinate of the end point.
	* @since 1.2
	*/
	public abstract double getX2();

	/**
	* Returns the Y coordinate of the end point in
	* <code>double</code> precision.
	* @return the Y coordinate of the end point.
	* @since 1.2
	*/
	public abstract double getY2();

	/**
	* Returns the end point.
	* @return a <code>Point</code> object that is the end point
	* of this <code>Point2D</code>.
	* @since 1.2
	*/
	public abstract Point2D getP2();

	/**
	* Sets the location of the end points and control point of this curve
	* to the specified <code>double</code> coordinates.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @since 1.2
	*/
	public abstract void setCurve(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2);

	/**
	* Sets the location of the end points and control points of this
	* <code>QuadCurve2D</code> to the <code>double</code> coordinates at
	* the specified offset in the specified array.
	* @param coords the array containing coordinate values
	* @param offset the index into the array from which to start
	* getting the coordinate values and assigning them to this
	* <code>QuadCurve2D</code>
	* @since 1.2
	*/
	public void setCurve(double[] coords, int offset) {
	setCurve(coords[offset + 0], coords[offset + 1],
	coords[offset + 2], coords[offset + 3],
	coords[offset + 4], coords[offset + 5]);
	}

	/**
	* Sets the location of the end points and control point of this
	* <code>QuadCurve2D</code> to the specified <code>Point2D</code>
	* coordinates.
	* @param p1 the start point
	* @param cp the control point
	* @param p2 the end point
	* @since 1.2
	*/
	public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
	setCurve(p1.getX(), p1.getY(),
	cp.getX(), cp.getY(),
	p2.getX(), p2.getY());
	}

	/**
	* Sets the location of the end points and control points of this
	* <code>QuadCurve2D</code> to the coordinates of the
	* <code>Point2D</code> objects at the specified offset in
	* the specified array.
	* @param pts an array containing <code>Point2D</code> that define
	* coordinate values
	* @param offset the index into <code>pts</code> from which to start
	* getting the coordinate values and assigning them to this
	* <code>QuadCurve2D</code>
	* @since 1.2
	*/
	public void setCurve(Point2D[] pts, int offset) {
	setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
	pts[offset + 1].getX(), pts[offset + 1].getY(),
	pts[offset + 2].getX(), pts[offset + 2].getY());
	}

	/**
	* Sets the location of the end points and control point of this
	* <code>QuadCurve2D</code> to the same as those in the specified
	* <code>QuadCurve2D</code>.
	* @param c the specified <code>QuadCurve2D</code>
	* @since 1.2
	*/
	public void setCurve(QuadCurve2D c) {
	setCurve(c.getX1(), c.getY1(),
	c.getCtrlX(), c.getCtrlY(),
	c.getX2(), c.getY2());
	}

	/**
	* Returns the square of the flatness, or maximum distance of a
	* control point from the line connecting the end points, of the
	* quadratic curve specified by the indicated control points.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @return the square of the flatness of the quadratic curve
	* defined by the specified coordinates.
	* @since 1.2
	*/
	public static double getFlatnessSq(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2) {
	return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
	}

	/**
	* Returns the flatness, or maximum distance of a
	* control point from the line connecting the end points, of the
	* quadratic curve specified by the indicated control points.
	*
	* @param x1 the X coordinate of the start point
	* @param y1 the Y coordinate of the start point
	* @param ctrlx the X coordinate of the control point
	* @param ctrly the Y coordinate of the control point
	* @param x2 the X coordinate of the end point
	* @param y2 the Y coordinate of the end point
	* @return the flatness of the quadratic curve defined by the
	* specified coordinates.
	* @since 1.2
	*/
	public static double getFlatness(double x1, double y1,
	double ctrlx, double ctrly,
	double x2, double y2) {
	return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
	}

	/**
	* Returns the square of the flatness, or maximum distance of a
	* control point from the line connecting the end points, of the
	* quadratic curve specified by the control points stored in the
	* indicated array at the indicated index.
	* @param coords an array containing coordinate values
	* @param offset the index into <code>coords</code> from which to
	* to start getting the values from the array
	* @return the flatness of the quadratic curve that is defined by the
	* values in the specified array at the specified index.
	* @since 1.2
	*/
	public static double getFlatnessSq(double coords[], int offset) {
	return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
	coords[offset + 4], coords[offset + 5],
	coords[offset + 2], coords[offset + 3]);
	}

	/**
	* Returns the flatness, or maximum distance of a
	* control point from the line connecting the end points, of the
	* quadratic curve specified by the control points stored in the
	* indicated array at the indicated index.
	* @param coords an array containing coordinate values
	* @param offset the index into <code>coords</code> from which to
	* start getting the coordinate values
	* @return the flatness of a quadratic curve defined by the
	* specified array at the specified offset.
	* @since 1.2
	*/
	public static double getFlatness(double coords[], int offset) {
	return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
	coords[offset + 4], coords[offset + 5],
	coords[offset + 2], coords[offset + 3]);
	}

	/**
	* Returns the square of the flatness, or maximum distance of a
	* control point from the line connecting the end points, of this
	* <code>QuadCurve2D</code>.
	* @return the square of the flatness of this
	* <code>QuadCurve2D</code>.
	* @since 1.2
	*/
	public double getFlatnessSq() {
	return Line2D.ptSegDistSq(getX1(), getY1(),
	getX2(), getY2(),
	getCtrlX(), getCtrlY());
	}

	/**
	* Returns the flatness, or maximum distance of a
	* control point from the line connecting the end points, of this
	* <code>QuadCurve2D</code>.
	* @return the flatness of this <code>QuadCurve2D</code>.
	* @since 1.2
	*/
	public double getFlatness() {
	return Line2D.ptSegDist(getX1(), getY1(),
	getX2(), getY2(),
	getCtrlX(), getCtrlY());
	}

	/**
	* Subdivides this <code>QuadCurve2D</code> and stores the resulting
	* two subdivided curves into the <code>left</code> and
	* <code>right</code> curve parameters.
	* Either or both of the <code>left</code> and <code>right</code>
	* objects can be the same as this <code>QuadCurve2D</code> or
	* <code>null</code>.
	* @param left the <code>QuadCurve2D</code> object for storing the
	* left or first half of the subdivided curve
	* @param right the <code>QuadCurve2D</code> object for storing the
	* right or second half of the subdivided curve
	* @since 1.2
	*/
	public void subdivide(QuadCurve2D left, QuadCurve2D right) {
	subdivide(this, left, right);
	}

	/**
	* Subdivides the quadratic curve specified by the <code>src</code>
	* parameter and stores the resulting two subdivided curves into the
	* <code>left</code> and <code>right</code> curve parameters.
	* Either or both of the <code>left</code> and <code>right</code>
	* objects can be the same as the <code>src</code> object or
	* <code>null</code>.
	* @param src the quadratic curve to be subdivided
	* @param left the <code>QuadCurve2D</code> object for storing the
	* left or first half of the subdivided curve
	* @param right the <code>QuadCurve2D</code> object for storing the
	* right or second half of the subdivided curve
	* @since 1.2
	*/
	public static void subdivide(QuadCurve2D src,
	QuadCurve2D left,
	QuadCurve2D right) {
	double x1 = src.getX1();
	double y1 = src.getY1();
	double ctrlx = src.getCtrlX();
	double ctrly = src.getCtrlY();
	double x2 = src.getX2();
	double y2 = src.getY2();
	double ctrlx1 = (x1 + ctrlx) / 2.0;
	double ctrly1 = (y1 + ctrly) / 2.0;
	double ctrlx2 = (x2 + ctrlx) / 2.0;
	double ctrly2 = (y2 + ctrly) / 2.0;
	ctrlx = (ctrlx1 + ctrlx2) / 2.0;
	ctrly = (ctrly1 + ctrly2) / 2.0;
	if (left != null) {
	left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
	}
	if (right != null) {
	right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
	}
	}

	/**
	* Subdivides the quadratic curve specified by the coordinates
	* stored in the <code>src</code> array at indices
	* <code>srcoff</code> through <code>srcoff</code> + 5
	* and stores the resulting two subdivided curves into the two
	* result arrays at the corresponding indices.
	* Either or both of the <code>left</code> and <code>right</code>
	* arrays can be <code>null</code> or a reference to the same array
	* and offset as the <code>src</code> array.
	* Note that the last point in the first subdivided curve is the
	* same as the first point in the second subdivided curve. Thus,
	* it is possible to pass the same array for <code>left</code> and
	* <code>right</code> and to use offsets such that
	* <code>rightoff</code> equals <code>leftoff</code> + 4 in order
	* to avoid allocating extra storage for this common point.
	* @param src the array holding the coordinates for the source curve
	* @param srcoff the offset into the array of the beginning of the
	* the 6 source coordinates
	* @param left the array for storing the coordinates for the first
	* half of the subdivided curve
	* @param leftoff the offset into the array of the beginning of the
	* the 6 left coordinates
	* @param right the array for storing the coordinates for the second
	* half of the subdivided curve
	* @param rightoff the offset into the array of the beginning of the
	* the 6 right coordinates
	* @since 1.2
	*/
	public static void subdivide(double src[], int srcoff,
	double left[], int leftoff,
	double right[], int rightoff) {
	double x1 = src[srcoff + 0];
	double y1 = src[srcoff + 1];
	double ctrlx = src[srcoff + 2];
	double ctrly = src[srcoff + 3];
	double x2 = src[srcoff + 4];
	double y2 = src[srcoff + 5];
	if (left != null) {
	left[leftoff + 0] = x1;
	left[leftoff + 1] = y1;
	}
	if (right != null) {
	right[rightoff + 4] = x2;
	right[rightoff + 5] = y2;
	}
	x1 = (x1 + ctrlx) / 2.0;
	y1 = (y1 + ctrly) / 2.0;
	x2 = (x2 + ctrlx) / 2.0;
	y2 = (y2 + ctrly) / 2.0;
	ctrlx = (x1 + x2) / 2.0;
	ctrly = (y1 + y2) / 2.0;
	if (left != null) {
	left[leftoff + 2] = x1;
	left[leftoff + 3] = y1;
	left[leftoff + 4] = ctrlx;
	left[leftoff + 5] = ctrly;
	}
	if (right != null) {
	right[rightoff + 0] = ctrlx;
	right[rightoff + 1] = ctrly;
	right[rightoff + 2] = x2;
	right[rightoff + 3] = y2;
	}
	}

	/**
	* Solves the quadratic whose coefficients are in the <code>eqn</code>
	* array and places the non-complex roots back into the same array,
	* returning the number of roots. The quadratic solved is represented
	* by the equation:
	* <pre>
	* eqn = {C, B, A};
	* ax^2 + bx + c = 0
	* </pre>
	* A return value of <code>-1</code> is used to distinguish a constant
	* equation, which might be always 0 or never 0, from an equation that
	* has no zeroes.
	* @param eqn the array that contains the quadratic coefficients
	* @return the number of roots, or <code>-1</code> if the equation is
	* a constant
	* @since 1.2
	*/
	public static int solveQuadratic(double eqn[]) {
	return solveQuadratic(eqn, eqn);
	}

	/**
	* Solves the quadratic whose coefficients are in the <code>eqn</code>
	* array and places the non-complex roots into the <code>res</code>
	* array, returning the number of roots.
	* The quadratic solved is represented by the equation:
	* <pre>
	* eqn = {C, B, A};
	* ax^2 + bx + c = 0
	* </pre>
	* A return value of <code>-1</code> is used to distinguish a constant
	* equation, which might be always 0 or never 0, from an equation that
	* has no zeroes.
	* @param eqn the specified array of coefficients to use to solve
	* the quadratic equation
	* @param res the array that contains the non-complex roots
	* resulting from the solution of the quadratic equation
	* @return the number of roots, or <code>-1</code> if the equation is
	* a constant.
	* @since 1.3
	*/
	public static int solveQuadratic(double eqn[], double res[]) {
	double a = eqn[2];
	double b = eqn[1];
	double c = eqn[0];
	int roots = 0;
	if (a == 0.0) {
	// The quadratic parabola has degenerated to a line.
	if (b == 0.0) {
	// The line has degenerated to a constant.
	return -1;
	}
	res[roots++] = -c / b;
	} else {
	// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
	double d = b * b - 4.0 * a * c;
	if (d < 0.0) {
	// If d < 0.0, then there are no roots
	return 0;
	}
	d = Math.sqrt(d);
	// For accuracy, calculate one root using:
	// (-b +/- d) / 2a
	// and the other using:
	// 2c / (-b +/- d)
	// Choose the sign of the +/- so that b+d gets larger in magnitude
	if (b < 0.0) {
	d = -d;
	}
	double q = (b + d) / -2.0;
	// We already tested a for being 0 above
	res[roots++] = q / a;
	if (q != 0.0) {
	res[roots++] = c / q;
	}
	}
	return roots;
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(double x, double y) {

	double x1 = getX1();
	double y1 = getY1();
	double xc = getCtrlX();
	double yc = getCtrlY();
	double x2 = getX2();
	double y2 = getY2();

	/*
	* We have a convex shape bounded by quad curve Pc(t)
	* and ine Pl(t).
	*
	* P1 = (x1, y1) - start point of curve
	* P2 = (x2, y2) - end point of curve
	* Pc = (xc, yc) - control point
	*
	* Pq(t) = P1(1 - t)^2 + 2Pct(1 - t) + P2*t^2 =
	* = (P1 - 2Pc + P2)t^2 + 2(Pc - P1)t + P1
	* Pl(t) = P1(1 - t) + P2t
	* t = [0:1]
	*
	* P = (x, y) - point of interest
	*
	* Let's look at second derivative of quad curve equation:
	*
	* Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
	* It's constant vector.
	*
	* Let's draw a line through P to be parallel to this
	* vector and find the intersection of the quad curve
	* and the line.
	*
	* Pq(t) is point of intersection if system of equations
	* below has the solution.
	*
	* L(s) = P + Pq''*s == Pq(t)
	* Pq''*s + (P - Pq(t)) == 0
	*
	* \| xq''*s + (x - xq(t)) == 0
	* \| yq''*s + (y - yq(t)) == 0
	*
	* This system has the solution if rank of its matrix equals to 1.
	* That is, determinant of the matrix should be zero.
	*
	* (y - yq(t))xq'' == (x - xq(t))yq''
	*
	* Let's solve this equation with 't' variable.
	* Also let kx = x1 - 2*xc + x2
	* ky = y1 - 2*yc + y2
	*
	* t0q = (1/2)((x - x1)ky - (y - y1)*kx) /
	* ((xc - x1)ky - (yc - y1)kx)
	*
	* Let's do the same for our line Pl(t):
	*
	* t0l = ((x - x1)ky - (y - y1)kx) /
	* ((x2 - x1)ky - (y2 - y1)kx)
	*
	* It's easy to check that t0q == t0l. This fact means
	* we can compute t0 only one time.
	*
	* In case t0 < 0 or t0 > 1, we have an intersections outside
	* of shape bounds. So, P is definitely out of shape.
	*
	* In case t0 is inside [0:1], we should calculate Pq(t0)
	* and Pl(t0). We have three points for now, and all of them
	* lie on one line. So, we just need to detect, is our point
	* of interest between points of intersections or not.
	*
	* If the denominator in the t0q and t0l equations is
	* zero, then the points must be collinear and so the
	* curve is degenerate and encloses no area. Thus the
	* result is false.
	*/
	double kx = x1 - 2 * xc + x2;
	double ky = y1 - 2 * yc + y2;
	double dx = x - x1;
	double dy = y - y1;
	double dxl = x2 - x1;
	double dyl = y2 - y1;

	double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
	if (t0 < 0 \|\| t0 > 1 \|\| t0 != t0) {
	return false;
	}

	double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
	double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
	double xl = dxl * t0 + x1;
	double yl = dyl * t0 + y1;

	return (x >= xb && x < xl) \|\|
	(x >= xl && x < xb) \|\|
	(y >= yb && y < yl) \|\|
	(y >= yl && y < yb);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(Point2D p) {
	return contains(p.getX(), p.getY());
	}

	/**
	* Fill an array with the coefficients of the parametric equation
	* in t, ready for solving against val with solveQuadratic.
	* We currently have:
	* val = Py(t) = C1(1-t)^2 + 2CPt(1-t) + C2*t^2
	* = C1 - 2C1t + C1t^2 + 2CPt - 2CPt^2 + C2t^2
	* = C1 + (2CP - 2C1)t + (C1 - 2CP + C2)*t^2
	* 0 = (C1 - val) + (2CP - 2C1)t + (C1 - 2CP + C2)*t^2
	* 0 = C + Bt + At^2
	* C = C1 - val
	* B = 2CP - 2C1
	* A = C1 - 2*CP + C2
	*/
	private static void fillEqn(double eqn[], double val,
	double c1, double cp, double c2) {
	eqn[0] = c1 - val;
	eqn[1] = cp + cp - c1 - c1;
	eqn[2] = c1 - cp - cp + c2;
	return;
	}

	/**
	* Evaluate the t values in the first num slots of the vals[] array
	* and place the evaluated values back into the same array. Only
	* evaluate t values that are within the range <0, 1>, including
	* the 0 and 1 ends of the range iff the include0 or include1
	* booleans are true. If an "inflection" equation is handed in,
	* then any points which represent a point of inflection for that
	* quadratic equation are also ignored.
	*/
	private static int evalQuadratic(double vals[], int num,
	boolean include0,
	boolean include1,
	double inflect[],
	double c1, double ctrl, double c2) {
	int j = 0;
	for (int i = 0; i < num; i++) {
	double t = vals[i];
	if ((include0 ? t >= 0 : t > 0) &&
	(include1 ? t <= 1 : t < 1) &&
	(inflect == null \|\|
	inflect[1] + 2inflect[2]t != 0))
	{
	double u = 1 - t;
	vals[j++] = c1uu + 2ctrltu + c2t*t;
	}
	}
	return j;
	}

	private static final int BELOW = -2;
	private static final int LOWEDGE = -1;
	private static final int INSIDE = 0;
	private static final int HIGHEDGE = 1;
	private static final int ABOVE = 2;

	/**
	* Determine where coord lies with respect to the range from
	* low to high. It is assumed that low <= high. The return
	* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
	* or ABOVE.
	*/
	private static int getTag(double coord, double low, double high) {
	if (coord <= low) {
	return (coord < low ? BELOW : LOWEDGE);
	}
	if (coord >= high) {
	return (coord > high ? ABOVE : HIGHEDGE);
	}
	return INSIDE;
	}

	/**
	* Determine if the pttag represents a coordinate that is already
	* in its test range, or is on the border with either of the two
	* opttags representing another coordinate that is "towards the
	* inside" of that test range. In other words, are either of the
	* two "opt" points "drawing the pt inward"?
	*/
	private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
	switch (pttag) {
	case BELOW:
	case ABOVE:
	default:
	return false;
	case LOWEDGE:
	return (opt1tag >= INSIDE \|\| opt2tag >= INSIDE);
	case INSIDE:
	return true;
	case HIGHEDGE:
	return (opt1tag <= INSIDE \|\| opt2tag <= INSIDE);
	}
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean intersects(double x, double y, double w, double h) {
	// Trivially reject non-existant rectangles
	if (w <= 0 \|\| h <= 0) {
	return false;
	}

	// Trivially accept if either endpoint is inside the rectangle
	// (not on its border since it may end there and not go inside)
	// Record where they lie with respect to the rectangle.
	// -1 => left, 0 => inside, 1 => right
	double x1 = getX1();
	double y1 = getY1();
	int x1tag = getTag(x1, x, x+w);
	int y1tag = getTag(y1, y, y+h);
	if (x1tag == INSIDE && y1tag == INSIDE) {
	return true;
	}
	double x2 = getX2();
	double y2 = getY2();
	int x2tag = getTag(x2, x, x+w);
	int y2tag = getTag(y2, y, y+h);
	if (x2tag == INSIDE && y2tag == INSIDE) {
	return true;
	}
	double ctrlx = getCtrlX();
	double ctrly = getCtrlY();
	int ctrlxtag = getTag(ctrlx, x, x+w);
	int ctrlytag = getTag(ctrly, y, y+h);

	// Trivially reject if all points are entirely to one side of
	// the rectangle.
	if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
	return false; // All points left
	}
	if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
	return false; // All points above
	}
	if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
	return false; // All points right
	}
	if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
	return false; // All points below
	}

	// Test for endpoints on the edge where either the segment
	// or the curve is headed "inwards" from them
	// Note: These tests are a superset of the fast endpoint tests
	// above and thus repeat those tests, but take more time
	// and cover more cases
	if (inwards(x1tag, x2tag, ctrlxtag) &&
	inwards(y1tag, y2tag, ctrlytag))
	{
	// First endpoint on border with either edge moving inside
	return true;
	}
	if (inwards(x2tag, x1tag, ctrlxtag) &&
	inwards(y2tag, y1tag, ctrlytag))
	{
	// Second endpoint on border with either edge moving inside
	return true;
	}

	// Trivially accept if endpoints span directly across the rectangle
	boolean xoverlap = (x1tag * x2tag <= 0);
	boolean yoverlap = (y1tag * y2tag <= 0);
	if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
	return true;
	}
	if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
	return true;
	}

	// We now know that both endpoints are outside the rectangle
	// but the 3 points are not all on one side of the rectangle.
	// Therefore the curve cannot be contained inside the rectangle,
	// but the rectangle might be contained inside the curve, or
	// the curve might intersect the boundary of the rectangle.

	double[] eqn = new double[3];
	double[] res = new double[3];
	if (!yoverlap) {
	// Both Y coordinates for the closing segment are above or
	// below the rectangle which means that we can only intersect
	// if the curve crosses the top (or bottom) of the rectangle
	// in more than one place and if those crossing locations
	// span the horizontal range of the rectangle.
	fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2);
	return (solveQuadratic(eqn, res) == 2 &&
	evalQuadratic(res, 2, true, true, null,
	x1, ctrlx, x2) == 2 &&
	getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
	}

	// Y ranges overlap. Now we examine the X ranges
	if (!xoverlap) {
	// Both X coordinates for the closing segment are left of
	// or right of the rectangle which means that we can only
	// intersect if the curve crosses the left (or right) edge
	// of the rectangle in more than one place and if those
	// crossing locations span the vertical range of the rectangle.
	fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2);
	return (solveQuadratic(eqn, res) == 2 &&
	evalQuadratic(res, 2, true, true, null,
	y1, ctrly, y2) == 2 &&
	getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
	}

	// The X and Y ranges of the endpoints overlap the X and Y
	// ranges of the rectangle, now find out how the endpoint
	// line segment intersects the Y range of the rectangle
	double dx = x2 - x1;
	double dy = y2 - y1;
	double k = y2 * x1 - x2 * y1;
	int c1tag, c2tag;
	if (y1tag == INSIDE) {
	c1tag = x1tag;
	} else {
	c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
	}
	if (y2tag == INSIDE) {
	c2tag = x2tag;
	} else {
	c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
	}
	// If the part of the line segment that intersects the Y range
	// of the rectangle crosses it horizontally - trivially accept
	if (c1tag * c2tag <= 0) {
	return true;
	}

	// Now we know that both the X and Y ranges intersect and that
	// the endpoint line segment does not directly cross the rectangle.
	//
	// We can almost treat this case like one of the cases above
	// where both endpoints are to one side, except that we will
	// only get one intersection of the curve with the vertical
	// side of the rectangle. This is because the endpoint segment
	// accounts for the other intersection.
	//
	// (Remember there is overlap in both the X and Y ranges which
	// means that the segment must cross at least one vertical edge
	// of the rectangle - in particular, the "near vertical side" -
	// leaving only one intersection for the curve.)
	//
	// Now we calculate the y tags of the two intersections on the
	// "near vertical side" of the rectangle. We will have one with
	// the endpoint segment, and one with the curve. If those two
	// vertical intersections overlap the Y range of the rectangle,
	// we have an intersection. Otherwise, we don't.

	// c1tag = vertical intersection class of the endpoint segment
	//
	// Choose the y tag of the endpoint that was not on the same
	// side of the rectangle as the subsegment calculated above.
	// Note that we can "steal" the existing Y tag of that endpoint
	// since it will be provably the same as the vertical intersection.
	c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

	// c2tag = vertical intersection class of the curve
	//
	// We have to calculate this one the straightforward way.
	// Note that the c2tag can still tell us which vertical edge
	// to test against.
	fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2);
	int num = solveQuadratic(eqn, res);

	// Note: We should be able to assert(num == 2); since the
	// X range "crosses" (not touches) the vertical boundary,
	// but we pass num to evalQuadratic for completeness.
	evalQuadratic(res, num, true, true, null, y1, ctrly, y2);

	// Note: We can assert(num evals == 1); since one of the
	// 2 crossings will be out of the [0,1] range.
	c2tag = getTag(res[0], y, y+h);

	// Finally, we have an intersection if the two crossings
	// overlap the Y range of the rectangle.
	return (c1tag * c2tag <= 0);
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean intersects(Rectangle2D r) {
	return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(double x, double y, double w, double h) {
	if (w <= 0 \|\| h <= 0) {
	return false;
	}
	// Assertion: Quadratic curves closed by connecting their
	// endpoints are always convex.
	return (contains(x, y) &&
	contains(x + w, y) &&
	contains(x + w, y + h) &&
	contains(x, y + h));
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public boolean contains(Rectangle2D r) {
	return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
	}

	/**
	* {@inheritDoc}
	* @since 1.2
	*/
	public Rectangle getBounds() {
	return getBounds2D().getBounds();
	}

	/**
	* Returns an iteration object that defines the boundary of the
	* shape of this <code>QuadCurve2D</code>.
	* The iterator for this class is not multi-threaded safe,
	* which means that this <code>QuadCurve2D</code> class does not
	* guarantee that modifications to the geometry of this
	* <code>QuadCurve2D</code> object do not affect any iterations of
	* that geometry that are already in process.
	* @param at an optional {@link AffineTransform} to apply to the
	* shape boundary
	* @return a {@link PathIterator} object that defines the boundary
	* of the shape.
	* @since 1.2
	*/
	public PathIterator getPathIterator(AffineTransform at) {
	return new QuadIterator(this, at);
	}

	/**
	* Returns an iteration object that defines the boundary of the
	* flattened shape of this <code>QuadCurve2D</code>.
	* The iterator for this class is not multi-threaded safe,
	* which means that this <code>QuadCurve2D</code> class does not
	* guarantee that modifications to the geometry of this
	* <code>QuadCurve2D</code> object do not affect any iterations of
	* that geometry that are already in process.
	* @param at an optional <code>AffineTransform</code> to apply
	* to the boundary of the shape
	* @param flatness the maximum distance that the control points for a
	* subdivided curve can be with respect to a line connecting
	* the end points of this curve before this curve is
	* replaced by a straight line connecting the end points.
	* @return a <code>PathIterator</code> object that defines the
	* flattened boundary of the shape.
	* @since 1.2
	*/
	public PathIterator getPathIterator(AffineTransform at, double flatness) {
	return new FlatteningPathIterator(getPathIterator(at), flatness);
	}

	/**
	* Creates a new object of the same class and with the same contents
	* as this object.
	*
	* @return a clone of this instance.
	* @exception OutOfMemoryError if there is not enough memory.
	* @see java.lang.Cloneable
	* @since 1.2
	*/
	public Object clone() {
	try {
	return super.clone();
	} catch (CloneNotSupportedException e) {
	// this shouldn't happen, since we are Cloneable
	throw new InternalError(e);
	}
	}
	}

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