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	/*
	* Copyright (c) 1998, 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 sun.awt.geom;

	import java.awt.geom.Rectangle2D;
	import java.awt.geom.PathIterator;
	import java.awt.geom.QuadCurve2D;
	import java.util.Vector;

	final class Order3 extends Curve {
	private double x0;
	private double y0;
	private double cx0;
	private double cy0;
	private double cx1;
	private double cy1;
	private double x1;
	private double y1;

	private double xmin;
	private double xmax;

	private double xcoeff0;
	private double xcoeff1;
	private double xcoeff2;
	private double xcoeff3;

	private double ycoeff0;
	private double ycoeff1;
	private double ycoeff2;
	private double ycoeff3;

	public static void insert(Vector curves, double tmp[],
	double x0, double y0,
	double cx0, double cy0,
	double cx1, double cy1,
	double x1, double y1,
	int direction)
	{
	int numparams = getHorizontalParams(y0, cy0, cy1, y1, tmp);
	if (numparams == 0) {
	// We are using addInstance here to avoid inserting horisontal
	// segments
	addInstance(curves, x0, y0, cx0, cy0, cx1, cy1, x1, y1, direction);
	return;
	}
	// Store coordinates for splitting at tmp[3..10]
	tmp[3] = x0; tmp[4] = y0;
	tmp[5] = cx0; tmp[6] = cy0;
	tmp[7] = cx1; tmp[8] = cy1;
	tmp[9] = x1; tmp[10] = y1;
	double t = tmp[0];
	if (numparams > 1 && t > tmp[1]) {
	// Perform a "2 element sort"...
	tmp[0] = tmp[1];
	tmp[1] = t;
	t = tmp[0];
	}
	split(tmp, 3, t);
	if (numparams > 1) {
	// Recalculate tmp[1] relative to the range [tmp[0]...1]
	t = (tmp[1] - t) / (1 - t);
	split(tmp, 9, t);
	}
	int index = 3;
	if (direction == DECREASING) {
	index += numparams * 6;
	}
	while (numparams >= 0) {
	addInstance(curves,
	tmp[index + 0], tmp[index + 1],
	tmp[index + 2], tmp[index + 3],
	tmp[index + 4], tmp[index + 5],
	tmp[index + 6], tmp[index + 7],
	direction);
	numparams--;
	if (direction == INCREASING) {
	index += 6;
	} else {
	index -= 6;
	}
	}
	}

	public static void addInstance(Vector curves,
	double x0, double y0,
	double cx0, double cy0,
	double cx1, double cy1,
	double x1, double y1,
	int direction) {
	if (y0 > y1) {
	curves.add(new Order3(x1, y1, cx1, cy1, cx0, cy0, x0, y0,
	-direction));
	} else if (y1 > y0) {
	curves.add(new Order3(x0, y0, cx0, cy0, cx1, cy1, x1, y1,
	direction));
	}
	}

	/*
	* Return the count of the number of horizontal sections of the
	* specified cubic Bezier curve. Put the parameters for the
	* horizontal sections into the specified <code>ret</code> array.
	* <p>
	* If we examine the parametric equation in t, we have:
	* Py(t) = C0(1-t)^3 + 3CP0 t(1-t)^2 + 3CP1 t^2(1-t) + C1 t^3
	* = C0 - 3C0t + 3C0t^2 - C0t^3 +
	* 3CP0t - 6CP0t^2 + 3CP0t^3 +
	* 3CP1t^2 - 3CP1t^3 +
	* C1t^3
	* Py(t) = (C1 - 3CP1 + 3CP0 - C0) t^3 +
	* (3C0 - 6CP0 + 3CP1) t^2 +
	* (3CP0 - 3C0) t +
	* (C0)
	* If we take the derivative, we get:
	* Py(t) = Dt^3 + At^2 + Bt + C
	* dPy(t) = 3Dt^2 + 2At + B = 0
	* 0 = 3(C1 - 3CP1 + 3*CP0 - C0)t^2
	* + 2(3CP1 - 6CP0 + 3C0)t
	* + (3CP0 - 3C0)
	* 0 = 3(C1 - 3CP1 + 3*CP0 - C0)t^2
	* + 32(CP1 - 2*CP0 + C0)t
	* + 3*(CP0 - C0)
	* 0 = (C1 - CP1 - CP1 - CP1 + CP0 + CP0 + CP0 - C0)t^2
	* + 2*(CP1 - CP0 - CP0 + C0)t
	* + (CP0 - C0)
	* 0 = (C1 - CP1 + CP0 - CP1 + CP0 - CP1 + CP0 - C0)t^2
	* + 2*(CP1 - CP0 - CP0 + C0)t
	* + (CP0 - C0)
	* 0 = ((C1 - CP1) - (CP1 - CP0) - (CP1 - CP0) + (CP0 - C0))t^2
	* + 2*((CP1 - CP0) - (CP0 - C0))t
	* + (CP0 - C0)
	* Note that this method will return 0 if the equation is a line,
	* which is either always horizontal or never horizontal.
	* Completely horizontal curves need to be eliminated by other
	* means outside of this method.
	*/
	public static int getHorizontalParams(double c0, double cp0,
	double cp1, double c1,
	double ret[]) {
	if (c0 <= cp0 && cp0 <= cp1 && cp1 <= c1) {
	return 0;
	}
	c1 -= cp1;
	cp1 -= cp0;
	cp0 -= c0;
	ret[0] = cp0;
	ret[1] = (cp1 - cp0) * 2;
	ret[2] = (c1 - cp1 - cp1 + cp0);
	int numroots = QuadCurve2D.solveQuadratic(ret, ret);
	int j = 0;
	for (int i = 0; i < numroots; i++) {
	double t = ret[i];
	// No splits at t==0 and t==1
	if (t > 0 && t < 1) {
	if (j < i) {
	ret[j] = t;
	}
	j++;
	}
	}
	return j;
	}

	/*
	* Split the cubic Bezier stored at coords[pos...pos+7] representing
	* the parametric range [0..1] into two subcurves representing the
	* parametric subranges [0..t] and [t..1]. Store the results back
	* into the array at coords[pos...pos+7] and coords[pos+6...pos+13].
	*/
	public static void split(double coords[], int pos, double t) {
	double x0, y0, cx0, cy0, cx1, cy1, x1, y1;
	coords[pos+12] = x1 = coords[pos+6];
	coords[pos+13] = y1 = coords[pos+7];
	cx1 = coords[pos+4];
	cy1 = coords[pos+5];
	x1 = cx1 + (x1 - cx1) * t;
	y1 = cy1 + (y1 - cy1) * t;
	x0 = coords[pos+0];
	y0 = coords[pos+1];
	cx0 = coords[pos+2];
	cy0 = coords[pos+3];
	x0 = x0 + (cx0 - x0) * t;
	y0 = y0 + (cy0 - y0) * t;
	cx0 = cx0 + (cx1 - cx0) * t;
	cy0 = cy0 + (cy1 - cy0) * t;
	cx1 = cx0 + (x1 - cx0) * t;
	cy1 = cy0 + (y1 - cy0) * t;
	cx0 = x0 + (cx0 - x0) * t;
	cy0 = y0 + (cy0 - y0) * t;
	coords[pos+2] = x0;
	coords[pos+3] = y0;
	coords[pos+4] = cx0;
	coords[pos+5] = cy0;
	coords[pos+6] = cx0 + (cx1 - cx0) * t;
	coords[pos+7] = cy0 + (cy1 - cy0) * t;
	coords[pos+8] = cx1;
	coords[pos+9] = cy1;
	coords[pos+10] = x1;
	coords[pos+11] = y1;
	}

	public Order3(double x0, double y0,
	double cx0, double cy0,
	double cx1, double cy1,
	double x1, double y1,
	int direction)
	{
	super(direction);
	// REMIND: Better accuracy in the root finding methods would
	// ensure that cys are in range. As it stands, they are never
	// more than "1 mantissa bit" out of range...
	if (cy0 < y0) cy0 = y0;
	if (cy1 > y1) cy1 = y1;
	this.x0 = x0;
	this.y0 = y0;
	this.cx0 = cx0;
	this.cy0 = cy0;
	this.cx1 = cx1;
	this.cy1 = cy1;
	this.x1 = x1;
	this.y1 = y1;
	xmin = Math.min(Math.min(x0, x1), Math.min(cx0, cx1));
	xmax = Math.max(Math.max(x0, x1), Math.max(cx0, cx1));
	xcoeff0 = x0;
	xcoeff1 = (cx0 - x0) * 3.0;
	xcoeff2 = (cx1 - cx0 - cx0 + x0) * 3.0;
	xcoeff3 = x1 - (cx1 - cx0) * 3.0 - x0;
	ycoeff0 = y0;
	ycoeff1 = (cy0 - y0) * 3.0;
	ycoeff2 = (cy1 - cy0 - cy0 + y0) * 3.0;
	ycoeff3 = y1 - (cy1 - cy0) * 3.0 - y0;
	YforT1 = YforT2 = YforT3 = y0;
	}

	public int getOrder() {
	return 3;
	}

	public double getXTop() {
	return x0;
	}

	public double getYTop() {
	return y0;
	}

	public double getXBot() {
	return x1;
	}

	public double getYBot() {
	return y1;
	}

	public double getXMin() {
	return xmin;
	}

	public double getXMax() {
	return xmax;
	}

	public double getX0() {
	return (direction == INCREASING) ? x0 : x1;
	}

	public double getY0() {
	return (direction == INCREASING) ? y0 : y1;
	}

	public double getCX0() {
	return (direction == INCREASING) ? cx0 : cx1;
	}

	public double getCY0() {
	return (direction == INCREASING) ? cy0 : cy1;
	}

	public double getCX1() {
	return (direction == DECREASING) ? cx0 : cx1;
	}

	public double getCY1() {
	return (direction == DECREASING) ? cy0 : cy1;
	}

	public double getX1() {
	return (direction == DECREASING) ? x0 : x1;
	}

	public double getY1() {
	return (direction == DECREASING) ? y0 : y1;
	}

	private double TforY1;
	private double YforT1;
	private double TforY2;
	private double YforT2;
	private double TforY3;
	private double YforT3;

	/*
	* Solve the cubic whose coefficients are in the a,b,c,d fields and
	* return the first root in the range [0, 1].
	* The cubic solved is represented by the equation:
	* x^3 + (ycoeff2)x^2 + (ycoeff1)x + (ycoeff0) = y
	* @return the first valid root (in the range [0, 1])
	*/
	public double TforY(double y) {
	if (y <= y0) return 0;
	if (y >= y1) return 1;
	if (y == YforT1) return TforY1;
	if (y == YforT2) return TforY2;
	if (y == YforT3) return TforY3;
	// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
	if (ycoeff3 == 0.0) {
	// The cubic degenerated to quadratic (or line or ...).
	return Order2.TforY(y, ycoeff0, ycoeff1, ycoeff2);
	}
	double a = ycoeff2 / ycoeff3;
	double b = ycoeff1 / ycoeff3;
	double c = (ycoeff0 - y) / ycoeff3;
	int roots = 0;
	double Q = (a * a - 3.0 * b) / 9.0;
	double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
	double R2 = R * R;
	double Q3 = Q * Q * Q;
	double a_3 = a / 3.0;
	double t;
	if (R2 < Q3) {
	double theta = Math.acos(R / Math.sqrt(Q3));
	Q = -2.0 * Math.sqrt(Q);
	t = refine(a, b, c, y, Q * Math.cos(theta / 3.0) - a_3);
	if (t < 0) {
	t = refine(a, b, c, y,
	Q * Math.cos((theta + Math.PI * 2.0)/ 3.0) - a_3);
	}
	if (t < 0) {
	t = refine(a, b, c, y,
	Q * Math.cos((theta - Math.PI * 2.0)/ 3.0) - a_3);
	}
	} else {
	boolean neg = (R < 0.0);
	double S = Math.sqrt(R2 - Q3);
	if (neg) {
	R = -R;
	}
	double A = Math.pow(R + S, 1.0 / 3.0);
	if (!neg) {
	A = -A;
	}
	double B = (A == 0.0) ? 0.0 : (Q / A);
	t = refine(a, b, c, y, (A + B) - a_3);
	}
	if (t < 0) {
	//throw new InternalError("bad t");
	double t0 = 0;
	double t1 = 1;
	while (true) {
	t = (t0 + t1) / 2;
	if (t == t0 \|\| t == t1) {
	break;
	}
	double yt = YforT(t);
	if (yt < y) {
	t0 = t;
	} else if (yt > y) {
	t1 = t;
	} else {
	break;
	}
	}
	}
	if (t >= 0) {
	TforY3 = TforY2;
	YforT3 = YforT2;
	TforY2 = TforY1;
	YforT2 = YforT1;
	TforY1 = t;
	YforT1 = y;
	}
	return t;
	}

	public double refine(double a, double b, double c,
	double target, double t)
	{
	if (t < -0.1 \|\| t > 1.1) {
	return -1;
	}
	double y = YforT(t);
	double t0, t1;
	if (y < target) {
	t0 = t;
	t1 = 1;
	} else {
	t0 = 0;
	t1 = t;
	}
	double origt = t;
	double origy = y;
	boolean useslope = true;
	while (y != target) {
	if (!useslope) {
	double t2 = (t0 + t1) / 2;
	if (t2 == t0 \|\| t2 == t1) {
	break;
	}
	t = t2;
	} else {
	double slope = dYforT(t, 1);
	if (slope == 0) {
	useslope = false;
	continue;
	}
	double t2 = t + ((target - y) / slope);
	if (t2 == t \|\| t2 <= t0 \|\| t2 >= t1) {
	useslope = false;
	continue;
	}
	t = t2;
	}
	y = YforT(t);
	if (y < target) {
	t0 = t;
	} else if (y > target) {
	t1 = t;
	} else {
	break;
	}
	}
	boolean verbose = false;
	if (false && t >= 0 && t <= 1) {
	y = YforT(t);
	long tdiff = diffbits(t, origt);
	long ydiff = diffbits(y, origy);
	long yerr = diffbits(y, target);
	if (yerr > 0 \|\| (verbose && tdiff > 0)) {
	System.out.println("target was y = "+target);
	System.out.println("original was y = "+origy+", t = "+origt);
	System.out.println("final was y = "+y+", t = "+t);
	System.out.println("t diff is "+tdiff);
	System.out.println("y diff is "+ydiff);
	System.out.println("y error is "+yerr);
	double tlow = prev(t);
	double ylow = YforT(tlow);
	double thi = next(t);
	double yhi = YforT(thi);
	if (Math.abs(target - ylow) < Math.abs(target - y) \|\|
	Math.abs(target - yhi) < Math.abs(target - y))
	{
	System.out.println("adjacent y's = ["+ylow+", "+yhi+"]");
	}
	}
	}
	return (t > 1) ? -1 : t;
	}

	public double XforY(double y) {
	if (y <= y0) {
	return x0;
	}
	if (y >= y1) {
	return x1;
	}
	return XforT(TforY(y));
	}

	public double XforT(double t) {
	return (((xcoeff3 * t) + xcoeff2) * t + xcoeff1) * t + xcoeff0;
	}

	public double YforT(double t) {
	return (((ycoeff3 * t) + ycoeff2) * t + ycoeff1) * t + ycoeff0;
	}

	public double dXforT(double t, int deriv) {
	switch (deriv) {
	case 0:
	return (((xcoeff3 * t) + xcoeff2) * t + xcoeff1) * t + xcoeff0;
	case 1:
	return ((3 * xcoeff3 * t) + 2 * xcoeff2) * t + xcoeff1;
	case 2:
	return (6 * xcoeff3 * t) + 2 * xcoeff2;
	case 3:
	return 6 * xcoeff3;
	default:
	return 0;
	}
	}

	public double dYforT(double t, int deriv) {
	switch (deriv) {
	case 0:
	return (((ycoeff3 * t) + ycoeff2) * t + ycoeff1) * t + ycoeff0;
	case 1:
	return ((3 * ycoeff3 * t) + 2 * ycoeff2) * t + ycoeff1;
	case 2:
	return (6 * ycoeff3 * t) + 2 * ycoeff2;
	case 3:
	return 6 * ycoeff3;
	default:
	return 0;
	}
	}

	public double nextVertical(double t0, double t1) {
	double eqn[] = {xcoeff1, 2 * xcoeff2, 3 * xcoeff3};
	int numroots = QuadCurve2D.solveQuadratic(eqn, eqn);
	for (int i = 0; i < numroots; i++) {
	if (eqn[i] > t0 && eqn[i] < t1) {
	t1 = eqn[i];
	}
	}
	return t1;
	}

	public void enlarge(Rectangle2D r) {
	r.add(x0, y0);
	double eqn[] = {xcoeff1, 2 * xcoeff2, 3 * xcoeff3};
	int numroots = QuadCurve2D.solveQuadratic(eqn, eqn);
	for (int i = 0; i < numroots; i++) {
	double t = eqn[i];
	if (t > 0 && t < 1) {
	r.add(XforT(t), YforT(t));
	}
	}
	r.add(x1, y1);
	}

	public Curve getSubCurve(double ystart, double yend, int dir) {
	if (ystart <= y0 && yend >= y1) {
	return getWithDirection(dir);
	}
	double eqn[] = new double[14];
	double t0, t1;
	t0 = TforY(ystart);
	t1 = TforY(yend);
	eqn[0] = x0;
	eqn[1] = y0;
	eqn[2] = cx0;
	eqn[3] = cy0;
	eqn[4] = cx1;
	eqn[5] = cy1;
	eqn[6] = x1;
	eqn[7] = y1;
	if (t0 > t1) {
	/* This happens in only rare cases where ystart is
	* very near yend and solving for the yend root ends
	* up stepping slightly lower in t than solving for
	* the ystart root.
	* Ideally we might want to skip this tiny little
	* segment and just fudge the surrounding coordinates
	* to bridge the gap left behind, but there is no way
	* to do that from here. Higher levels could
	* potentially eliminate these tiny "fixup" segments,
	* but not without a lot of extra work on the code that
	* coalesces chains of curves into subpaths. The
	* simplest solution for now is to just reorder the t
	* values and chop out a miniscule curve piece.
	*/
	double t = t0;
	t0 = t1;
	t1 = t;
	}
	if (t1 < 1) {
	split(eqn, 0, t1);
	}
	int i;
	if (t0 <= 0) {
	i = 0;
	} else {
	split(eqn, 0, t0 / t1);
	i = 6;
	}
	return new Order3(eqn[i+0], ystart,
	eqn[i+2], eqn[i+3],
	eqn[i+4], eqn[i+5],
	eqn[i+6], yend,
	dir);
	}

	public Curve getReversedCurve() {
	return new Order3(x0, y0, cx0, cy0, cx1, cy1, x1, y1, -direction);
	}

	public int getSegment(double coords[]) {
	if (direction == INCREASING) {
	coords[0] = cx0;
	coords[1] = cy0;
	coords[2] = cx1;
	coords[3] = cy1;
	coords[4] = x1;
	coords[5] = y1;
	} else {
	coords[0] = cx1;
	coords[1] = cy1;
	coords[2] = cx0;
	coords[3] = cy0;
	coords[4] = x0;
	coords[5] = y0;
	}
	return PathIterator.SEG_CUBICTO;
	}

	public String controlPointString() {
	return (("("+round(getCX0())+", "+round(getCY0())+"), ")+
	("("+round(getCX1())+", "+round(getCY1())+"), "));
	}
	}

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