com.sun.javafx.geom.Order3 Maven / Gradle / Ivy
/*
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* 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
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*/
package com.sun.javafx.geom;
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));
}
}
/**
* [A double version of what is in QuadCurve2D...]
* Solves the quadratic whose coefficients are in the eqn
* array and places the non-complex roots into the res
* array, returning the number of roots.
* The quadratic solved is represented by the equation:
*
* eqn = {C, B, A};
* ax^2 + bx + c = 0
*
* A return value of -1 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 -1 if the equation is
* a constant.
*/
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 == 0f) {
// The quadratic parabola has degenerated to a line.
if (b == 0f) {
// 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 - 4f * a * c;
if (d < 0f) {
// 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 < 0f) {
d = -d;
}
double q = (b + d) / -2f;
// We already tested a for being 0 above
res[roots++] = q / a;
if (q != 0f) {
res[roots++] = c / q;
}
}
return roots;
}
/*
* 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 ret array.
*
* 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 - 3*CP1 + 3*CP0 - C0)t^2
* + 2*(3*CP1 - 6*CP0 + 3*C0)t
* + (3*CP0 - 3*C0)
* 0 = 3*(C1 - 3*CP1 + 3*CP0 - C0)t^2
* + 3*2*(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 = 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;
}
@Override
public int getOrder() {
return 3;
}
@Override
public double getXTop() {
return x0;
}
@Override
public double getYTop() {
return y0;
}
@Override
public double getXBot() {
return x1;
}
@Override
public double getYBot() {
return y1;
}
@Override
public double getXMin() {
return xmin;
}
@Override
public double getXMax() {
return xmax;
}
@Override
public double getX0() {
return (direction == INCREASING) ? x0 : x1;
}
@Override
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;
}
@Override
public double getX1() {
return (direction == DECREASING) ? x0 : x1;
}
@Override
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])
*/
@Override
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;
}
@Override
public double XforY(double y) {
if (y <= y0) {
return x0;
}
if (y >= y1) {
return x1;
}
return XforT(TforY(y));
}
@Override
public double XforT(double t) {
return (((xcoeff3 * t) + xcoeff2) * t + xcoeff1) * t + xcoeff0;
}
@Override
public double YforT(double t) {
return (((ycoeff3 * t) + ycoeff2) * t + ycoeff1) * t + ycoeff0;
}
@Override
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;
}
}
@Override
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;
}
}
@Override
public double nextVertical(double t0, double t1) {
double eqn[] = {xcoeff1, 2 * xcoeff2, 3 * xcoeff3};
int numroots = solveQuadratic(eqn, eqn);
for (int i = 0; i < numroots; i++) {
if (eqn[i] > t0 && eqn[i] < t1) {
t1 = eqn[i];
}
}
return t1;
}
@Override
public void enlarge(RectBounds r) {
r.add((float) x0, (float) y0);
double eqn[] = {xcoeff1, 2 * xcoeff2, 3 * xcoeff3};
int numroots = solveQuadratic(eqn, eqn);
for (int i = 0; i < numroots; i++) {
double t = eqn[i];
if (t > 0 && t < 1) {
r.add((float) XforT(t), (float) YforT(t));
}
}
r.add((float) x1, (float) y1);
}
@Override
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 modify 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);
}
@Override
public Curve getReversedCurve() {
return new Order3(x0, y0, cx0, cy0, cx1, cy1, x1, y1, -direction);
}
@Override
public int getSegment(float coords[]) {
if (direction == INCREASING) {
coords[0] = (float) cx0;
coords[1] = (float) cy0;
coords[2] = (float) cx1;
coords[3] = (float) cy1;
coords[4] = (float) x1;
coords[5] = (float) y1;
} else {
coords[0] = (float) cx1;
coords[1] = (float) cy1;
coords[2] = (float) cx0;
coords[3] = (float) cy0;
coords[4] = (float) x0;
coords[5] = (float) y0;
}
return PathIterator.SEG_CUBICTO;
}
@Override
public String controlPointString() {
return (("("+round(getCX0())+", "+round(getCY0())+"), ")+
("("+round(getCX1())+", "+round(getCY1())+"), "));
}
}