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/*
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* Copyright (c) 2007, 2017, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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package sun.java2d.marlin;
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import static java.lang.Math.PI;
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import static java.lang.Math.cos;
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import static java.lang.Math.sqrt;
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import static java.lang.Math.cbrt;
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import static java.lang.Math.acos;
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final class DHelpers implements MarlinConst {
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private DHelpers() {
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throw new Error("This is a non instantiable class");
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}
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static boolean within(final double x, final double y, final double err) {
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final double d = y - x;
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return (d <= err && d >= -err);
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}
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static int quadraticRoots(final double a, final double b,
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final double c, double[] zeroes, final int off)
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{
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int ret = off;
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double t;
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if (a != 0.0d) {
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final double dis = b*b - 4*a*c;
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if (dis > 0.0d) {
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final double sqrtDis = Math.sqrt(dis);
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// depending on the sign of b we use a slightly different
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// algorithm than the traditional one to find one of the roots
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// so we can avoid adding numbers of different signs (which
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// might result in loss of precision).
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if (b >= 0.0d) {
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zeroes[ret++] = (2.0d * c) / (-b - sqrtDis);
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zeroes[ret++] = (-b - sqrtDis) / (2.0d * a);
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} else {
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zeroes[ret++] = (-b + sqrtDis) / (2.0d * a);
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zeroes[ret++] = (2.0d * c) / (-b + sqrtDis);
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}
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} else if (dis == 0.0d) {
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t = (-b) / (2.0d * a);
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zeroes[ret++] = t;
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}
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} else {
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if (b != 0.0d) {
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t = (-c) / b;
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zeroes[ret++] = t;
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}
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}
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return ret - off;
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}
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// find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
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static int cubicRootsInAB(double d, double a, double b, double c,
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double[] pts, final int off,
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final double A, final double B)
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{
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if (d == 0.0d) {
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int num = quadraticRoots(a, b, c, pts, off);
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return filterOutNotInAB(pts, off, num, A, B) - off;
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}
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// From Graphics Gems:
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// http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
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// (also from awt.geom.CubicCurve2D. But here we don't need as
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// much accuracy and we don't want to create arrays so we use
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// our own customized version).
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// normal form: x^3 + ax^2 + bx + c = 0
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a /= d;
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b /= d;
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c /= d;
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// substitute x = y - A/3 to eliminate quadratic term:
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// x^3 +Px + Q = 0
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//
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// Since we actually need P/3 and Q/2 for all of the
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// calculations that follow, we will calculate
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// p = P/3
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// q = Q/2
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// instead and use those values for simplicity of the code.
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double sq_A = a * a;
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double p = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
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double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * a * b + c);
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// use Cardano's formula
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double cb_p = p * p * p;
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double D = q * q + cb_p;
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int num;
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if (D < 0.0d) {
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// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
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final double phi = (1.0d/3.0d) * acos(-q / sqrt(-cb_p));
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final double t = 2.0d * sqrt(-p);
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pts[ off+0 ] = ( t * cos(phi));
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pts[ off+1 ] = (-t * cos(phi + (PI / 3.0d)));
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pts[ off+2 ] = (-t * cos(phi - (PI / 3.0d)));
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num = 3;
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} else {
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final double sqrt_D = sqrt(D);
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final double u = cbrt(sqrt_D - q);
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final double v = - cbrt(sqrt_D + q);
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pts[ off ] = (u + v);
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num = 1;
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if (within(D, 0.0d, 1e-8d)) {
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pts[off+1] = -(pts[off] / 2.0d);
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num = 2;
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}
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}
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final double sub = (1.0d/3.0d) * a;
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for (int i = 0; i < num; ++i) {
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pts[ off+i ] -= sub;
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}
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return filterOutNotInAB(pts, off, num, A, B) - off;
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}
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static double evalCubic(final double a, final double b,
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final double c, final double d,
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final double t)
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{
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return t * (t * (t * a + b) + c) + d;
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}
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static double evalQuad(final double a, final double b,
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final double c, final double t)
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{
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return t * (t * a + b) + c;
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}
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// returns the index 1 past the last valid element remaining after filtering
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static int filterOutNotInAB(double[] nums, final int off, final int len,
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final double a, final double b)
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{
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int ret = off;
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for (int i = off, end = off + len; i < end; i++) {
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if (nums[i] >= a && nums[i] < b) {
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nums[ret++] = nums[i];
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}
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}
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return ret;
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}
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static double polyLineLength(double[] poly, final int off, final int nCoords) {
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assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";
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double acc = 0.0d;
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for (int i = off + 2; i < off + nCoords; i += 2) {
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acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]);
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}
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return acc;
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}
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static double linelen(double x1, double y1, double x2, double y2) {
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final double dx = x2 - x1;
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final double dy = y2 - y1;
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return Math.sqrt(dx*dx + dy*dy);
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}
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static void subdivide(double[] src, int srcoff, double[] left, int leftoff,
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double[] right, int rightoff, int type)
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{
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switch(type) {
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case 6:
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DHelpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
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return;
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case 8:
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DHelpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
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return;
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default:
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throw new InternalError("Unsupported curve type");
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}
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}
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static void isort(double[] a, int off, int len) {
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for (int i = off + 1, end = off + len; i < end; i++) {
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double ai = a[i];
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int j = i - 1;
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for (; j >= off && a[j] > ai; j--) {
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a[j+1] = a[j];
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}
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a[j+1] = ai;
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}
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}
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// Most of these are copied from classes in java.awt.geom because we need
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// both single and double precision variants of these functions, and Line2D,
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// CubicCurve2D, QuadCurve2D don't provide them.
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/**
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* Subdivides the cubic curve specified by the coordinates
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* stored in the <code>src</code> array at indices <code>srcoff</code>
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* through (<code>srcoff</code> + 7) and stores the
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* resulting two subdivided curves into the two result arrays at the
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* corresponding indices.
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* Either or both of the <code>left</code> and <code>right</code>
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* arrays may be <code>null</code> or a reference to the same array
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* as the <code>src</code> array.
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* Note that the last point in the first subdivided curve is the
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* same as the first point in the second subdivided curve. Thus,
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* it is possible to pass the same array for <code>left</code>
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* and <code>right</code> and to use offsets, such as <code>rightoff</code>
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* equals (<code>leftoff</code> + 6), in order
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* to avoid allocating extra storage for this common point.
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* @param src the array holding the coordinates for the source curve
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* @param srcoff the offset into the array of the beginning of the
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* the 6 source coordinates
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* @param left the array for storing the coordinates for the first
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* half of the subdivided curve
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* @param leftoff the offset into the array of the beginning of the
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* the 6 left coordinates
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* @param right the array for storing the coordinates for the second
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* half of the subdivided curve
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* @param rightoff the offset into the array of the beginning of the
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* the 6 right coordinates
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* @since 1.7
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*/
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static void subdivideCubic(double[] src, int srcoff,
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double[] left, int leftoff,
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double[] right, int rightoff)
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{
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double x1 = src[srcoff + 0];
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double y1 = src[srcoff + 1];
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double ctrlx1 = src[srcoff + 2];
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double ctrly1 = src[srcoff + 3];
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double ctrlx2 = src[srcoff + 4];
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double ctrly2 = src[srcoff + 5];
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double x2 = src[srcoff + 6];
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double y2 = src[srcoff + 7];
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if (left != null) {
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left[leftoff + 0] = x1;
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left[leftoff + 1] = y1;
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}
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if (right != null) {
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right[rightoff + 6] = x2;
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right[rightoff + 7] = y2;
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}
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x1 = (x1 + ctrlx1) / 2.0d;
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y1 = (y1 + ctrly1) / 2.0d;
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x2 = (x2 + ctrlx2) / 2.0d;
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y2 = (y2 + ctrly2) / 2.0d;
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double centerx = (ctrlx1 + ctrlx2) / 2.0d;
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double centery = (ctrly1 + ctrly2) / 2.0d;
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ctrlx1 = (x1 + centerx) / 2.0d;
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ctrly1 = (y1 + centery) / 2.0d;
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ctrlx2 = (x2 + centerx) / 2.0d;
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ctrly2 = (y2 + centery) / 2.0d;
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centerx = (ctrlx1 + ctrlx2) / 2.0d;
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centery = (ctrly1 + ctrly2) / 2.0d;
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if (left != null) {
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left[leftoff + 2] = x1;
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left[leftoff + 3] = y1;
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left[leftoff + 4] = ctrlx1;
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left[leftoff + 5] = ctrly1;
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left[leftoff + 6] = centerx;
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left[leftoff + 7] = centery;
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}
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if (right != null) {
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right[rightoff + 0] = centerx;
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right[rightoff + 1] = centery;
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right[rightoff + 2] = ctrlx2;
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right[rightoff + 3] = ctrly2;
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right[rightoff + 4] = x2;
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right[rightoff + 5] = y2;
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}
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}
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static void subdivideCubicAt(double t, double[] src, int srcoff,
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double[] left, int leftoff,
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double[] right, int rightoff)
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{
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double x1 = src[srcoff + 0];
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double y1 = src[srcoff + 1];
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double ctrlx1 = src[srcoff + 2];
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double ctrly1 = src[srcoff + 3];
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double ctrlx2 = src[srcoff + 4];
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double ctrly2 = src[srcoff + 5];
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double x2 = src[srcoff + 6];
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double y2 = src[srcoff + 7];
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if (left != null) {
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left[leftoff + 0] = x1;
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left[leftoff + 1] = y1;
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}
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if (right != null) {
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right[rightoff + 6] = x2;
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right[rightoff + 7] = y2;
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}
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x1 = x1 + t * (ctrlx1 - x1);
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y1 = y1 + t * (ctrly1 - y1);
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x2 = ctrlx2 + t * (x2 - ctrlx2);
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y2 = ctrly2 + t * (y2 - ctrly2);
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double centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
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double centery = ctrly1 + t * (ctrly2 - ctrly1);
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ctrlx1 = x1 + t * (centerx - x1);
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ctrly1 = y1 + t * (centery - y1);
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ctrlx2 = centerx + t * (x2 - centerx);
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ctrly2 = centery + t * (y2 - centery);
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centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
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centery = ctrly1 + t * (ctrly2 - ctrly1);
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if (left != null) {
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left[leftoff + 2] = x1;
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left[leftoff + 3] = y1;
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left[leftoff + 4] = ctrlx1;
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left[leftoff + 5] = ctrly1;
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left[leftoff + 6] = centerx;
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left[leftoff + 7] = centery;
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}
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if (right != null) {
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right[rightoff + 0] = centerx;
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right[rightoff + 1] = centery;
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right[rightoff + 2] = ctrlx2;
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right[rightoff + 3] = ctrly2;
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right[rightoff + 4] = x2;
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right[rightoff + 5] = y2;
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}
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}
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static void subdivideQuad(double[] src, int srcoff,
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double[] left, int leftoff,
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double[] right, int rightoff)
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{
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double x1 = src[srcoff + 0];
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double y1 = src[srcoff + 1];
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double ctrlx = src[srcoff + 2];
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double ctrly = src[srcoff + 3];
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double x2 = src[srcoff + 4];
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double y2 = src[srcoff + 5];
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if (left != null) {
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left[leftoff + 0] = x1;
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left[leftoff + 1] = y1;
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}
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if (right != null) {
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right[rightoff + 4] = x2;
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right[rightoff + 5] = y2;
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}
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x1 = (x1 + ctrlx) / 2.0d;
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y1 = (y1 + ctrly) / 2.0d;
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x2 = (x2 + ctrlx) / 2.0d;
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y2 = (y2 + ctrly) / 2.0d;
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ctrlx = (x1 + x2) / 2.0d;
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ctrly = (y1 + y2) / 2.0d;
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if (left != null) {
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left[leftoff + 2] = x1;
|
|
373 |
left[leftoff + 3] = y1;
|
|
374 |
left[leftoff + 4] = ctrlx;
|
|
375 |
left[leftoff + 5] = ctrly;
|
|
376 |
}
|
|
377 |
if (right != null) {
|
|
378 |
right[rightoff + 0] = ctrlx;
|
|
379 |
right[rightoff + 1] = ctrly;
|
|
380 |
right[rightoff + 2] = x2;
|
|
381 |
right[rightoff + 3] = y2;
|
|
382 |
}
|
|
383 |
}
|
|
384 |
|
|
385 |
static void subdivideQuadAt(double t, double[] src, int srcoff,
|
|
386 |
double[] left, int leftoff,
|
|
387 |
double[] right, int rightoff)
|
|
388 |
{
|
|
389 |
double x1 = src[srcoff + 0];
|
|
390 |
double y1 = src[srcoff + 1];
|
|
391 |
double ctrlx = src[srcoff + 2];
|
|
392 |
double ctrly = src[srcoff + 3];
|
|
393 |
double x2 = src[srcoff + 4];
|
|
394 |
double y2 = src[srcoff + 5];
|
|
395 |
if (left != null) {
|
|
396 |
left[leftoff + 0] = x1;
|
|
397 |
left[leftoff + 1] = y1;
|
|
398 |
}
|
|
399 |
if (right != null) {
|
|
400 |
right[rightoff + 4] = x2;
|
|
401 |
right[rightoff + 5] = y2;
|
|
402 |
}
|
|
403 |
x1 = x1 + t * (ctrlx - x1);
|
|
404 |
y1 = y1 + t * (ctrly - y1);
|
|
405 |
x2 = ctrlx + t * (x2 - ctrlx);
|
|
406 |
y2 = ctrly + t * (y2 - ctrly);
|
|
407 |
ctrlx = x1 + t * (x2 - x1);
|
|
408 |
ctrly = y1 + t * (y2 - y1);
|
|
409 |
if (left != null) {
|
|
410 |
left[leftoff + 2] = x1;
|
|
411 |
left[leftoff + 3] = y1;
|
|
412 |
left[leftoff + 4] = ctrlx;
|
|
413 |
left[leftoff + 5] = ctrly;
|
|
414 |
}
|
|
415 |
if (right != null) {
|
|
416 |
right[rightoff + 0] = ctrlx;
|
|
417 |
right[rightoff + 1] = ctrly;
|
|
418 |
right[rightoff + 2] = x2;
|
|
419 |
right[rightoff + 3] = y2;
|
|
420 |
}
|
|
421 |
}
|
|
422 |
|
|
423 |
static void subdivideAt(double t, double[] src, int srcoff,
|
|
424 |
double[] left, int leftoff,
|
|
425 |
double[] right, int rightoff, int size)
|
|
426 |
{
|
|
427 |
switch(size) {
|
|
428 |
case 8:
|
|
429 |
subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
|
|
430 |
return;
|
|
431 |
case 6:
|
|
432 |
subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
|
|
433 |
return;
|
|
434 |
}
|
|
435 |
}
|
|
436 |
}
|