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458 lines
16 KiB
Java
458 lines
16 KiB
Java
/*
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* Copyright (c) 2007, 2011, 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 com.jpexs.graphics;
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import java.util.Arrays;
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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 Helpers {
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private Helpers() {
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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 float x, final float y, final float err) {
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final float d = y - x;
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return (d <= err && d >= -err);
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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 float a, final float b,
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final float c, float[] zeroes, final int off)
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{
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int ret = off;
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float t;
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if (a != 0f) {
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final float dis = b*b - 4*a*c;
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if (dis > 0) {
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final float sqrtDis = (float)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) {
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zeroes[ret++] = (2 * c) / (-b - sqrtDis);
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zeroes[ret++] = (-b - sqrtDis) / (2 * a);
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} else {
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zeroes[ret++] = (-b + sqrtDis) / (2 * a);
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zeroes[ret++] = (2 * c) / (-b + sqrtDis);
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}
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} else if (dis == 0f) {
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t = (-b) / (2 * a);
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zeroes[ret++] = t;
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}
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} else {
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if (b != 0f) {
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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(float d, float a, float b, float c,
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float[] pts, final int off,
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final float A, final float B)
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{
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if (d == 0) {
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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 = 1.0/3 * (-1.0/3 * sq_A + b);
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double q = 1.0/2 * (2.0/27 * a * sq_A - 1.0/3 * 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) {
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// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
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final double phi = 1.0/3 * acos(-q / sqrt(-cb_p));
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final double t = 2 * sqrt(-p);
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pts[ off+0 ] = (float)( t * cos(phi));
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pts[ off+1 ] = (float)(-t * cos(phi + PI / 3));
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pts[ off+2 ] = (float)(-t * cos(phi - PI / 3));
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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 ] = (float)(u + v);
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num = 1;
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if (within(D, 0, 1e-8)) {
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pts[off+1] = -(pts[off] / 2);
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num = 2;
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}
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}
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final float sub = 1.0f/3 * 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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// These use a hardcoded factor of 2 for increasing sizes. Perhaps this
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// should be provided as an argument.
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static float[] widenArray(float[] in, final int cursize, final int numToAdd) {
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if (in.length >= cursize + numToAdd) {
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return in;
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}
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return Arrays.copyOf(in, 2 * (cursize + numToAdd));
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}
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static int[] widenArray(int[] in, final int cursize, final int numToAdd) {
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if (in.length >= cursize + numToAdd) {
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return in;
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}
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return Arrays.copyOf(in, 2 * (cursize + numToAdd));
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}
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static float evalCubic(final float a, final float b,
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final float c, final float d,
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final float 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 float evalQuad(final float a, final float b,
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final float c, final float 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(float[] nums, final int off, final int len,
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final float a, final float b)
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{
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int ret = off;
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for (int i = off; i < off + len; 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 float polyLineLength(float[] poly, final int off, final int nCoords) {
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assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";
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float acc = 0;
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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 float linelen(float x1, float y1, float x2, float y2) {
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final float dx = x2 - x1;
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final float dy = y2 - y1;
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return (float)Math.sqrt(dx*dx + dy*dy);
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}
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static void subdivide(float[] src, int srcoff, float[] left, int leftoff,
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float[] 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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Helpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
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break;
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case 8:
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Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
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break;
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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(float[] a, int off, int len) {
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for (int i = off + 1; i < off + len; i++) {
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float 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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// float versions of these functions, and Line2D, CubicCurve2D,
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// 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(float src[], int srcoff,
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float left[], int leftoff,
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float right[], int rightoff)
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{
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float x1 = src[srcoff + 0];
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float y1 = src[srcoff + 1];
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float ctrlx1 = src[srcoff + 2];
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float ctrly1 = src[srcoff + 3];
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float ctrlx2 = src[srcoff + 4];
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float ctrly2 = src[srcoff + 5];
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float x2 = src[srcoff + 6];
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float 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) / 2.0f;
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y1 = (y1 + ctrly1) / 2.0f;
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x2 = (x2 + ctrlx2) / 2.0f;
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y2 = (y2 + ctrly2) / 2.0f;
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float centerx = (ctrlx1 + ctrlx2) / 2.0f;
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float centery = (ctrly1 + ctrly2) / 2.0f;
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ctrlx1 = (x1 + centerx) / 2.0f;
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ctrly1 = (y1 + centery) / 2.0f;
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ctrlx2 = (x2 + centerx) / 2.0f;
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ctrly2 = (y2 + centery) / 2.0f;
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centerx = (ctrlx1 + ctrlx2) / 2.0f;
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centery = (ctrly1 + ctrly2) / 2.0f;
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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(float t, float src[], int srcoff,
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float left[], int leftoff,
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float right[], int rightoff)
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{
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float x1 = src[srcoff + 0];
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float y1 = src[srcoff + 1];
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float ctrlx1 = src[srcoff + 2];
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float ctrly1 = src[srcoff + 3];
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float ctrlx2 = src[srcoff + 4];
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float ctrly2 = src[srcoff + 5];
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float x2 = src[srcoff + 6];
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float 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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float centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
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float 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(float src[], int srcoff,
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float left[], int leftoff,
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float right[], int rightoff)
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{
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float x1 = src[srcoff + 0];
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float y1 = src[srcoff + 1];
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float ctrlx = src[srcoff + 2];
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float ctrly = src[srcoff + 3];
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float x2 = src[srcoff + 4];
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float 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) / 2.0f;
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y1 = (y1 + ctrly) / 2.0f;
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x2 = (x2 + ctrlx) / 2.0f;
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y2 = (y2 + ctrly) / 2.0f;
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ctrlx = (x1 + x2) / 2.0f;
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ctrly = (y1 + y2) / 2.0f;
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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] = ctrlx;
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left[leftoff + 5] = ctrly;
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}
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if (right != null) {
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right[rightoff + 0] = ctrlx;
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right[rightoff + 1] = ctrly;
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right[rightoff + 2] = x2;
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right[rightoff + 3] = y2;
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}
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}
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static void subdivideQuadAt(float t, float src[], int srcoff,
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float left[], int leftoff,
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float right[], int rightoff)
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{
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float x1 = src[srcoff + 0];
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float y1 = src[srcoff + 1];
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float ctrlx = src[srcoff + 2];
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float ctrly = src[srcoff + 3];
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float x2 = src[srcoff + 4];
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float 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 + t * (ctrlx - x1);
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y1 = y1 + t * (ctrly - y1);
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x2 = ctrlx + t * (x2 - ctrlx);
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y2 = ctrly + t * (y2 - ctrly);
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ctrlx = x1 + t * (x2 - x1);
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ctrly = y1 + t * (y2 - y1);
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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] = ctrlx;
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left[leftoff + 5] = ctrly;
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}
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if (right != null) {
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right[rightoff + 0] = ctrlx;
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right[rightoff + 1] = ctrly;
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right[rightoff + 2] = x2;
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right[rightoff + 3] = y2;
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}
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}
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static void subdivideAt(float t, float src[], int srcoff,
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float left[], int leftoff,
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float right[], int rightoff, int size)
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{
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switch(size) {
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case 8:
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subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
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break;
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case 6:
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subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
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break;
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}
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}
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} |