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/*
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* Copyright (c) 2007, 2015, 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 java.util.Iterator;
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final class Curve {
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float ax, ay, bx, by, cx, cy, dx, dy;
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float dax, day, dbx, dby;
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// shared iterator instance
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private final BreakPtrIterator iterator = new BreakPtrIterator();
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Curve() {
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}
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void set(float[] points, int type) {
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switch(type) {
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case 8:
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set(points[0], points[1],
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points[2], points[3],
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points[4], points[5],
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points[6], points[7]);
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return;
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case 6:
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set(points[0], points[1],
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points[2], points[3],
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points[4], points[5]);
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return;
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default:
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throw new InternalError("Curves can only be cubic or quadratic");
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}
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}
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void set(float x1, float y1,
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float x2, float y2,
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float x3, float y3,
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float x4, float y4)
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{
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ax = 3f * (x2 - x3) + x4 - x1;
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ay = 3f * (y2 - y3) + y4 - y1;
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bx = 3f * (x1 - 2f * x2 + x3);
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by = 3f * (y1 - 2f * y2 + y3);
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cx = 3f * (x2 - x1);
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cy = 3f * (y2 - y1);
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dx = x1;
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dy = y1;
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dax = 3f * ax; day = 3f * ay;
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dbx = 2f * bx; dby = 2f * by;
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}
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void set(float x1, float y1,
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float x2, float y2,
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float x3, float y3)
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{
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ax = 0f; ay = 0f;
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bx = x1 - 2f * x2 + x3;
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by = y1 - 2f * y2 + y3;
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cx = 2f * (x2 - x1);
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cy = 2f * (y2 - y1);
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dx = x1;
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dy = y1;
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dax = 0f; day = 0f;
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dbx = 2f * bx; dby = 2f * by;
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}
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float xat(float t) {
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return t * (t * (t * ax + bx) + cx) + dx;
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}
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float yat(float t) {
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return t * (t * (t * ay + by) + cy) + dy;
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}
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float dxat(float t) {
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return t * (t * dax + dbx) + cx;
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}
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float dyat(float t) {
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return t * (t * day + dby) + cy;
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}
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int dxRoots(float[] roots, int off) {
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return Helpers.quadraticRoots(dax, dbx, cx, roots, off);
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}
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int dyRoots(float[] roots, int off) {
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return Helpers.quadraticRoots(day, dby, cy, roots, off);
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}
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int infPoints(float[] pts, int off) {
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// inflection point at t if -f'(t)x*f''(t)y + f'(t)y*f''(t)x == 0
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// Fortunately, this turns out to be quadratic, so there are at
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// most 2 inflection points.
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final float a = dax * dby - dbx * day;
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final float b = 2f * (cy * dax - day * cx);
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final float c = cy * dbx - cx * dby;
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return Helpers.quadraticRoots(a, b, c, pts, off);
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}
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// finds points where the first and second derivative are
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// perpendicular. This happens when g(t) = f'(t)*f''(t) == 0 (where
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// * is a dot product). Unfortunately, we have to solve a cubic.
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private int perpendiculardfddf(float[] pts, int off) {
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assert pts.length >= off + 4;
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// these are the coefficients of some multiple of g(t) (not g(t),
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// because the roots of a polynomial are not changed after multiplication
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// by a constant, and this way we save a few multiplications).
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final float a = 2f * (dax*dax + day*day);
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final float b = 3f * (dax*dbx + day*dby);
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final float c = 2f * (dax*cx + day*cy) + dbx*dbx + dby*dby;
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final float d = dbx*cx + dby*cy;
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return Helpers.cubicRootsInAB(a, b, c, d, pts, off, 0f, 1f);
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}
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// Tries to find the roots of the function ROC(t)-w in [0, 1). It uses
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// a variant of the false position algorithm to find the roots. False
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// position requires that 2 initial values x0,x1 be given, and that the
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// function must have opposite signs at those values. To find such
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// values, we need the local extrema of the ROC function, for which we
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// need the roots of its derivative; however, it's harder to find the
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// roots of the derivative in this case than it is to find the roots
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// of the original function. So, we find all points where this curve's
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// first and second derivative are perpendicular, and we pretend these
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// are our local extrema. There are at most 3 of these, so we will check
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// at most 4 sub-intervals of (0,1). ROC has asymptotes at inflection
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// points, so roc-w can have at least 6 roots. This shouldn't be a
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// problem for what we're trying to do (draw a nice looking curve).
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int rootsOfROCMinusW(float[] roots, int off, final float w, final float err) {
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// no OOB exception, because by now off<=6, and roots.length >= 10
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assert off <= 6 && roots.length >= 10;
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int ret = off;
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int numPerpdfddf = perpendiculardfddf(roots, off);
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float t0 = 0, ft0 = ROCsq(t0) - w*w;
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roots[off + numPerpdfddf] = 1f; // always check interval end points
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numPerpdfddf++;
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for (int i = off; i < off + numPerpdfddf; i++) {
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float t1 = roots[i], ft1 = ROCsq(t1) - w*w;
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if (ft0 == 0f) {
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roots[ret++] = t0;
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} else if (ft1 * ft0 < 0f) { // have opposite signs
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// (ROC(t)^2 == w^2) == (ROC(t) == w) is true because
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// ROC(t) >= 0 for all t.
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roots[ret++] = falsePositionROCsqMinusX(t0, t1, w*w, err);
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}
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t0 = t1;
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ft0 = ft1;
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}
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return ret - off;
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}
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private static float eliminateInf(float x) {
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return (x == Float.POSITIVE_INFINITY ? Float.MAX_VALUE :
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(x == Float.NEGATIVE_INFINITY ? Float.MIN_VALUE : x));
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}
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// A slight modification of the false position algorithm on wikipedia.
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// This only works for the ROCsq-x functions. It might be nice to have
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// the function as an argument, but that would be awkward in java6.
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// TODO: It is something to consider for java8 (or whenever lambda
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// expressions make it into the language), depending on how closures
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// and turn out. Same goes for the newton's method
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// algorithm in Helpers.java
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private float falsePositionROCsqMinusX(float x0, float x1,
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final float x, final float err)
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{
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final int iterLimit = 100;
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int side = 0;
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float t = x1, ft = eliminateInf(ROCsq(t) - x);
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float s = x0, fs = eliminateInf(ROCsq(s) - x);
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float r = s, fr;
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for (int i = 0; i < iterLimit && Math.abs(t - s) > err * Math.abs(t + s); i++) {
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r = (fs * t - ft * s) / (fs - ft);
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fr = ROCsq(r) - x;
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if (sameSign(fr, ft)) {
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ft = fr; t = r;
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if (side < 0) {
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fs /= (1 << (-side));
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side--;
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} else {
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side = -1;
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}
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} else if (fr * fs > 0) {
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fs = fr; s = r;
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if (side > 0) {
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ft /= (1 << side);
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side++;
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} else {
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side = 1;
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}
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} else {
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break;
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}
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}
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return r;
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}
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private static boolean sameSign(float x, float y) {
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// another way is to test if x*y > 0. This is bad for small x, y.
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return (x < 0f && y < 0f) || (x > 0f && y > 0f);
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}
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// returns the radius of curvature squared at t of this curve
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// see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)
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private float ROCsq(final float t) {
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// dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency
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final float dx = t * (t * dax + dbx) + cx;
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final float dy = t * (t * day + dby) + cy;
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final float ddx = 2f * dax * t + dbx;
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final float ddy = 2f * day * t + dby;
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final float dx2dy2 = dx*dx + dy*dy;
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final float ddx2ddy2 = ddx*ddx + ddy*ddy;
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final float ddxdxddydy = ddx*dx + ddy*dy;
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return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy));
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}
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// curve to be broken should be in pts
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// this will change the contents of pts but not Ts
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// TODO: There's no reason for Ts to be an array. All we need is a sequence
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// of t values at which to subdivide. An array statisfies this condition,
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// but is unnecessarily restrictive. Ts should be an Iterator<Float> instead.
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// Doing this will also make dashing easier, since we could easily make
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// LengthIterator an Iterator<Float> and feed it to this function to simplify
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// the loop in Dasher.somethingTo.
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BreakPtrIterator breakPtsAtTs(final float[] pts, final int type,
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final float[] Ts, final int numTs)
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{
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assert pts.length >= 2*type && numTs <= Ts.length;
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// initialize shared iterator:
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iterator.init(pts, type, Ts, numTs);
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return iterator;
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}
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static final class BreakPtrIterator {
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private int nextCurveIdx;
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private int curCurveOff;
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private float prevT;
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private float[] pts;
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private int type;
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private float[] ts;
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private int numTs;
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void init(final float[] pts, final int type,
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final float[] ts, final int numTs) {
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this.pts = pts;
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this.type = type;
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this.ts = ts;
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this.numTs = numTs;
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nextCurveIdx = 0;
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curCurveOff = 0;
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prevT = 0f;
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}
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public boolean hasNext() {
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return nextCurveIdx <= numTs;
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}
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public int next() {
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int ret;
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if (nextCurveIdx < numTs) {
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float curT = ts[nextCurveIdx];
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float splitT = (curT - prevT) / (1f - prevT);
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Helpers.subdivideAt(splitT,
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pts, curCurveOff,
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pts, 0,
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pts, type, type);
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prevT = curT;
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ret = 0;
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curCurveOff = type;
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} else {
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ret = curCurveOff;
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}
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nextCurveIdx++;
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return ret;
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}
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}
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}
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