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385ad9e160
Clipping implemented in Dasher (curve subdivision at clip edges) + higher quality(curve, subpixels) + new path simplifier Reviewed-by: prr, serb
265 lines
10 KiB
Java
265 lines
10 KiB
Java
/*
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* Copyright (c) 2007, 2018, 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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final class DCurve {
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double ax, ay, bx, by, cx, cy, dx, dy;
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double dax, day, dbx, dby;
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DCurve() {
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}
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void set(final double[] points, final int type) {
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// if instead of switch (perf + most probable cases first)
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if (type == 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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} else if (type == 4) {
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set(points[0], points[1],
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points[2], points[3]);
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} else {
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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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}
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}
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void set(final double x1, final double y1,
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final double x2, final double y2,
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final double x3, final double y3,
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final double x4, final double y4)
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{
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final double dx32 = 3.0d * (x3 - x2);
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final double dy32 = 3.0d * (y3 - y2);
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final double dx21 = 3.0d * (x2 - x1);
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final double dy21 = 3.0d * (y2 - y1);
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ax = (x4 - x1) - dx32; // A = P3 - P0 - 3 (P2 - P1) = (P3 - P0) + 3 (P1 - P2)
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ay = (y4 - y1) - dy32;
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bx = (dx32 - dx21); // B = 3 (P2 - P1) - 3(P1 - P0) = 3 (P2 + P0) - 6 P1
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by = (dy32 - dy21);
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cx = dx21; // C = 3 (P1 - P0)
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cy = dy21;
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dx = x1; // D = P0
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dy = y1;
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dax = 3.0d * ax;
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day = 3.0d * ay;
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dbx = 2.0d * bx;
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dby = 2.0d * by;
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}
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void set(final double x1, final double y1,
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final double x2, final double y2,
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final double x3, final double y3)
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{
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final double dx21 = (x2 - x1);
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final double dy21 = (y2 - y1);
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ax = 0.0d; // A = 0
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ay = 0.0d;
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bx = (x3 - x2) - dx21; // B = P3 - P0 - 2 P2
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by = (y3 - y2) - dy21;
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cx = 2.0d * dx21; // C = 2 (P2 - P1)
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cy = 2.0d * dy21;
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dx = x1; // D = P1
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dy = y1;
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dax = 0.0d;
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day = 0.0d;
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dbx = 2.0d * bx;
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dby = 2.0d * by;
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}
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void set(final double x1, final double y1,
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final double x2, final double y2)
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{
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final double dx21 = (x2 - x1);
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final double dy21 = (y2 - y1);
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ax = 0.0d; // A = 0
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ay = 0.0d;
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bx = 0.0d; // B = 0
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by = 0.0d;
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cx = dx21; // C = (P2 - P1)
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cy = dy21;
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dx = x1; // D = P1
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dy = y1;
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dax = 0.0d;
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day = 0.0d;
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dbx = 0.0d;
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dby = 0.0d;
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}
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int dxRoots(final double[] roots, final int off) {
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return DHelpers.quadraticRoots(dax, dbx, cx, roots, off);
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}
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int dyRoots(final double[] roots, final int off) {
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return DHelpers.quadraticRoots(day, dby, cy, roots, off);
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}
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int infPoints(final double[] pts, final 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 double a = dax * dby - dbx * day;
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final double b = 2.0d * (cy * dax - day * cx);
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final double c = cy * dbx - cx * dby;
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return DHelpers.quadraticRoots(a, b, c, pts, off);
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}
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int xPoints(final double[] ts, final int off, final double x)
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{
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return DHelpers.cubicRootsInAB(ax, bx, cx, dx - x, ts, off, 0.0d, 1.0d);
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}
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int yPoints(final double[] ts, final int off, final double y)
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{
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return DHelpers.cubicRootsInAB(ay, by, cy, dy - y, ts, off, 0.0d, 1.0d);
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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(final double[] pts, final 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 double a = 2.0d * (dax * dax + day * day);
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final double b = 3.0d * (dax * dbx + day * dby);
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final double c = 2.0d * (dax * cx + day * cy) + dbx * dbx + dby * dby;
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final double d = dbx * cx + dby * cy;
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return DHelpers.cubicRootsInAB(a, b, c, d, pts, off, 0.0d, 1.0d);
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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(final double[] roots, final int off, final double w2, final double 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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final int end = off + perpendiculardfddf(roots, off);
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roots[end] = 1.0d; // always check interval end points
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double t0 = 0.0d, ft0 = ROCsq(t0) - w2;
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for (int i = off; i <= end; i++) {
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double t1 = roots[i], ft1 = ROCsq(t1) - w2;
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if (ft0 == 0.0d) {
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roots[ret++] = t0;
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} else if (ft1 * ft0 < 0.0d) { // 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, w2, 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 double eliminateInf(final double x) {
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return (x == Double.POSITIVE_INFINITY ? Double.MAX_VALUE :
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(x == Double.NEGATIVE_INFINITY ? Double.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 DHelpers.java
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private double falsePositionROCsqMinusX(final double t0, final double t1,
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final double w2, final double err)
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{
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final int iterLimit = 100;
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int side = 0;
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double t = t1, ft = eliminateInf(ROCsq(t) - w2);
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double s = t0, fs = eliminateInf(ROCsq(s) - w2);
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double 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) - w2;
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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 > 0.0d) {
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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(final double x, final double 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 < 0.0d && y < 0.0d) || (x > 0.0d && y > 0.0d);
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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 double ROCsq(final double t) {
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final double dx = t * (t * dax + dbx) + cx;
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final double dy = t * (t * day + dby) + cy;
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final double ddx = 2.0d * dax * t + dbx;
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final double ddy = 2.0d * day * t + dby;
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final double dx2dy2 = dx * dx + dy * dy;
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final double ddx2ddy2 = ddx * ddx + ddy * ddy;
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final double 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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}
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