--- /dev/null 2017-04-22 10:40:35.471249043 +0200 +++ new/src/java.desktop/share/classes/sun/java2d/marlin/DCurve.java 2017-04-22 13:16:10.524585914 +0200 @@ -0,0 +1,237 @@ +/* + * Copyright (c) 2007, 2016, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. Oracle designates this + * particular file as subject to the "Classpath" exception as provided + * by Oracle in the LICENSE file that accompanied this code. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package sun.java2d.marlin; + +final class DCurve { + + double ax, ay, bx, by, cx, cy, dx, dy; + double dax, day, dbx, dby; + + DCurve() { + } + + void set(double[] points, int type) { + switch(type) { + case 8: + set(points[0], points[1], + points[2], points[3], + points[4], points[5], + points[6], points[7]); + return; + case 6: + set(points[0], points[1], + points[2], points[3], + points[4], points[5]); + return; + default: + throw new InternalError("Curves can only be cubic or quadratic"); + } + } + + void set(double x1, double y1, + double x2, double y2, + double x3, double y3, + double x4, double y4) + { + ax = 3.0d * (x2 - x3) + x4 - x1; + ay = 3.0d * (y2 - y3) + y4 - y1; + bx = 3.0d * (x1 - 2.0d * x2 + x3); + by = 3.0d * (y1 - 2.0d * y2 + y3); + cx = 3.0d * (x2 - x1); + cy = 3.0d * (y2 - y1); + dx = x1; + dy = y1; + dax = 3.0d * ax; day = 3.0d * ay; + dbx = 2.0d * bx; dby = 2.0d * by; + } + + void set(double x1, double y1, + double x2, double y2, + double x3, double y3) + { + ax = 0.0d; ay = 0.0d; + bx = x1 - 2.0d * x2 + x3; + by = y1 - 2.0d * y2 + y3; + cx = 2.0d * (x2 - x1); + cy = 2.0d * (y2 - y1); + dx = x1; + dy = y1; + dax = 0.0d; day = 0.0d; + dbx = 2.0d * bx; dby = 2.0d * by; + } + + double xat(double t) { + return t * (t * (t * ax + bx) + cx) + dx; + } + double yat(double t) { + return t * (t * (t * ay + by) + cy) + dy; + } + + double dxat(double t) { + return t * (t * dax + dbx) + cx; + } + + double dyat(double t) { + return t * (t * day + dby) + cy; + } + + int dxRoots(double[] roots, int off) { + return DHelpers.quadraticRoots(dax, dbx, cx, roots, off); + } + + int dyRoots(double[] roots, int off) { + return DHelpers.quadraticRoots(day, dby, cy, roots, off); + } + + int infPoints(double[] pts, int off) { + // inflection point at t if -f'(t)x*f''(t)y + f'(t)y*f''(t)x == 0 + // Fortunately, this turns out to be quadratic, so there are at + // most 2 inflection points. + final double a = dax * dby - dbx * day; + final double b = 2.0d * (cy * dax - day * cx); + final double c = cy * dbx - cx * dby; + + return DHelpers.quadraticRoots(a, b, c, pts, off); + } + + // finds points where the first and second derivative are + // perpendicular. This happens when g(t) = f'(t)*f''(t) == 0 (where + // * is a dot product). Unfortunately, we have to solve a cubic. + private int perpendiculardfddf(double[] pts, int off) { + assert pts.length >= off + 4; + + // these are the coefficients of some multiple of g(t) (not g(t), + // because the roots of a polynomial are not changed after multiplication + // by a constant, and this way we save a few multiplications). + final double a = 2.0d * (dax*dax + day*day); + final double b = 3.0d * (dax*dbx + day*dby); + final double c = 2.0d * (dax*cx + day*cy) + dbx*dbx + dby*dby; + final double d = dbx*cx + dby*cy; + return DHelpers.cubicRootsInAB(a, b, c, d, pts, off, 0.0d, 1.0d); + } + + // Tries to find the roots of the function ROC(t)-w in [0, 1). It uses + // a variant of the false position algorithm to find the roots. False + // position requires that 2 initial values x0,x1 be given, and that the + // function must have opposite signs at those values. To find such + // values, we need the local extrema of the ROC function, for which we + // need the roots of its derivative; however, it's harder to find the + // roots of the derivative in this case than it is to find the roots + // of the original function. So, we find all points where this curve's + // first and second derivative are perpendicular, and we pretend these + // are our local extrema. There are at most 3 of these, so we will check + // at most 4 sub-intervals of (0,1). ROC has asymptotes at inflection + // points, so roc-w can have at least 6 roots. This shouldn't be a + // problem for what we're trying to do (draw a nice looking curve). + int rootsOfROCMinusW(double[] roots, int off, final double w, final double err) { + // no OOB exception, because by now off<=6, and roots.length >= 10 + assert off <= 6 && roots.length >= 10; + int ret = off; + int numPerpdfddf = perpendiculardfddf(roots, off); + double t0 = 0.0d, ft0 = ROCsq(t0) - w*w; + roots[off + numPerpdfddf] = 1.0d; // always check interval end points + numPerpdfddf++; + for (int i = off; i < off + numPerpdfddf; i++) { + double t1 = roots[i], ft1 = ROCsq(t1) - w*w; + if (ft0 == 0.0d) { + roots[ret++] = t0; + } else if (ft1 * ft0 < 0.0d) { // have opposite signs + // (ROC(t)^2 == w^2) == (ROC(t) == w) is true because + // ROC(t) >= 0 for all t. + roots[ret++] = falsePositionROCsqMinusX(t0, t1, w*w, err); + } + t0 = t1; + ft0 = ft1; + } + + return ret - off; + } + + private static double eliminateInf(double x) { + return (x == Double.POSITIVE_INFINITY ? Double.MAX_VALUE : + (x == Double.NEGATIVE_INFINITY ? Double.MIN_VALUE : x)); + } + + // A slight modification of the false position algorithm on wikipedia. + // This only works for the ROCsq-x functions. It might be nice to have + // the function as an argument, but that would be awkward in java6. + // TODO: It is something to consider for java8 (or whenever lambda + // expressions make it into the language), depending on how closures + // and turn out. Same goes for the newton's method + // algorithm in DHelpers.java + private double falsePositionROCsqMinusX(double x0, double x1, + final double x, final double err) + { + final int iterLimit = 100; + int side = 0; + double t = x1, ft = eliminateInf(ROCsq(t) - x); + double s = x0, fs = eliminateInf(ROCsq(s) - x); + double r = s, fr; + for (int i = 0; i < iterLimit && Math.abs(t - s) > err * Math.abs(t + s); i++) { + r = (fs * t - ft * s) / (fs - ft); + fr = ROCsq(r) - x; + if (sameSign(fr, ft)) { + ft = fr; t = r; + if (side < 0) { + fs /= (1 << (-side)); + side--; + } else { + side = -1; + } + } else if (fr * fs > 0) { + fs = fr; s = r; + if (side > 0) { + ft /= (1 << side); + side++; + } else { + side = 1; + } + } else { + break; + } + } + return r; + } + + private static boolean sameSign(double x, double y) { + // another way is to test if x*y > 0. This is bad for small x, y. + return (x < 0.0d && y < 0.0d) || (x > 0.0d && y > 0.0d); + } + + // returns the radius of curvature squared at t of this curve + // see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications) + private double ROCsq(final double t) { + // dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency + final double dx = t * (t * dax + dbx) + cx; + final double dy = t * (t * day + dby) + cy; + final double ddx = 2.0d * dax * t + dbx; + final double ddy = 2.0d * day * t + dby; + final double dx2dy2 = dx*dx + dy*dy; + final double ddx2ddy2 = ddx*ddx + ddy*ddy; + final double ddxdxddydy = ddx*dx + ddy*dy; + return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy)); + } +}