--- a/src/java.desktop/share/classes/sun/java2d/pisces/Curve.java Tue Nov 21 12:27:45 2017 +0300
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,290 +0,0 @@
-/*
- * Copyright (c) 2007, 2011, 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.pisces;
-
-import java.util.Iterator;
-
-final class Curve {
-
- float ax, ay, bx, by, cx, cy, dx, dy;
- float dax, day, dbx, dby;
-
- Curve() {
- }
-
- void set(float[] points, int type) {
- switch(type) {
- case 8:
- set(points[0], points[1],
- points[2], points[3],
- points[4], points[5],
- points[6], points[7]);
- break;
- case 6:
- set(points[0], points[1],
- points[2], points[3],
- points[4], points[5]);
- break;
- default:
- throw new InternalError("Curves can only be cubic or quadratic");
- }
- }
-
- void set(float x1, float y1,
- float x2, float y2,
- float x3, float y3,
- float x4, float y4)
- {
- ax = 3 * (x2 - x3) + x4 - x1;
- ay = 3 * (y2 - y3) + y4 - y1;
- bx = 3 * (x1 - 2 * x2 + x3);
- by = 3 * (y1 - 2 * y2 + y3);
- cx = 3 * (x2 - x1);
- cy = 3 * (y2 - y1);
- dx = x1;
- dy = y1;
- dax = 3 * ax; day = 3 * ay;
- dbx = 2 * bx; dby = 2 * by;
- }
-
- void set(float x1, float y1,
- float x2, float y2,
- float x3, float y3)
- {
- ax = ay = 0f;
-
- bx = x1 - 2 * x2 + x3;
- by = y1 - 2 * y2 + y3;
- cx = 2 * (x2 - x1);
- cy = 2 * (y2 - y1);
- dx = x1;
- dy = y1;
- dax = 0; day = 0;
- dbx = 2 * bx; dby = 2 * by;
- }
-
- float xat(float t) {
- return t * (t * (t * ax + bx) + cx) + dx;
- }
- float yat(float t) {
- return t * (t * (t * ay + by) + cy) + dy;
- }
-
- float dxat(float t) {
- return t * (t * dax + dbx) + cx;
- }
-
- float dyat(float t) {
- return t * (t * day + dby) + cy;
- }
-
- int dxRoots(float[] roots, int off) {
- return Helpers.quadraticRoots(dax, dbx, cx, roots, off);
- }
-
- int dyRoots(float[] roots, int off) {
- return Helpers.quadraticRoots(day, dby, cy, roots, off);
- }
-
- int infPoints(float[] 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 float a = dax * dby - dbx * day;
- final float b = 2 * (cy * dax - day * cx);
- final float c = cy * dbx - cx * dby;
-
- return Helpers.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(float[] 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 float a = 2*(dax*dax + day*day);
- final float b = 3*(dax*dbx + day*dby);
- final float c = 2*(dax*cx + day*cy) + dbx*dbx + dby*dby;
- final float d = dbx*cx + dby*cy;
- return Helpers.cubicRootsInAB(a, b, c, d, pts, off, 0f, 1f);
- }
-
- // 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(float[] roots, int off, final float w, final float 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);
- float t0 = 0, ft0 = ROCsq(t0) - w*w;
- roots[off + numPerpdfddf] = 1f; // always check interval end points
- numPerpdfddf++;
- for (int i = off; i < off + numPerpdfddf; i++) {
- float t1 = roots[i], ft1 = ROCsq(t1) - w*w;
- if (ft0 == 0f) {
- roots[ret++] = t0;
- } else if (ft1 * ft0 < 0f) { // 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 float eliminateInf(float x) {
- return (x == Float.POSITIVE_INFINITY ? Float.MAX_VALUE :
- (x == Float.NEGATIVE_INFINITY ? Float.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 Helpers.java
- private float falsePositionROCsqMinusX(float x0, float x1,
- final float x, final float err)
- {
- final int iterLimit = 100;
- int side = 0;
- float t = x1, ft = eliminateInf(ROCsq(t) - x);
- float s = x0, fs = eliminateInf(ROCsq(s) - x);
- float 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 && y < 0) || (x > 0 && y > 0);
- }
-
- // returns the radius of curvature squared at t of this curve
- // see http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)
- private float ROCsq(final float t) {
- // dx=xat(t) and dy=yat(t). These calls have been inlined for efficiency
- final float dx = t * (t * dax + dbx) + cx;
- final float dy = t * (t * day + dby) + cy;
- final float ddx = 2 * dax * t + dbx;
- final float ddy = 2 * day * t + dby;
- final float dx2dy2 = dx*dx + dy*dy;
- final float ddx2ddy2 = ddx*ddx + ddy*ddy;
- final float ddxdxddydy = ddx*dx + ddy*dy;
- return dx2dy2*((dx2dy2*dx2dy2) / (dx2dy2 * ddx2ddy2 - ddxdxddydy*ddxdxddydy));
- }
-
- // curve to be broken should be in pts
- // this will change the contents of pts but not Ts
- // TODO: There's no reason for Ts to be an array. All we need is a sequence
- // of t values at which to subdivide. An array statisfies this condition,
- // but is unnecessarily restrictive. Ts should be an Iterator<Float> instead.
- // Doing this will also make dashing easier, since we could easily make
- // LengthIterator an Iterator<Float> and feed it to this function to simplify
- // the loop in Dasher.somethingTo.
- static Iterator<Integer> breakPtsAtTs(final float[] pts, final int type,
- final float[] Ts, final int numTs)
- {
- assert pts.length >= 2*type && numTs <= Ts.length;
- return new Iterator<Integer>() {
- // these prevent object creation and destruction during autoboxing.
- // Because of this, the compiler should be able to completely
- // eliminate the boxing costs.
- final Integer i0 = 0;
- final Integer itype = type;
- int nextCurveIdx = 0;
- Integer curCurveOff = i0;
- float prevT = 0;
-
- @Override public boolean hasNext() {
- return nextCurveIdx < numTs + 1;
- }
-
- @Override public Integer next() {
- Integer ret;
- if (nextCurveIdx < numTs) {
- float curT = Ts[nextCurveIdx];
- float splitT = (curT - prevT) / (1 - prevT);
- Helpers.subdivideAt(splitT,
- pts, curCurveOff,
- pts, 0,
- pts, type, type);
- prevT = curT;
- ret = i0;
- curCurveOff = itype;
- } else {
- ret = curCurveOff;
- }
- nextCurveIdx++;
- return ret;
- }
-
- @Override public void remove() {}
- };
- }
-}
-