--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/jdk/src/java.desktop/share/classes/sun/java2d/marlin/DHelpers.java Wed May 17 22:05:11 2017 +0200
@@ -0,0 +1,436 @@
+/*
+ * Copyright (c) 2007, 2017, 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;
+
+import static java.lang.Math.PI;
+import static java.lang.Math.cos;
+import static java.lang.Math.sqrt;
+import static java.lang.Math.cbrt;
+import static java.lang.Math.acos;
+
+final class DHelpers implements MarlinConst {
+
+ private DHelpers() {
+ throw new Error("This is a non instantiable class");
+ }
+
+ static boolean within(final double x, final double y, final double err) {
+ final double d = y - x;
+ return (d <= err && d >= -err);
+ }
+
+ static int quadraticRoots(final double a, final double b,
+ final double c, double[] zeroes, final int off)
+ {
+ int ret = off;
+ double t;
+ if (a != 0.0d) {
+ final double dis = b*b - 4*a*c;
+ if (dis > 0.0d) {
+ final double sqrtDis = Math.sqrt(dis);
+ // depending on the sign of b we use a slightly different
+ // algorithm than the traditional one to find one of the roots
+ // so we can avoid adding numbers of different signs (which
+ // might result in loss of precision).
+ if (b >= 0.0d) {
+ zeroes[ret++] = (2.0d * c) / (-b - sqrtDis);
+ zeroes[ret++] = (-b - sqrtDis) / (2.0d * a);
+ } else {
+ zeroes[ret++] = (-b + sqrtDis) / (2.0d * a);
+ zeroes[ret++] = (2.0d * c) / (-b + sqrtDis);
+ }
+ } else if (dis == 0.0d) {
+ t = (-b) / (2.0d * a);
+ zeroes[ret++] = t;
+ }
+ } else {
+ if (b != 0.0d) {
+ t = (-c) / b;
+ zeroes[ret++] = t;
+ }
+ }
+ return ret - off;
+ }
+
+ // find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
+ static int cubicRootsInAB(double d, double a, double b, double c,
+ double[] pts, final int off,
+ final double A, final double B)
+ {
+ if (d == 0.0d) {
+ int num = quadraticRoots(a, b, c, pts, off);
+ return filterOutNotInAB(pts, off, num, A, B) - off;
+ }
+ // From Graphics Gems:
+ // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
+ // (also from awt.geom.CubicCurve2D. But here we don't need as
+ // much accuracy and we don't want to create arrays so we use
+ // our own customized version).
+
+ // normal form: x^3 + ax^2 + bx + c = 0
+ a /= d;
+ b /= d;
+ c /= d;
+
+ // substitute x = y - A/3 to eliminate quadratic term:
+ // x^3 +Px + Q = 0
+ //
+ // Since we actually need P/3 and Q/2 for all of the
+ // calculations that follow, we will calculate
+ // p = P/3
+ // q = Q/2
+ // instead and use those values for simplicity of the code.
+ double sq_A = a * a;
+ double p = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
+ double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * a * b + c);
+
+ // use Cardano's formula
+
+ double cb_p = p * p * p;
+ double D = q * q + cb_p;
+
+ int num;
+ if (D < 0.0d) {
+ // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
+ final double phi = (1.0d/3.0d) * acos(-q / sqrt(-cb_p));
+ final double t = 2.0d * sqrt(-p);
+
+ pts[ off+0 ] = ( t * cos(phi));
+ pts[ off+1 ] = (-t * cos(phi + (PI / 3.0d)));
+ pts[ off+2 ] = (-t * cos(phi - (PI / 3.0d)));
+ num = 3;
+ } else {
+ final double sqrt_D = sqrt(D);
+ final double u = cbrt(sqrt_D - q);
+ final double v = - cbrt(sqrt_D + q);
+
+ pts[ off ] = (u + v);
+ num = 1;
+
+ if (within(D, 0.0d, 1e-8d)) {
+ pts[off+1] = -(pts[off] / 2.0d);
+ num = 2;
+ }
+ }
+
+ final double sub = (1.0d/3.0d) * a;
+
+ for (int i = 0; i < num; ++i) {
+ pts[ off+i ] -= sub;
+ }
+
+ return filterOutNotInAB(pts, off, num, A, B) - off;
+ }
+
+ static double evalCubic(final double a, final double b,
+ final double c, final double d,
+ final double t)
+ {
+ return t * (t * (t * a + b) + c) + d;
+ }
+
+ static double evalQuad(final double a, final double b,
+ final double c, final double t)
+ {
+ return t * (t * a + b) + c;
+ }
+
+ // returns the index 1 past the last valid element remaining after filtering
+ static int filterOutNotInAB(double[] nums, final int off, final int len,
+ final double a, final double b)
+ {
+ int ret = off;
+ for (int i = off, end = off + len; i < end; i++) {
+ if (nums[i] >= a && nums[i] < b) {
+ nums[ret++] = nums[i];
+ }
+ }
+ return ret;
+ }
+
+ static double polyLineLength(double[] poly, final int off, final int nCoords) {
+ assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";
+ double acc = 0.0d;
+ for (int i = off + 2; i < off + nCoords; i += 2) {
+ acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]);
+ }
+ return acc;
+ }
+
+ static double linelen(double x1, double y1, double x2, double y2) {
+ final double dx = x2 - x1;
+ final double dy = y2 - y1;
+ return Math.sqrt(dx*dx + dy*dy);
+ }
+
+ static void subdivide(double[] src, int srcoff, double[] left, int leftoff,
+ double[] right, int rightoff, int type)
+ {
+ switch(type) {
+ case 6:
+ DHelpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
+ return;
+ case 8:
+ DHelpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
+ return;
+ default:
+ throw new InternalError("Unsupported curve type");
+ }
+ }
+
+ static void isort(double[] a, int off, int len) {
+ for (int i = off + 1, end = off + len; i < end; i++) {
+ double ai = a[i];
+ int j = i - 1;
+ for (; j >= off && a[j] > ai; j--) {
+ a[j+1] = a[j];
+ }
+ a[j+1] = ai;
+ }
+ }
+
+ // Most of these are copied from classes in java.awt.geom because we need
+ // both single and double precision variants of these functions, and Line2D,
+ // CubicCurve2D, QuadCurve2D don't provide them.
+ /**
+ * Subdivides the cubic curve specified by the coordinates
+ * stored in the <code>src</code> array at indices <code>srcoff</code>
+ * through (<code>srcoff</code> + 7) and stores the
+ * resulting two subdivided curves into the two result arrays at the
+ * corresponding indices.
+ * Either or both of the <code>left</code> and <code>right</code>
+ * arrays may be <code>null</code> or a reference to the same array
+ * as the <code>src</code> array.
+ * Note that the last point in the first subdivided curve is the
+ * same as the first point in the second subdivided curve. Thus,
+ * it is possible to pass the same array for <code>left</code>
+ * and <code>right</code> and to use offsets, such as <code>rightoff</code>
+ * equals (<code>leftoff</code> + 6), in order
+ * to avoid allocating extra storage for this common point.
+ * @param src the array holding the coordinates for the source curve
+ * @param srcoff the offset into the array of the beginning of the
+ * the 6 source coordinates
+ * @param left the array for storing the coordinates for the first
+ * half of the subdivided curve
+ * @param leftoff the offset into the array of the beginning of the
+ * the 6 left coordinates
+ * @param right the array for storing the coordinates for the second
+ * half of the subdivided curve
+ * @param rightoff the offset into the array of the beginning of the
+ * the 6 right coordinates
+ * @since 1.7
+ */
+ static void subdivideCubic(double[] src, int srcoff,
+ double[] left, int leftoff,
+ double[] right, int rightoff)
+ {
+ double x1 = src[srcoff + 0];
+ double y1 = src[srcoff + 1];
+ double ctrlx1 = src[srcoff + 2];
+ double ctrly1 = src[srcoff + 3];
+ double ctrlx2 = src[srcoff + 4];
+ double ctrly2 = src[srcoff + 5];
+ double x2 = src[srcoff + 6];
+ double y2 = src[srcoff + 7];
+ if (left != null) {
+ left[leftoff + 0] = x1;
+ left[leftoff + 1] = y1;
+ }
+ if (right != null) {
+ right[rightoff + 6] = x2;
+ right[rightoff + 7] = y2;
+ }
+ x1 = (x1 + ctrlx1) / 2.0d;
+ y1 = (y1 + ctrly1) / 2.0d;
+ x2 = (x2 + ctrlx2) / 2.0d;
+ y2 = (y2 + ctrly2) / 2.0d;
+ double centerx = (ctrlx1 + ctrlx2) / 2.0d;
+ double centery = (ctrly1 + ctrly2) / 2.0d;
+ ctrlx1 = (x1 + centerx) / 2.0d;
+ ctrly1 = (y1 + centery) / 2.0d;
+ ctrlx2 = (x2 + centerx) / 2.0d;
+ ctrly2 = (y2 + centery) / 2.0d;
+ centerx = (ctrlx1 + ctrlx2) / 2.0d;
+ centery = (ctrly1 + ctrly2) / 2.0d;
+ if (left != null) {
+ left[leftoff + 2] = x1;
+ left[leftoff + 3] = y1;
+ left[leftoff + 4] = ctrlx1;
+ left[leftoff + 5] = ctrly1;
+ left[leftoff + 6] = centerx;
+ left[leftoff + 7] = centery;
+ }
+ if (right != null) {
+ right[rightoff + 0] = centerx;
+ right[rightoff + 1] = centery;
+ right[rightoff + 2] = ctrlx2;
+ right[rightoff + 3] = ctrly2;
+ right[rightoff + 4] = x2;
+ right[rightoff + 5] = y2;
+ }
+ }
+
+
+ static void subdivideCubicAt(double t, double[] src, int srcoff,
+ double[] left, int leftoff,
+ double[] right, int rightoff)
+ {
+ double x1 = src[srcoff + 0];
+ double y1 = src[srcoff + 1];
+ double ctrlx1 = src[srcoff + 2];
+ double ctrly1 = src[srcoff + 3];
+ double ctrlx2 = src[srcoff + 4];
+ double ctrly2 = src[srcoff + 5];
+ double x2 = src[srcoff + 6];
+ double y2 = src[srcoff + 7];
+ if (left != null) {
+ left[leftoff + 0] = x1;
+ left[leftoff + 1] = y1;
+ }
+ if (right != null) {
+ right[rightoff + 6] = x2;
+ right[rightoff + 7] = y2;
+ }
+ x1 = x1 + t * (ctrlx1 - x1);
+ y1 = y1 + t * (ctrly1 - y1);
+ x2 = ctrlx2 + t * (x2 - ctrlx2);
+ y2 = ctrly2 + t * (y2 - ctrly2);
+ double centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
+ double centery = ctrly1 + t * (ctrly2 - ctrly1);
+ ctrlx1 = x1 + t * (centerx - x1);
+ ctrly1 = y1 + t * (centery - y1);
+ ctrlx2 = centerx + t * (x2 - centerx);
+ ctrly2 = centery + t * (y2 - centery);
+ centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
+ centery = ctrly1 + t * (ctrly2 - ctrly1);
+ if (left != null) {
+ left[leftoff + 2] = x1;
+ left[leftoff + 3] = y1;
+ left[leftoff + 4] = ctrlx1;
+ left[leftoff + 5] = ctrly1;
+ left[leftoff + 6] = centerx;
+ left[leftoff + 7] = centery;
+ }
+ if (right != null) {
+ right[rightoff + 0] = centerx;
+ right[rightoff + 1] = centery;
+ right[rightoff + 2] = ctrlx2;
+ right[rightoff + 3] = ctrly2;
+ right[rightoff + 4] = x2;
+ right[rightoff + 5] = y2;
+ }
+ }
+
+ static void subdivideQuad(double[] src, int srcoff,
+ double[] left, int leftoff,
+ double[] right, int rightoff)
+ {
+ double x1 = src[srcoff + 0];
+ double y1 = src[srcoff + 1];
+ double ctrlx = src[srcoff + 2];
+ double ctrly = src[srcoff + 3];
+ double x2 = src[srcoff + 4];
+ double y2 = src[srcoff + 5];
+ if (left != null) {
+ left[leftoff + 0] = x1;
+ left[leftoff + 1] = y1;
+ }
+ if (right != null) {
+ right[rightoff + 4] = x2;
+ right[rightoff + 5] = y2;
+ }
+ x1 = (x1 + ctrlx) / 2.0d;
+ y1 = (y1 + ctrly) / 2.0d;
+ x2 = (x2 + ctrlx) / 2.0d;
+ y2 = (y2 + ctrly) / 2.0d;
+ ctrlx = (x1 + x2) / 2.0d;
+ ctrly = (y1 + y2) / 2.0d;
+ if (left != null) {
+ left[leftoff + 2] = x1;
+ left[leftoff + 3] = y1;
+ left[leftoff + 4] = ctrlx;
+ left[leftoff + 5] = ctrly;
+ }
+ if (right != null) {
+ right[rightoff + 0] = ctrlx;
+ right[rightoff + 1] = ctrly;
+ right[rightoff + 2] = x2;
+ right[rightoff + 3] = y2;
+ }
+ }
+
+ static void subdivideQuadAt(double t, double[] src, int srcoff,
+ double[] left, int leftoff,
+ double[] right, int rightoff)
+ {
+ double x1 = src[srcoff + 0];
+ double y1 = src[srcoff + 1];
+ double ctrlx = src[srcoff + 2];
+ double ctrly = src[srcoff + 3];
+ double x2 = src[srcoff + 4];
+ double y2 = src[srcoff + 5];
+ if (left != null) {
+ left[leftoff + 0] = x1;
+ left[leftoff + 1] = y1;
+ }
+ if (right != null) {
+ right[rightoff + 4] = x2;
+ right[rightoff + 5] = y2;
+ }
+ x1 = x1 + t * (ctrlx - x1);
+ y1 = y1 + t * (ctrly - y1);
+ x2 = ctrlx + t * (x2 - ctrlx);
+ y2 = ctrly + t * (y2 - ctrly);
+ ctrlx = x1 + t * (x2 - x1);
+ ctrly = y1 + t * (y2 - y1);
+ if (left != null) {
+ left[leftoff + 2] = x1;
+ left[leftoff + 3] = y1;
+ left[leftoff + 4] = ctrlx;
+ left[leftoff + 5] = ctrly;
+ }
+ if (right != null) {
+ right[rightoff + 0] = ctrlx;
+ right[rightoff + 1] = ctrly;
+ right[rightoff + 2] = x2;
+ right[rightoff + 3] = y2;
+ }
+ }
+
+ static void subdivideAt(double t, double[] src, int srcoff,
+ double[] left, int leftoff,
+ double[] right, int rightoff, int size)
+ {
+ switch(size) {
+ case 8:
+ subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
+ return;
+ case 6:
+ subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
+ return;
+ }
+ }
+}