| /* |
| * 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; |
| } |
| } |
| } |