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android / platform / external / chromium_org / third_party / skia / src / 1e314552f45eb34b41ce56a40d3abdbd6ab695fe / . / core / SkGeometry.cpp
blob: 76d3a3f4f6ccbf2255aa1bff99ca89280c98cdde [file] [log] [blame]
epoger@google.com685cfc02011-07-28 14:26:00 +0000[diff] [blame]1/*
2 * Copyright 2006 The Android Open Source Project
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]8#include "SkGeometry.h"
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]9#include "SkMatrix.h"
10
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]11bool SkXRayCrossesLine(const SkXRay& pt, const SkPoint pts[2], bool* ambiguous) {
12 if (ambiguous) {
13 *ambiguous = false;
14 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]15 // Determine quick discards.
16 // Consider query line going exactly through point 0 to not
17 // intersect, for symmetry with SkXRayCrossesMonotonicCubic.
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]18 if (pt.fY == pts[0].fY) {
19 if (ambiguous) {
20 *ambiguous = true;
21 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]22 return false;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]23 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]24 if (pt.fY < pts[0].fY && pt.fY < pts[1].fY)
25 return false;
26 if (pt.fY > pts[0].fY && pt.fY > pts[1].fY)
27 return false;
28 if (pt.fX > pts[0].fX && pt.fX > pts[1].fX)
29 return false;
30 // Determine degenerate cases
31 if (SkScalarNearlyZero(pts[0].fY - pts[1].fY))
32 return false;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]33 if (SkScalarNearlyZero(pts[0].fX - pts[1].fX)) {
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]34 // We've already determined the query point lies within the
35 // vertical range of the line segment.
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]36 if (pt.fX <= pts[0].fX) {
37 if (ambiguous) {
38 *ambiguous = (pt.fY == pts[1].fY);
39 }
40 return true;
41 }
42 return false;
43 }
44 // Ambiguity check
45 if (pt.fY == pts[1].fY) {
46 if (pt.fX <= pts[1].fX) {
47 if (ambiguous) {
48 *ambiguous = true;
49 }
50 return true;
51 }
52 return false;
53 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]54 // Full line segment evaluation
55 SkScalar delta_y = pts[1].fY - pts[0].fY;
56 SkScalar delta_x = pts[1].fX - pts[0].fX;
57 SkScalar slope = SkScalarDiv(delta_y, delta_x);
58 SkScalar b = pts[0].fY - SkScalarMul(slope, pts[0].fX);
59 // Solve for x coordinate at y = pt.fY
60 SkScalar x = SkScalarDiv(pt.fY - b, slope);
61 return pt.fX <= x;
62}
63
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]64/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes
65 involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul.
66 May also introduce overflow of fixed when we compute our setup.
67*/
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]68// #define DIRECT_EVAL_OF_POLYNOMIALS
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]69
70////////////////////////////////////////////////////////////////////////
71
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]72static int is_not_monotonic(SkScalar a, SkScalar b, SkScalar c) {
73 SkScalar ab = a - b;
74 SkScalar bc = b - c;
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]75 if (ab < 0) {
76 bc = -bc;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]77 }
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]78 return ab == 0 || bc < 0;
79}
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]80
81////////////////////////////////////////////////////////////////////////
82
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]83static bool is_unit_interval(SkScalar x) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]84 return x > 0 && x < SK_Scalar1;
85}
86
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]87static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]88 SkASSERT(ratio);
89
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]90 if (numer < 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]91 numer = -numer;
92 denom = -denom;
93 }
94
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]95 if (denom == 0 || numer == 0 || numer >= denom) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]96 return 0;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]97 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]98
99 SkScalar r = SkScalarDiv(numer, denom);
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]100 if (SkScalarIsNaN(r)) {
101 return 0;
102 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]103 SkASSERT(r >= 0 && r < SK_Scalar1);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]104 if (r == 0) { // catch underflow if numer <<<< denom
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]105 return 0;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]106 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]107 *ratio = r;
108 return 1;
109}
110
111/** From Numerical Recipes in C.
112
113 Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])
114 x1 = Q / A
115 x2 = C / Q
116*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]117int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]118 SkASSERT(roots);
119
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]120 if (A == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]121 return valid_unit_divide(-C, B, roots);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]122 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]123
124 SkScalar* r = roots;
125
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]126 SkScalar R = B*B - 4*A*C;
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]127 if (R < 0 || SkScalarIsNaN(R)) { // complex roots
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]128 return 0;
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]129 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]130 R = SkScalarSqrt(R);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]131
132 SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;
133 r += valid_unit_divide(Q, A, r);
134 r += valid_unit_divide(C, Q, r);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]135 if (r - roots == 2) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]136 if (roots[0] > roots[1])
137 SkTSwap<SkScalar>(roots[0], roots[1]);
138 else if (roots[0] == roots[1]) // nearly-equal?
139 r -= 1; // skip the double root
140 }
141 return (int)(r - roots);
142}
143
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]144///////////////////////////////////////////////////////////////////////////////
145///////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]146
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]147static SkScalar eval_quad(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]148 SkASSERT(src);
149 SkASSERT(t >= 0 && t <= SK_Scalar1);
150
151#ifdef DIRECT_EVAL_OF_POLYNOMIALS
152 SkScalar C = src[0];
153 SkScalar A = src[4] - 2 * src[2] + C;
154 SkScalar B = 2 * (src[2] - C);
155 return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
156#else
157 SkScalar ab = SkScalarInterp(src[0], src[2], t);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]158 SkScalar bc = SkScalarInterp(src[2], src[4], t);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]159 return SkScalarInterp(ab, bc, t);
160#endif
161}
162
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]163static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]164 SkScalar A = src[4] - 2 * src[2] + src[0];
165 SkScalar B = src[2] - src[0];
166
167 return 2 * SkScalarMulAdd(A, t, B);
168}
169
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]170static SkScalar eval_quad_derivative_at_half(const SkScalar src[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]171 SkScalar A = src[4] - 2 * src[2] + src[0];
172 SkScalar B = src[2] - src[0];
173 return A + 2 * B;
174}
175
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]176void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
177 SkVector* tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]178 SkASSERT(src);
179 SkASSERT(t >= 0 && t <= SK_Scalar1);
180
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]181 if (pt) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]182 pt->set(eval_quad(&src[0].fX, t), eval_quad(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]183 }
184 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]185 tangent->set(eval_quad_derivative(&src[0].fX, t),
186 eval_quad_derivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]187 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]188}
189
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]190void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]191 SkASSERT(src);
192
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]193 if (pt) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]194 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
195 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
196 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
197 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
198 pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
199 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]200 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]201 tangent->set(eval_quad_derivative_at_half(&src[0].fX),
202 eval_quad_derivative_at_half(&src[0].fY));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]203 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]204}
205
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]206static void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]207 SkScalar ab = SkScalarInterp(src[0], src[2], t);
208 SkScalar bc = SkScalarInterp(src[2], src[4], t);
209
210 dst[0] = src[0];
211 dst[2] = ab;
212 dst[4] = SkScalarInterp(ab, bc, t);
213 dst[6] = bc;
214 dst[8] = src[4];
215}
216
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]217void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]218 SkASSERT(t > 0 && t < SK_Scalar1);
219
220 interp_quad_coords(&src[0].fX, &dst[0].fX, t);
221 interp_quad_coords(&src[0].fY, &dst[0].fY, t);
222}
223
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]224void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]225 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
226 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
227 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
228 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
229
230 dst[0] = src[0];
231 dst[1].set(x01, y01);
232 dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
233 dst[3].set(x12, y12);
234 dst[4] = src[2];
235}
236
237/** Quad'(t) = At + B, where
238 A = 2(a - 2b + c)
239 B = 2(b - a)
240 Solve for t, only if it fits between 0 < t < 1
241*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]242int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]243 /* At + B == 0
244 t = -B / A
245 */
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]246 return valid_unit_divide(a - b, a - b - b + c, tValue);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]247}
248
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]249static inline void flatten_double_quad_extrema(SkScalar coords[14]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]250 coords[2] = coords[6] = coords[4];
251}
252
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]253/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]254 stored in dst[]. Guarantees that the 1/2 quads will be monotonic.
255 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]256int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]257 SkASSERT(src);
258 SkASSERT(dst);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]259
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]260 SkScalar a = src[0].fY;
261 SkScalar b = src[1].fY;
262 SkScalar c = src[2].fY;
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]263
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]264 if (is_not_monotonic(a, b, c)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]265 SkScalar tValue;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]266 if (valid_unit_divide(a - b, a - b - b + c, &tValue)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]267 SkChopQuadAt(src, dst, tValue);
268 flatten_double_quad_extrema(&dst[0].fY);
269 return 1;
270 }
271 // if we get here, we need to force dst to be monotonic, even though
272 // we couldn't compute a unit_divide value (probably underflow).
273 b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;
274 }
275 dst[0].set(src[0].fX, a);
276 dst[1].set(src[1].fX, b);
277 dst[2].set(src[2].fX, c);
278 return 0;
279}
280
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]281/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is
282 stored in dst[]. Guarantees that the 1/2 quads will be monotonic.
283 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]284int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) {
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]285 SkASSERT(src);
286 SkASSERT(dst);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]287
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]288 SkScalar a = src[0].fX;
289 SkScalar b = src[1].fX;
290 SkScalar c = src[2].fX;
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]291
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]292 if (is_not_monotonic(a, b, c)) {
293 SkScalar tValue;
294 if (valid_unit_divide(a - b, a - b - b + c, &tValue)) {
295 SkChopQuadAt(src, dst, tValue);
296 flatten_double_quad_extrema(&dst[0].fX);
297 return 1;
298 }
299 // if we get here, we need to force dst to be monotonic, even though
300 // we couldn't compute a unit_divide value (probably underflow).
301 b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;
302 }
303 dst[0].set(a, src[0].fY);
304 dst[1].set(b, src[1].fY);
305 dst[2].set(c, src[2].fY);
306 return 0;
307}
308
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]309// F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2
310// F'(t) = 2 (b - a) + 2 (a - 2b + c) t
311// F''(t) = 2 (a - 2b + c)
312//
313// A = 2 (b - a)
314// B = 2 (a - 2b + c)
315//
316// Maximum curvature for a quadratic means solving
317// Fx' Fx'' + Fy' Fy'' = 0
318//
319// t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2)
320//
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]321SkScalar SkFindQuadMaxCurvature(const SkPoint src[3]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]322 SkScalar Ax = src[1].fX - src[0].fX;
323 SkScalar Ay = src[1].fY - src[0].fY;
324 SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX;
325 SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY;
326 SkScalar t = 0; // 0 means don't chop
327
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]328 (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t);
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]329 return t;
330}
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]331
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]332int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) {
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]333 SkScalar t = SkFindQuadMaxCurvature(src);
334 if (t == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]335 memcpy(dst, src, 3 * sizeof(SkPoint));
336 return 1;
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]337 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]338 SkChopQuadAt(src, dst, t);
339 return 2;
340 }
341}
342
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]343#define SK_ScalarTwoThirds (0.666666666f)
reed@google.com007593e2011-07-27 13:54:36 +0000[diff] [blame]344
345void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) {
346 const SkScalar scale = SK_ScalarTwoThirds;
347 dst[0] = src[0];
348 dst[1].set(src[0].fX + SkScalarMul(src[1].fX - src[0].fX, scale),
349 src[0].fY + SkScalarMul(src[1].fY - src[0].fY, scale));
350 dst[2].set(src[2].fX + SkScalarMul(src[1].fX - src[2].fX, scale),
351 src[2].fY + SkScalarMul(src[1].fY - src[2].fY, scale));
352 dst[3] = src[2];
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]353}
354
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]355//////////////////////////////////////////////////////////////////////////////
356///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS /////
357//////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]358
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]359static void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]360 coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0];
361 coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]);
362 coeff[2] = 3*(pt[2] - pt[0]);
363 coeff[3] = pt[0];
364}
365
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]366void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]367 SkASSERT(pts);
368
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]369 if (cx) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]370 get_cubic_coeff(&pts[0].fX, cx);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]371 }
372 if (cy) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]373 get_cubic_coeff(&pts[0].fY, cy);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]374 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]375}
376
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]377static SkScalar eval_cubic(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]378 SkASSERT(src);
379 SkASSERT(t >= 0 && t <= SK_Scalar1);
380
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]381 if (t == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]382 return src[0];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]383 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]384
385#ifdef DIRECT_EVAL_OF_POLYNOMIALS
386 SkScalar D = src[0];
387 SkScalar A = src[6] + 3*(src[2] - src[4]) - D;
388 SkScalar B = 3*(src[4] - src[2] - src[2] + D);
389 SkScalar C = 3*(src[2] - D);
390
391 return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D);
392#else
393 SkScalar ab = SkScalarInterp(src[0], src[2], t);
394 SkScalar bc = SkScalarInterp(src[2], src[4], t);
395 SkScalar cd = SkScalarInterp(src[4], src[6], t);
396 SkScalar abc = SkScalarInterp(ab, bc, t);
397 SkScalar bcd = SkScalarInterp(bc, cd, t);
398 return SkScalarInterp(abc, bcd, t);
399#endif
400}
401
402/** return At^2 + Bt + C
403*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]404static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]405 SkASSERT(t >= 0 && t <= SK_Scalar1);
406
407 return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
408}
409
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]410static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]411 SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
412 SkScalar B = 2*(src[4] - 2 * src[2] + src[0]);
413 SkScalar C = src[2] - src[0];
414
415 return eval_quadratic(A, B, C, t);
416}
417
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]418static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]419 SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
420 SkScalar B = src[4] - 2 * src[2] + src[0];
421
422 return SkScalarMulAdd(A, t, B);
423}
424
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]425void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc,
426 SkVector* tangent, SkVector* curvature) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]427 SkASSERT(src);
428 SkASSERT(t >= 0 && t <= SK_Scalar1);
429
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]430 if (loc) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]431 loc->set(eval_cubic(&src[0].fX, t), eval_cubic(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]432 }
433 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]434 tangent->set(eval_cubic_derivative(&src[0].fX, t),
435 eval_cubic_derivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]436 }
437 if (curvature) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]438 curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
439 eval_cubic_2ndDerivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]440 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]441}
442
443/** Cubic'(t) = At^2 + Bt + C, where
444 A = 3(-a + 3(b - c) + d)
445 B = 6(a - 2b + c)
446 C = 3(b - a)
447 Solve for t, keeping only those that fit betwee 0 < t < 1
448*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]449int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
450 SkScalar tValues[2]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]451 // we divide A,B,C by 3 to simplify
452 SkScalar A = d - a + 3*(b - c);
453 SkScalar B = 2*(a - b - b + c);
454 SkScalar C = b - a;
455
456 return SkFindUnitQuadRoots(A, B, C, tValues);
457}
458
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]459static void interp_cubic_coords(const SkScalar* src, SkScalar* dst,
460 SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]461 SkScalar ab = SkScalarInterp(src[0], src[2], t);
462 SkScalar bc = SkScalarInterp(src[2], src[4], t);
463 SkScalar cd = SkScalarInterp(src[4], src[6], t);
464 SkScalar abc = SkScalarInterp(ab, bc, t);
465 SkScalar bcd = SkScalarInterp(bc, cd, t);
466 SkScalar abcd = SkScalarInterp(abc, bcd, t);
467
468 dst[0] = src[0];
469 dst[2] = ab;
470 dst[4] = abc;
471 dst[6] = abcd;
472 dst[8] = bcd;
473 dst[10] = cd;
474 dst[12] = src[6];
475}
476
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]477void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]478 SkASSERT(t > 0 && t < SK_Scalar1);
479
480 interp_cubic_coords(&src[0].fX, &dst[0].fX, t);
481 interp_cubic_coords(&src[0].fY, &dst[0].fY, t);
482}
483
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]484/* http://code.google.com/p/skia/issues/detail?id=32
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]485
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]486 This test code would fail when we didn't check the return result of
487 valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is
488 that after the first chop, the parameters to valid_unit_divide are equal
489 (thanks to finite float precision and rounding in the subtracts). Thus
490 even though the 2nd tValue looks < 1.0, after we renormalize it, we end
491 up with 1.0, hence the need to check and just return the last cubic as
492 a degenerate clump of 4 points in the sampe place.
493
494 static void test_cubic() {
495 SkPoint src[4] = {
496 { 556.25000, 523.03003 },
497 { 556.23999, 522.96002 },
498 { 556.21997, 522.89001 },
499 { 556.21997, 522.82001 }
500 };
501 SkPoint dst[10];
502 SkScalar tval[] = { 0.33333334f, 0.99999994f };
503 SkChopCubicAt(src, dst, tval, 2);
504 }
505 */
506
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]507void SkChopCubicAt(const SkPoint src[4], SkPoint dst[],
508 const SkScalar tValues[], int roots) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]509#ifdef SK_DEBUG
510 {
511 for (int i = 0; i < roots - 1; i++)
512 {
513 SkASSERT(is_unit_interval(tValues[i]));
514 SkASSERT(is_unit_interval(tValues[i+1]));
515 SkASSERT(tValues[i] < tValues[i+1]);
516 }
517 }
518#endif
519
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]520 if (dst) {
521 if (roots == 0) { // nothing to chop
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]522 memcpy(dst, src, 4*sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]523 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]524 SkScalar t = tValues[0];
525 SkPoint tmp[4];
526
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]527 for (int i = 0; i < roots; i++) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]528 SkChopCubicAt(src, dst, t);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]529 if (i == roots - 1) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]530 break;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]531 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]532
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]533 dst += 3;
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]534 // have src point to the remaining cubic (after the chop)
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]535 memcpy(tmp, dst, 4 * sizeof(SkPoint));
536 src = tmp;
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]537
538 // watch out in case the renormalized t isn't in range
539 if (!valid_unit_divide(tValues[i+1] - tValues[i],
540 SK_Scalar1 - tValues[i], &t)) {
541 // if we can't, just create a degenerate cubic
542 dst[4] = dst[5] = dst[6] = src[3];
543 break;
544 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]545 }
546 }
547 }
548}
549
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]550void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]551 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
552 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
553 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
554 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
555 SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX);
556 SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY);
557
558 SkScalar x012 = SkScalarAve(x01, x12);
559 SkScalar y012 = SkScalarAve(y01, y12);
560 SkScalar x123 = SkScalarAve(x12, x23);
561 SkScalar y123 = SkScalarAve(y12, y23);
562
563 dst[0] = src[0];
564 dst[1].set(x01, y01);
565 dst[2].set(x012, y012);
566 dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123));
567 dst[4].set(x123, y123);
568 dst[5].set(x23, y23);
569 dst[6] = src[3];
570}
571
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]572static void flatten_double_cubic_extrema(SkScalar coords[14]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]573 coords[4] = coords[8] = coords[6];
574}
575
576/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
577 the resulting beziers are monotonic in Y. This is called by the scan converter.
578 Depending on what is returned, dst[] is treated as follows
579 0 dst[0..3] is the original cubic
580 1 dst[0..3] and dst[3..6] are the two new cubics
581 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
582 If dst == null, it is ignored and only the count is returned.
583*/
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]584int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]585 SkScalar tValues[2];
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]586 int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY,
587 src[3].fY, tValues);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]588
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]589 SkChopCubicAt(src, dst, tValues, roots);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]590 if (dst && roots > 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]591 // we do some cleanup to ensure our Y extrema are flat
592 flatten_double_cubic_extrema(&dst[0].fY);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]593 if (roots == 2) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]594 flatten_double_cubic_extrema(&dst[3].fY);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]595 }
596 }
597 return roots;
598}
599
600int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) {
601 SkScalar tValues[2];
602 int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX,
603 src[3].fX, tValues);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]604
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]605 SkChopCubicAt(src, dst, tValues, roots);
606 if (dst && roots > 0) {
607 // we do some cleanup to ensure our Y extrema are flat
608 flatten_double_cubic_extrema(&dst[0].fX);
609 if (roots == 2) {
610 flatten_double_cubic_extrema(&dst[3].fX);
611 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]612 }
613 return roots;
614}
615
616/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html
617
618 Inflection means that curvature is zero.
619 Curvature is [F' x F''] / [F'^3]
620 So we solve F'x X F''y - F'y X F''y == 0
621 After some canceling of the cubic term, we get
622 A = b - a
623 B = c - 2b + a
624 C = d - 3c + 3b - a
625 (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0
626*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]627int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]628 SkScalar Ax = src[1].fX - src[0].fX;
629 SkScalar Ay = src[1].fY - src[0].fY;
630 SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX;
631 SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY;
632 SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX;
633 SkScalar Cy = src[3].fY + 3 * (src[1].fY - src[2].fY) - src[0].fY;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]634
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]635 return SkFindUnitQuadRoots(Bx*Cy - By*Cx, Ax*Cy - Ay*Cx, Ax*By - Ay*Bx, tValues);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]636}
637
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]638int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]639 SkScalar tValues[2];
640 int count = SkFindCubicInflections(src, tValues);
641
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]642 if (dst) {
643 if (count == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]644 memcpy(dst, src, 4 * sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]645 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]646 SkChopCubicAt(src, dst, tValues, count);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]647 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]648 }
649 return count + 1;
650}
651
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]652template <typename T> void bubble_sort(T array[], int count) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]653 for (int i = count - 1; i > 0; --i)
654 for (int j = i; j > 0; --j)
655 if (array[j] < array[j-1])
656 {
657 T tmp(array[j]);
658 array[j] = array[j-1];
659 array[j-1] = tmp;
660 }
661}
662
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]663/**
664 * Given an array and count, remove all pair-wise duplicates from the array,
665 * keeping the existing sorting, and return the new count
666 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]667static int collaps_duplicates(SkScalar array[], int count) {
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]668 for (int n = count; n > 1; --n) {
669 if (array[0] == array[1]) {
670 for (int i = 1; i < n; ++i) {
671 array[i - 1] = array[i];
672 }
673 count -= 1;
674 } else {
675 array += 1;
676 }
677 }
678 return count;
679}
680
681#ifdef SK_DEBUG
682
683#define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array)
684
685static void test_collaps_duplicates() {
686 static bool gOnce;
687 if (gOnce) { return; }
688 gOnce = true;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]689 const SkScalar src0[] = { 0 };
690 const SkScalar src1[] = { 0, 0 };
691 const SkScalar src2[] = { 0, 1 };
692 const SkScalar src3[] = { 0, 0, 0 };
693 const SkScalar src4[] = { 0, 0, 1 };
694 const SkScalar src5[] = { 0, 1, 1 };
695 const SkScalar src6[] = { 0, 1, 2 };
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]696 const struct {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]697 const SkScalar* fData;
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]698 int fCount;
699 int fCollapsedCount;
700 } data[] = {
701 { TEST_COLLAPS_ENTRY(src0), 1 },
702 { TEST_COLLAPS_ENTRY(src1), 1 },
703 { TEST_COLLAPS_ENTRY(src2), 2 },
704 { TEST_COLLAPS_ENTRY(src3), 1 },
705 { TEST_COLLAPS_ENTRY(src4), 2 },
706 { TEST_COLLAPS_ENTRY(src5), 2 },
707 { TEST_COLLAPS_ENTRY(src6), 3 },
708 };
709 for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]710 SkScalar dst[3];
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]711 memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0]));
712 int count = collaps_duplicates(dst, data[i].fCount);
713 SkASSERT(data[i].fCollapsedCount == count);
714 for (int j = 1; j < count; ++j) {
715 SkASSERT(dst[j-1] < dst[j]);
716 }
717 }
718}
719#endif
720
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]721static SkScalar SkScalarCubeRoot(SkScalar x) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]722 return SkScalarPow(x, 0.3333333f);
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]723}
724
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]725/* Solve coeff(t) == 0, returning the number of roots that
726 lie withing 0 < t < 1.
727 coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]728
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]729 Eliminates repeated roots (so that all tValues are distinct, and are always
730 in increasing order.
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]731*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]732static int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) {
733 if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]734 return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);
735 }
736
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]737 SkScalar a, b, c, Q, R;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]738
739 {
740 SkASSERT(coeff[0] != 0);
741
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]742 SkScalar inva = SkScalarInvert(coeff[0]);
743 a = coeff[1] * inva;
744 b = coeff[2] * inva;
745 c = coeff[3] * inva;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]746 }
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]747 Q = (a*a - b*3) / 9;
748 R = (2*a*a*a - 9*a*b + 27*c) / 54;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]749
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]750 SkScalar Q3 = Q * Q * Q;
751 SkScalar R2MinusQ3 = R * R - Q3;
752 SkScalar adiv3 = a / 3;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]753
754 SkScalar* roots = tValues;
755 SkScalar r;
756
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]757 if (R2MinusQ3 < 0) { // we have 3 real roots
758 SkScalar theta = SkScalarACos(R / SkScalarSqrt(Q3));
759 SkScalar neg2RootQ = -2 * SkScalarSqrt(Q);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]760
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]761 r = neg2RootQ * SkScalarCos(theta/3) - adiv3;
762 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]763 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]764 }
765 r = neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3;
766 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]767 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]768 }
769 r = neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3;
770 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]771 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]772 }
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]773 SkDEBUGCODE(test_collaps_duplicates();)
774
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]775 // now sort the roots
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]776 int count = (int)(roots - tValues);
777 SkASSERT((unsigned)count <= 3);
778 bubble_sort(tValues, count);
779 count = collaps_duplicates(tValues, count);
780 roots = tValues + count; // so we compute the proper count below
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]781 } else { // we have 1 real root
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]782 SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3);
783 A = SkScalarCubeRoot(A);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]784 if (R > 0) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]785 A = -A;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]786 }
787 if (A != 0) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]788 A += Q / A;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]789 }
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]790 r = A - adiv3;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]791 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]792 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]793 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]794 }
795
796 return (int)(roots - tValues);
797}
798
799/* Looking for F' dot F'' == 0
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]800
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]801 A = b - a
802 B = c - 2b + a
803 C = d - 3c + 3b - a
804
805 F' = 3Ct^2 + 6Bt + 3A
806 F'' = 6Ct + 6B
807
808 F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
809*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]810static void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]811 SkScalar a = src[2] - src[0];
812 SkScalar b = src[4] - 2 * src[2] + src[0];
813 SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0];
814
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]815 coeff[0] = c * c;
816 coeff[1] = 3 * b * c;
817 coeff[2] = 2 * b * b + c * a;
818 coeff[3] = a * b;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]819}
820
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]821/* Looking for F' dot F'' == 0
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]822
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]823 A = b - a
824 B = c - 2b + a
825 C = d - 3c + 3b - a
826
827 F' = 3Ct^2 + 6Bt + 3A
828 F'' = 6Ct + 6B
829
830 F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
831*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]832int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]833 SkScalar coeffX[4], coeffY[4];
834 int i;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]835
836 formulate_F1DotF2(&src[0].fX, coeffX);
837 formulate_F1DotF2(&src[0].fY, coeffY);
838
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]839 for (i = 0; i < 4; i++) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]840 coeffX[i] += coeffY[i];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]841 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]842
843 SkScalar t[3];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]844 int count = solve_cubic_poly(coeffX, t);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]845 int maxCount = 0;
846
847 // now remove extrema where the curvature is zero (mins)
848 // !!!! need a test for this !!!!
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]849 for (i = 0; i < count; i++) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]850 // if (not_min_curvature())
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]851 if (t[i] > 0 && t[i] < SK_Scalar1) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]852 tValues[maxCount++] = t[i];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]853 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]854 }
855 return maxCount;
856}
857
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]858int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
859 SkScalar tValues[3]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]860 SkScalar t_storage[3];
861
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]862 if (tValues == NULL) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]863 tValues = t_storage;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]864 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]865
866 int count = SkFindCubicMaxCurvature(src, tValues);
867
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]868 if (dst) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]869 if (count == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]870 memcpy(dst, src, 4 * sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]871 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]872 SkChopCubicAt(src, dst, tValues, count);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]873 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]874 }
875 return count + 1;
876}
877
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]878bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
879 bool* ambiguous) {
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]880 if (ambiguous) {
881 *ambiguous = false;
882 }
883
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]884 // Find the minimum and maximum y of the extrema, which are the
885 // first and last points since this cubic is monotonic
886 SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY);
887 SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY);
888
889 if (pt.fY == cubic[0].fY
890 || pt.fY < min_y
891 || pt.fY > max_y) {
892 // The query line definitely does not cross the curve
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]893 if (ambiguous) {
894 *ambiguous = (pt.fY == cubic[0].fY);
895 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]896 return false;
897 }
898
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]899 bool pt_at_extremum = (pt.fY == cubic[3].fY);
900
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]901 SkScalar min_x =
902 SkMinScalar(
903 SkMinScalar(
904 SkMinScalar(cubic[0].fX, cubic[1].fX),
905 cubic[2].fX),
906 cubic[3].fX);
907 if (pt.fX < min_x) {
908 // The query line definitely crosses the curve
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]909 if (ambiguous) {
910 *ambiguous = pt_at_extremum;
911 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]912 return true;
913 }
914
915 SkScalar max_x =
916 SkMaxScalar(
917 SkMaxScalar(
918 SkMaxScalar(cubic[0].fX, cubic[1].fX),
919 cubic[2].fX),
920 cubic[3].fX);
921 if (pt.fX > max_x) {
922 // The query line definitely does not cross the curve
923 return false;
924 }
925
926 // Do a binary search to find the parameter value which makes y as
927 // close as possible to the query point. See whether the query
928 // line's origin is to the left of the associated x coordinate.
929
930 // kMaxIter is chosen as the number of mantissa bits for a float,
931 // since there's no way we are going to get more precision by
932 // iterating more times than that.
933 const int kMaxIter = 23;
934 SkPoint eval;
935 int iter = 0;
936 SkScalar upper_t;
937 SkScalar lower_t;
938 // Need to invert direction of t parameter if cubic goes up
939 // instead of down
940 if (cubic[3].fY > cubic[0].fY) {
941 upper_t = SK_Scalar1;
commit-bot@chromium.orgdfc928c2013-11-25 19:44:07 +0000[diff] [blame]942 lower_t = 0;
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]943 } else {
commit-bot@chromium.orgdfc928c2013-11-25 19:44:07 +0000[diff] [blame]944 upper_t = 0;
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]945 lower_t = SK_Scalar1;
946 }
947 do {
948 SkScalar t = SkScalarAve(upper_t, lower_t);
949 SkEvalCubicAt(cubic, t, &eval, NULL, NULL);
950 if (pt.fY > eval.fY) {
951 lower_t = t;
952 } else {
953 upper_t = t;
954 }
955 } while (++iter < kMaxIter
956 && !SkScalarNearlyZero(eval.fY - pt.fY));
957 if (pt.fX <= eval.fX) {
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]958 if (ambiguous) {
959 *ambiguous = pt_at_extremum;
960 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]961 return true;
962 }
963 return false;
964}
965
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]966int SkNumXRayCrossingsForCubic(const SkXRay& pt, const SkPoint cubic[4], bool* ambiguous) {
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]967 int num_crossings = 0;
968 SkPoint monotonic_cubics[10];
969 int num_monotonic_cubics = SkChopCubicAtYExtrema(cubic, monotonic_cubics);
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]970 if (ambiguous) {
971 *ambiguous = false;
972 }
973 bool locally_ambiguous;
974 if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[0], &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]975 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]976 if (ambiguous) {
977 *ambiguous |= locally_ambiguous;
978 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]979 if (num_monotonic_cubics > 0)
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]980 if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[3], &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]981 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]982 if (ambiguous) {
983 *ambiguous |= locally_ambiguous;
984 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]985 if (num_monotonic_cubics > 1)
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]986 if (SkXRayCrossesMonotonicCubic(pt, &monotonic_cubics[6], &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]987 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]988 if (ambiguous) {
989 *ambiguous |= locally_ambiguous;
990 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]991 return num_crossings;
992}
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]993
994///////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]995
996/* Find t value for quadratic [a, b, c] = d.
997 Return 0 if there is no solution within [0, 1)
998*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]999static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1000 // At^2 + Bt + C = d
1001 SkScalar A = a - 2 * b + c;
1002 SkScalar B = 2 * (b - a);
1003 SkScalar C = a - d;
1004
1005 SkScalar roots[2];
1006 int count = SkFindUnitQuadRoots(A, B, C, roots);
1007
1008 SkASSERT(count <= 1);
1009 return count == 1 ? roots[0] : 0;
1010}
1011
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1012/* given a quad-curve and a point (x,y), chop the quad at that point and place
skia.committer@gmail.com937bf442013-09-28 07:01:33 +0000[diff] [blame]1013 the new off-curve point and endpoint into 'dest'.
skia.committer@gmail.com6f1f1592013-07-10 07:00:58 +0000[diff] [blame]1014 Should only return false if the computed pos is the start of the curve
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1015 (i.e. root == 0)
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1016*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1017static bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y,
1018 SkPoint* dest) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1019 const SkScalar* base;
1020 SkScalar value;
1021
1022 if (SkScalarAbs(x) < SkScalarAbs(y)) {
1023 base = &quad[0].fX;
1024 value = x;
1025 } else {
1026 base = &quad[0].fY;
1027 value = y;
1028 }
1029
1030 // note: this returns 0 if it thinks value is out of range, meaning the
1031 // root might return something outside of [0, 1)
1032 SkScalar t = quad_solve(base[0], base[2], base[4], value);
1033
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1034 if (t > 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1035 SkPoint tmp[5];
1036 SkChopQuadAt(quad, tmp, t);
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1037 dest[0] = tmp[1];
robertphillips@google.coma9531cd2013-09-27 17:05:59 +0000[diff] [blame]1038 dest[1].set(x, y);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1039 return true;
1040 } else {
1041 /* t == 0 means either the value triggered a root outside of [0, 1)
1042 For our purposes, we can ignore the <= 0 roots, but we want to
1043 catch the >= 1 roots (which given our caller, will basically mean
1044 a root of 1, give-or-take numerical instability). If we are in the
1045 >= 1 case, return the existing offCurve point.
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]1046
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1047 The test below checks to see if we are close to the "end" of the
1048 curve (near base[4]). Rather than specifying a tolerance, I just
1049 check to see if value is on to the right/left of the middle point
1050 (depending on the direction/sign of the end points).
1051 */
1052 if ((base[0] < base[4] && value > base[2]) ||
1053 (base[0] > base[4] && value < base[2])) // should root have been 1
1054 {
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1055 dest[0] = quad[1];
1056 dest[1].set(x, y);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1057 return true;
1058 }
1059 }
1060 return false;
1061}
1062
1063static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = {
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1064// The mid point of the quadratic arc approximation is half way between the two
1065// control points. The float epsilon adjustment moves the on curve point out by
1066// two bits, distributing the convex test error between the round rect approximation
1067// and the convex cross product sign equality test.
1068#define SK_MID_RRECT_OFFSET (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2
1069 { SK_Scalar1, 0 },
1070 { SK_Scalar1, SK_ScalarTanPIOver8 },
1071 { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET },
1072 { SK_ScalarTanPIOver8, SK_Scalar1 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1073
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1074 { 0, SK_Scalar1 },
1075 { -SK_ScalarTanPIOver8, SK_Scalar1 },
1076 { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET },
1077 { -SK_Scalar1, SK_ScalarTanPIOver8 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1078
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1079 { -SK_Scalar1, 0 },
1080 { -SK_Scalar1, -SK_ScalarTanPIOver8 },
1081 { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET },
1082 { -SK_ScalarTanPIOver8, -SK_Scalar1 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1083
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1084 { 0, -SK_Scalar1 },
1085 { SK_ScalarTanPIOver8, -SK_Scalar1 },
1086 { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET },
1087 { SK_Scalar1, -SK_ScalarTanPIOver8 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1088
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1089 { SK_Scalar1, 0 }
1090#undef SK_MID_RRECT_OFFSET
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1091};
1092
1093int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
1094 SkRotationDirection dir, const SkMatrix* userMatrix,
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1095 SkPoint quadPoints[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1096 // rotate by x,y so that uStart is (1.0)
1097 SkScalar x = SkPoint::DotProduct(uStart, uStop);
1098 SkScalar y = SkPoint::CrossProduct(uStart, uStop);
1099
1100 SkScalar absX = SkScalarAbs(x);
1101 SkScalar absY = SkScalarAbs(y);
1102
1103 int pointCount;
1104
1105 // check for (effectively) coincident vectors
1106 // this can happen if our angle is nearly 0 or nearly 180 (y == 0)
1107 // ... we use the dot-prod to distinguish between 0 and 180 (x > 0)
1108 if (absY <= SK_ScalarNearlyZero && x > 0 &&
1109 ((y >= 0 && kCW_SkRotationDirection == dir) ||
1110 (y <= 0 && kCCW_SkRotationDirection == dir))) {
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]1111
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1112 // just return the start-point
1113 quadPoints[0].set(SK_Scalar1, 0);
1114 pointCount = 1;
1115 } else {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1116 if (dir == kCCW_SkRotationDirection) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1117 y = -y;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1118 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1119 // what octant (quadratic curve) is [xy] in?
1120 int oct = 0;
1121 bool sameSign = true;
1122
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1123 if (0 == y) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1124 oct = 4; // 180
1125 SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1126 } else if (0 == x) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1127 SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1128 oct = y > 0 ? 2 : 6; // 90 : 270
1129 } else {
1130 if (y < 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1131 oct += 4;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1132 }
1133 if ((x < 0) != (y < 0)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1134 oct += 2;
1135 sameSign = false;
1136 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1137 if ((absX < absY) == sameSign) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1138 oct += 1;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1139 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1140 }
1141
1142 int wholeCount = oct << 1;
1143 memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint));
1144
1145 const SkPoint* arc = &gQuadCirclePts[wholeCount];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame^]1146 if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1147 wholeCount += 2;
1148 }
1149 pointCount = wholeCount + 1;
1150 }
1151
1152 // now handle counter-clockwise and the initial unitStart rotation
1153 SkMatrix matrix;
1154 matrix.setSinCos(uStart.fY, uStart.fX);
1155 if (dir == kCCW_SkRotationDirection) {
1156 matrix.preScale(SK_Scalar1, -SK_Scalar1);
1157 }
1158 if (userMatrix) {
1159 matrix.postConcat(*userMatrix);
1160 }
1161 matrix.mapPoints(quadPoints, pointCount);
1162 return pointCount;
1163}
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1164
1165///////////////////////////////////////////////////////////////////////////////
1166
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1167// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w)
1168// ------------------------------------------
1169// ((1 - t)^2 + t^2 + 2 (1 - t) t w)
1170//
1171// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0}
1172// ------------------------------------------------
1173// {t^2 (2 - 2 w), t (-2 + 2 w), 1}
1174//
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1175
1176// Take the parametric specification for the conic (either X or Y) and return
1177// in coeff[] the coefficients for the simple quadratic polynomial
1178// coeff[0] for t^2
1179// coeff[1] for t
1180// coeff[2] for constant term
1181//
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1182static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1183 SkASSERT(src);
1184 SkASSERT(t >= 0 && t <= SK_Scalar1);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1185
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1186 SkScalar src2w = SkScalarMul(src[2], w);
1187 SkScalar C = src[0];
1188 SkScalar A = src[4] - 2 * src2w + C;
1189 SkScalar B = 2 * (src2w - C);
1190 SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1191
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1192 B = 2 * (w - SK_Scalar1);
1193 C = SK_Scalar1;
1194 A = -B;
1195 SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1196
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1197 return SkScalarDiv(numer, denom);
1198}
1199
1200// F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w)
1201//
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1202// t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w)
1203// t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w)
1204// t^0 : -2 P0 w + 2 P1 w
1205//
1206// We disregard magnitude, so we can freely ignore the denominator of F', and
1207// divide the numerator by 2
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1208//
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1209// coeff[0] for t^2
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1210// coeff[1] for t^1
1211// coeff[2] for t^0
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1212//
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1213static void conic_deriv_coeff(const SkScalar src[], SkScalar w, SkScalar coeff[3]) {
1214 const SkScalar P20 = src[4] - src[0];
1215 const SkScalar P10 = src[2] - src[0];
1216 const SkScalar wP10 = w * P10;
1217 coeff[0] = w * P20 - P20;
1218 coeff[1] = P20 - 2 * wP10;
1219 coeff[2] = wP10;
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1220}
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1221
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1222static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1223 SkScalar coeff[3];
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1224 conic_deriv_coeff(coord, w, coeff);
1225 return t * (t * coeff[0] + coeff[1]) + coeff[2];
1226}
1227
1228static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
1229 SkScalar coeff[3];
1230 conic_deriv_coeff(src, w, coeff);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1231
1232 SkScalar tValues[2];
1233 int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues);
1234 SkASSERT(0 == roots || 1 == roots);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1235
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1236 if (1 == roots) {
1237 *t = tValues[0];
1238 return true;
1239 }
1240 return false;
1241}
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1242
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1243struct SkP3D {
1244 SkScalar fX, fY, fZ;
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1245
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1246 void set(SkScalar x, SkScalar y, SkScalar z) {
1247 fX = x; fY = y; fZ = z;
1248 }
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1249
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1250 void projectDown(SkPoint* dst) const {
1251 dst->set(fX / fZ, fY / fZ);
1252 }
1253};
1254
commit-bot@chromium.org15dd6a52014-01-28 14:36:52 +0000[diff] [blame]1255// We only interpolate one dimension at a time (the first, at +0, +3, +6).
1256static void p3d_interp(const SkScalar src[7], SkScalar dst[7], SkScalar t) {
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1257 SkScalar ab = SkScalarInterp(src[0], src[3], t);
1258 SkScalar bc = SkScalarInterp(src[3], src[6], t);
1259 dst[0] = ab;
1260 dst[3] = SkScalarInterp(ab, bc, t);
1261 dst[6] = bc;
1262}
1263
1264static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) {
1265 dst[0].set(src[0].fX * 1, src[0].fY * 1, 1);
1266 dst[1].set(src[1].fX * w, src[1].fY * w, w);
1267 dst[2].set(src[2].fX * 1, src[2].fY * 1, 1);
1268}
1269
reed@google.com4e1502a2013-05-07 20:42:35 +0000[diff] [blame]1270void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const {
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1271 SkASSERT(t >= 0 && t <= SK_Scalar1);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1272
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1273 if (pt) {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1274 pt->set(conic_eval_pos(&fPts[0].fX, fW, t),
1275 conic_eval_pos(&fPts[0].fY, fW, t));
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1276 }
reed@google.com4e1502a2013-05-07 20:42:35 +0000[diff] [blame]1277 if (tangent) {
1278 tangent->set(conic_eval_tan(&fPts[0].fX, fW, t),
1279 conic_eval_tan(&fPts[0].fY, fW, t));
1280 }
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1281}
1282
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1283void SkConic::chopAt(SkScalar t, SkConic dst[2]) const {
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1284 SkP3D tmp[3], tmp2[3];
1285
1286 ratquad_mapTo3D(fPts, fW, tmp);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1287
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1288 p3d_interp(&tmp[0].fX, &tmp2[0].fX, t);
1289 p3d_interp(&tmp[0].fY, &tmp2[0].fY, t);
1290 p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1291
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1292 dst[0].fPts[0] = fPts[0];
1293 tmp2[0].projectDown(&dst[0].fPts[1]);
1294 tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2];
1295 tmp2[2].projectDown(&dst[1].fPts[1]);
1296 dst[1].fPts[2] = fPts[2];
1297
mike@reedtribe.org464a1532013-04-13 10:51:51 +0000[diff] [blame]1298 // to put in "standard form", where w0 and w2 are both 1, we compute the
1299 // new w1 as sqrt(w1*w1/w0*w2)
1300 // or
1301 // w1 /= sqrt(w0*w2)
1302 //
1303 // However, in our case, we know that for dst[0], w0 == 1, and for dst[1], w2 == 1
1304 //
1305 SkScalar root = SkScalarSqrt(tmp2[1].fZ);
1306 dst[0].fW = tmp2[0].fZ / root;
1307 dst[1].fW = tmp2[2].fZ / root;
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1308}
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1309
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1310static SkScalar subdivide_w_value(SkScalar w) {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1311 return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1312}
1313
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1314void SkConic::chop(SkConic dst[2]) const {
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1315 SkScalar scale = SkScalarInvert(SK_Scalar1 + fW);
1316 SkScalar p1x = fW * fPts[1].fX;
1317 SkScalar p1y = fW * fPts[1].fY;
1318 SkScalar mx = (fPts[0].fX + 2 * p1x + fPts[2].fX) * scale * SK_ScalarHalf;
1319 SkScalar my = (fPts[0].fY + 2 * p1y + fPts[2].fY) * scale * SK_ScalarHalf;
1320
1321 dst[0].fPts[0] = fPts[0];
1322 dst[0].fPts[1].set((fPts[0].fX + p1x) * scale,
1323 (fPts[0].fY + p1y) * scale);
1324 dst[0].fPts[2].set(mx, my);
1325
1326 dst[1].fPts[0].set(mx, my);
1327 dst[1].fPts[1].set((p1x + fPts[2].fX) * scale,
1328 (p1y + fPts[2].fY) * scale);
1329 dst[1].fPts[2] = fPts[2];
1330
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1331 dst[0].fW = dst[1].fW = subdivide_w_value(fW);
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1332}
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1333
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1334/*
1335 * "High order approximation of conic sections by quadratic splines"
1336 * by Michael Floater, 1993
1337 */
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1338#define AS_QUAD_ERROR_SETUP \
1339 SkScalar a = fW - 1; \
1340 SkScalar k = a / (4 * (2 + a)); \
1341 SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \
1342 SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY);
1343
1344void SkConic::computeAsQuadError(SkVector* err) const {
1345 AS_QUAD_ERROR_SETUP
1346 err->set(x, y);
1347}
1348
1349bool SkConic::asQuadTol(SkScalar tol) const {
1350 AS_QUAD_ERROR_SETUP
1351 return (x * x + y * y) <= tol * tol;
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1352}
1353
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1354int SkConic::computeQuadPOW2(SkScalar tol) const {
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1355 AS_QUAD_ERROR_SETUP
1356 SkScalar error = SkScalarSqrt(x * x + y * y) - tol;
1357
1358 if (error <= 0) {
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1359 return 0;
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1360 }
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1361 uint32_t ierr = (uint32_t)error;
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1362 return (34 - SkCLZ(ierr)) >> 1;
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1363}
1364
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1365static SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) {
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1366 SkASSERT(level >= 0);
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1367
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1368 if (0 == level) {
1369 memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint));
1370 return pts + 2;
1371 } else {
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1372 SkConic dst[2];
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1373 src.chop(dst);
1374 --level;
1375 pts = subdivide(dst[0], pts, level);
1376 return subdivide(dst[1], pts, level);
1377 }
1378}
1379
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1380int SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const {
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1381 SkASSERT(pow2 >= 0);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1382 *pts = fPts[0];
reed@google.com901641b2013-04-15 15:23:38 +0000[diff] [blame]1383 SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1384 SkASSERT(endPts - pts == (2 * (1 << pow2) + 1));
1385 return 1 << pow2;
1386}
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1387
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1388bool SkConic::findXExtrema(SkScalar* t) const {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1389 return conic_find_extrema(&fPts[0].fX, fW, t);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1390}
1391
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1392bool SkConic::findYExtrema(SkScalar* t) const {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1393 return conic_find_extrema(&fPts[0].fY, fW, t);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1394}
1395
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1396bool SkConic::chopAtXExtrema(SkConic dst[2]) const {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1397 SkScalar t;
1398 if (this->findXExtrema(&t)) {
1399 this->chopAt(t, dst);
1400 // now clean-up the middle, since we know t was meant to be at
1401 // an X-extrema
1402 SkScalar value = dst[0].fPts[2].fX;
1403 dst[0].fPts[1].fX = value;
1404 dst[1].fPts[0].fX = value;
1405 dst[1].fPts[1].fX = value;
1406 return true;
1407 }
1408 return false;
1409}
1410
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1411bool SkConic::chopAtYExtrema(SkConic dst[2]) const {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1412 SkScalar t;
1413 if (this->findYExtrema(&t)) {
1414 this->chopAt(t, dst);
1415 // now clean-up the middle, since we know t was meant to be at
1416 // an Y-extrema
1417 SkScalar value = dst[0].fPts[2].fY;
1418 dst[0].fPts[1].fY = value;
1419 dst[1].fPts[0].fY = value;
1420 dst[1].fPts[1].fY = value;
1421 return true;
1422 }
1423 return false;
1424}
1425
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1426void SkConic::computeTightBounds(SkRect* bounds) const {
mike@reedtribe.orgc7325912013-04-17 02:25:33 +0000[diff] [blame]1427 SkPoint pts[4];
1428 pts[0] = fPts[0];
1429 pts[1] = fPts[2];
1430 int count = 2;
1431
1432 SkScalar t;
1433 if (this->findXExtrema(&t)) {
1434 this->evalAt(t, &pts[count++]);
1435 }
1436 if (this->findYExtrema(&t)) {
1437 this->evalAt(t, &pts[count++]);
1438 }
1439 bounds->set(pts, count);
1440}
1441
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1442void SkConic::computeFastBounds(SkRect* bounds) const {
mike@reedtribe.orgc7325912013-04-17 02:25:33 +0000[diff] [blame]1443 bounds->set(fPts, 3);
1444}