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android / platform / external / chromium_org / third_party / skia / src / c982421ab827d09eeb631f044c40312930f4a75b / . / core / SkGeometry.cpp
blob: 646dfb05b9d4f8eddf59c3e0d8ea694c93fabcd3 [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
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]11bool SkXRayCrossesLine(const SkXRay& pt,
12 const SkPoint pts[2],
13 bool* ambiguous) {
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]14 if (ambiguous) {
15 *ambiguous = false;
16 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]17 // Determine quick discards.
18 // Consider query line going exactly through point 0 to not
19 // intersect, for symmetry with SkXRayCrossesMonotonicCubic.
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]20 if (pt.fY == pts[0].fY) {
21 if (ambiguous) {
22 *ambiguous = true;
23 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]24 return false;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]25 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]26 if (pt.fY < pts[0].fY && pt.fY < pts[1].fY)
27 return false;
28 if (pt.fY > pts[0].fY && pt.fY > pts[1].fY)
29 return false;
30 if (pt.fX > pts[0].fX && pt.fX > pts[1].fX)
31 return false;
32 // Determine degenerate cases
33 if (SkScalarNearlyZero(pts[0].fY - pts[1].fY))
34 return false;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]35 if (SkScalarNearlyZero(pts[0].fX - pts[1].fX)) {
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]36 // We've already determined the query point lies within the
37 // vertical range of the line segment.
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]38 if (pt.fX <= pts[0].fX) {
39 if (ambiguous) {
40 *ambiguous = (pt.fY == pts[1].fY);
41 }
42 return true;
43 }
44 return false;
45 }
46 // Ambiguity check
47 if (pt.fY == pts[1].fY) {
48 if (pt.fX <= pts[1].fX) {
49 if (ambiguous) {
50 *ambiguous = true;
51 }
52 return true;
53 }
54 return false;
55 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]56 // Full line segment evaluation
57 SkScalar delta_y = pts[1].fY - pts[0].fY;
58 SkScalar delta_x = pts[1].fX - pts[0].fX;
59 SkScalar slope = SkScalarDiv(delta_y, delta_x);
60 SkScalar b = pts[0].fY - SkScalarMul(slope, pts[0].fX);
61 // Solve for x coordinate at y = pt.fY
62 SkScalar x = SkScalarDiv(pt.fY - b, slope);
63 return pt.fX <= x;
64}
65
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]66/** If defined, this makes eval_quad and eval_cubic do more setup (sometimes
67 involving integer multiplies by 2 or 3, but fewer calls to SkScalarMul.
68 May also introduce overflow of fixed when we compute our setup.
69*/
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]70// #define DIRECT_EVAL_OF_POLYNOMIALS
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]71
72////////////////////////////////////////////////////////////////////////
73
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]74static int is_not_monotonic(SkScalar a, SkScalar b, SkScalar c) {
75 SkScalar ab = a - b;
76 SkScalar bc = b - c;
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]77 if (ab < 0) {
78 bc = -bc;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]79 }
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]80 return ab == 0 || bc < 0;
81}
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]82
83////////////////////////////////////////////////////////////////////////
84
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]85static bool is_unit_interval(SkScalar x) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]86 return x > 0 && x < SK_Scalar1;
87}
88
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]89static int valid_unit_divide(SkScalar numer, SkScalar denom, SkScalar* ratio) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]90 SkASSERT(ratio);
91
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]92 if (numer < 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]93 numer = -numer;
94 denom = -denom;
95 }
96
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]97 if (denom == 0 || numer == 0 || numer >= denom) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]98 return 0;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]99 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]100
101 SkScalar r = SkScalarDiv(numer, denom);
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]102 if (SkScalarIsNaN(r)) {
103 return 0;
104 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]105 SkASSERT(r >= 0 && r < SK_Scalar1);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]106 if (r == 0) { // catch underflow if numer <<<< denom
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]107 return 0;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]108 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]109 *ratio = r;
110 return 1;
111}
112
113/** From Numerical Recipes in C.
114
115 Q = -1/2 (B + sign(B) sqrt[B*B - 4*A*C])
116 x1 = Q / A
117 x2 = C / Q
118*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]119int SkFindUnitQuadRoots(SkScalar A, SkScalar B, SkScalar C, SkScalar roots[2]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]120 SkASSERT(roots);
121
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]122 if (A == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]123 return valid_unit_divide(-C, B, roots);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]124 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]125
126 SkScalar* r = roots;
127
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]128 SkScalar R = B*B - 4*A*C;
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]129 if (R < 0 || SkScalarIsNaN(R)) { // complex roots
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]130 return 0;
reed@android.com7c83e1c2010-03-08 17:44:42 +0000[diff] [blame]131 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]132 R = SkScalarSqrt(R);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]133
134 SkScalar Q = (B < 0) ? -(B-R)/2 : -(B+R)/2;
135 r += valid_unit_divide(Q, A, r);
136 r += valid_unit_divide(C, Q, r);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]137 if (r - roots == 2) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]138 if (roots[0] > roots[1])
139 SkTSwap<SkScalar>(roots[0], roots[1]);
140 else if (roots[0] == roots[1]) // nearly-equal?
141 r -= 1; // skip the double root
142 }
143 return (int)(r - roots);
144}
145
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]146///////////////////////////////////////////////////////////////////////////////
147///////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]148
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]149static SkScalar eval_quad(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]150 SkASSERT(src);
151 SkASSERT(t >= 0 && t <= SK_Scalar1);
152
153#ifdef DIRECT_EVAL_OF_POLYNOMIALS
154 SkScalar C = src[0];
155 SkScalar A = src[4] - 2 * src[2] + C;
156 SkScalar B = 2 * (src[2] - C);
157 return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
158#else
159 SkScalar ab = SkScalarInterp(src[0], src[2], t);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]160 SkScalar bc = SkScalarInterp(src[2], src[4], t);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]161 return SkScalarInterp(ab, bc, t);
162#endif
163}
164
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]165static SkScalar eval_quad_derivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]166 SkScalar A = src[4] - 2 * src[2] + src[0];
167 SkScalar B = src[2] - src[0];
168
169 return 2 * SkScalarMulAdd(A, t, B);
170}
171
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]172static SkScalar eval_quad_derivative_at_half(const SkScalar src[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]173 SkScalar A = src[4] - 2 * src[2] + src[0];
174 SkScalar B = src[2] - src[0];
175 return A + 2 * B;
176}
177
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]178void SkEvalQuadAt(const SkPoint src[3], SkScalar t, SkPoint* pt,
179 SkVector* tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]180 SkASSERT(src);
181 SkASSERT(t >= 0 && t <= SK_Scalar1);
182
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]183 if (pt) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]184 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]185 }
186 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]187 tangent->set(eval_quad_derivative(&src[0].fX, t),
188 eval_quad_derivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]189 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]190}
191
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]192void SkEvalQuadAtHalf(const SkPoint src[3], SkPoint* pt, SkVector* tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]193 SkASSERT(src);
194
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]195 if (pt) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]196 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
197 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
198 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
199 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
200 pt->set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
201 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]202 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]203 tangent->set(eval_quad_derivative_at_half(&src[0].fX),
204 eval_quad_derivative_at_half(&src[0].fY));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]205 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]206}
207
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]208static void interp_quad_coords(const SkScalar* src, SkScalar* dst, SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]209 SkScalar ab = SkScalarInterp(src[0], src[2], t);
210 SkScalar bc = SkScalarInterp(src[2], src[4], t);
211
212 dst[0] = src[0];
213 dst[2] = ab;
214 dst[4] = SkScalarInterp(ab, bc, t);
215 dst[6] = bc;
216 dst[8] = src[4];
217}
218
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]219void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]220 SkASSERT(t > 0 && t < SK_Scalar1);
221
222 interp_quad_coords(&src[0].fX, &dst[0].fX, t);
223 interp_quad_coords(&src[0].fY, &dst[0].fY, t);
224}
225
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]226void SkChopQuadAtHalf(const SkPoint src[3], SkPoint dst[5]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]227 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
228 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
229 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
230 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
231
232 dst[0] = src[0];
233 dst[1].set(x01, y01);
234 dst[2].set(SkScalarAve(x01, x12), SkScalarAve(y01, y12));
235 dst[3].set(x12, y12);
236 dst[4] = src[2];
237}
238
239/** Quad'(t) = At + B, where
240 A = 2(a - 2b + c)
241 B = 2(b - a)
242 Solve for t, only if it fits between 0 < t < 1
243*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]244int SkFindQuadExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar tValue[1]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]245 /* At + B == 0
246 t = -B / A
247 */
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]248 return valid_unit_divide(a - b, a - b - b + c, tValue);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]249}
250
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]251static inline void flatten_double_quad_extrema(SkScalar coords[14]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]252 coords[2] = coords[6] = coords[4];
253}
254
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]255/* 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]256 stored in dst[]. Guarantees that the 1/2 quads will be monotonic.
257 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]258int SkChopQuadAtYExtrema(const SkPoint src[3], SkPoint dst[5]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]259 SkASSERT(src);
260 SkASSERT(dst);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]261
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]262 SkScalar a = src[0].fY;
263 SkScalar b = src[1].fY;
264 SkScalar c = src[2].fY;
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]265
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]266 if (is_not_monotonic(a, b, c)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]267 SkScalar tValue;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]268 if (valid_unit_divide(a - b, a - b - b + c, &tValue)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]269 SkChopQuadAt(src, dst, tValue);
270 flatten_double_quad_extrema(&dst[0].fY);
271 return 1;
272 }
273 // if we get here, we need to force dst to be monotonic, even though
274 // we couldn't compute a unit_divide value (probably underflow).
275 b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;
276 }
277 dst[0].set(src[0].fX, a);
278 dst[1].set(src[1].fX, b);
279 dst[2].set(src[2].fX, c);
280 return 0;
281}
282
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]283/* Returns 0 for 1 quad, and 1 for two quads, either way the answer is
284 stored in dst[]. Guarantees that the 1/2 quads will be monotonic.
285 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]286int SkChopQuadAtXExtrema(const SkPoint src[3], SkPoint dst[5]) {
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]287 SkASSERT(src);
288 SkASSERT(dst);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]289
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]290 SkScalar a = src[0].fX;
291 SkScalar b = src[1].fX;
292 SkScalar c = src[2].fX;
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]293
reed@android.com001bd972009-11-17 18:47:52 +0000[diff] [blame]294 if (is_not_monotonic(a, b, c)) {
295 SkScalar tValue;
296 if (valid_unit_divide(a - b, a - b - b + c, &tValue)) {
297 SkChopQuadAt(src, dst, tValue);
298 flatten_double_quad_extrema(&dst[0].fX);
299 return 1;
300 }
301 // if we get here, we need to force dst to be monotonic, even though
302 // we couldn't compute a unit_divide value (probably underflow).
303 b = SkScalarAbs(a - b) < SkScalarAbs(b - c) ? a : c;
304 }
305 dst[0].set(a, src[0].fY);
306 dst[1].set(b, src[1].fY);
307 dst[2].set(c, src[2].fY);
308 return 0;
309}
310
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]311// F(t) = a (1 - t) ^ 2 + 2 b t (1 - t) + c t ^ 2
312// F'(t) = 2 (b - a) + 2 (a - 2b + c) t
313// F''(t) = 2 (a - 2b + c)
314//
315// A = 2 (b - a)
316// B = 2 (a - 2b + c)
317//
318// Maximum curvature for a quadratic means solving
319// Fx' Fx'' + Fy' Fy'' = 0
320//
321// t = - (Ax Bx + Ay By) / (Bx ^ 2 + By ^ 2)
322//
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]323SkScalar SkFindQuadMaxCurvature(const SkPoint src[3]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]324 SkScalar Ax = src[1].fX - src[0].fX;
325 SkScalar Ay = src[1].fY - src[0].fY;
326 SkScalar Bx = src[0].fX - src[1].fX - src[1].fX + src[2].fX;
327 SkScalar By = src[0].fY - src[1].fY - src[1].fY + src[2].fY;
328 SkScalar t = 0; // 0 means don't chop
329
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]330 (void)valid_unit_divide(-(Ax * Bx + Ay * By), Bx * Bx + By * By, &t);
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]331 return t;
332}
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]333
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]334int SkChopQuadAtMaxCurvature(const SkPoint src[3], SkPoint dst[5]) {
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]335 SkScalar t = SkFindQuadMaxCurvature(src);
336 if (t == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]337 memcpy(dst, src, 3 * sizeof(SkPoint));
338 return 1;
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]339 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]340 SkChopQuadAt(src, dst, t);
341 return 2;
342 }
343}
344
reed@google.com3c541f92013-12-17 16:44:46 +0000[diff] [blame]345#define SK_ScalarTwoThirds (0.666666666f)
reed@google.com007593e2011-07-27 13:54:36 +0000[diff] [blame]346
347void SkConvertQuadToCubic(const SkPoint src[3], SkPoint dst[4]) {
348 const SkScalar scale = SK_ScalarTwoThirds;
349 dst[0] = src[0];
350 dst[1].set(src[0].fX + SkScalarMul(src[1].fX - src[0].fX, scale),
351 src[0].fY + SkScalarMul(src[1].fY - src[0].fY, scale));
352 dst[2].set(src[2].fX + SkScalarMul(src[1].fX - src[2].fX, scale),
353 src[2].fY + SkScalarMul(src[1].fY - src[2].fY, scale));
354 dst[3] = src[2];
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]355}
356
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]357//////////////////////////////////////////////////////////////////////////////
358///// CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS // CUBICS /////
359//////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]360
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]361static void get_cubic_coeff(const SkScalar pt[], SkScalar coeff[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]362 coeff[0] = pt[6] + 3*(pt[2] - pt[4]) - pt[0];
363 coeff[1] = 3*(pt[4] - pt[2] - pt[2] + pt[0]);
364 coeff[2] = 3*(pt[2] - pt[0]);
365 coeff[3] = pt[0];
366}
367
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]368void SkGetCubicCoeff(const SkPoint pts[4], SkScalar cx[4], SkScalar cy[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]369 SkASSERT(pts);
370
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]371 if (cx) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]372 get_cubic_coeff(&pts[0].fX, cx);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]373 }
374 if (cy) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]375 get_cubic_coeff(&pts[0].fY, cy);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]376 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]377}
378
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]379static SkScalar eval_cubic(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]380 SkASSERT(src);
381 SkASSERT(t >= 0 && t <= SK_Scalar1);
382
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]383 if (t == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]384 return src[0];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]385 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]386
387#ifdef DIRECT_EVAL_OF_POLYNOMIALS
388 SkScalar D = src[0];
389 SkScalar A = src[6] + 3*(src[2] - src[4]) - D;
390 SkScalar B = 3*(src[4] - src[2] - src[2] + D);
391 SkScalar C = 3*(src[2] - D);
392
393 return SkScalarMulAdd(SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C), t, D);
394#else
395 SkScalar ab = SkScalarInterp(src[0], src[2], t);
396 SkScalar bc = SkScalarInterp(src[2], src[4], t);
397 SkScalar cd = SkScalarInterp(src[4], src[6], t);
398 SkScalar abc = SkScalarInterp(ab, bc, t);
399 SkScalar bcd = SkScalarInterp(bc, cd, t);
400 return SkScalarInterp(abc, bcd, t);
401#endif
402}
403
404/** return At^2 + Bt + C
405*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]406static SkScalar eval_quadratic(SkScalar A, SkScalar B, SkScalar C, SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]407 SkASSERT(t >= 0 && t <= SK_Scalar1);
408
409 return SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
410}
411
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]412static SkScalar eval_cubic_derivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]413 SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
414 SkScalar B = 2*(src[4] - 2 * src[2] + src[0]);
415 SkScalar C = src[2] - src[0];
416
417 return eval_quadratic(A, B, C, t);
418}
419
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]420static SkScalar eval_cubic_2ndDerivative(const SkScalar src[], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]421 SkScalar A = src[6] + 3*(src[2] - src[4]) - src[0];
422 SkScalar B = src[4] - 2 * src[2] + src[0];
423
424 return SkScalarMulAdd(A, t, B);
425}
426
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]427void SkEvalCubicAt(const SkPoint src[4], SkScalar t, SkPoint* loc,
428 SkVector* tangent, SkVector* curvature) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]429 SkASSERT(src);
430 SkASSERT(t >= 0 && t <= SK_Scalar1);
431
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]432 if (loc) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]433 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]434 }
435 if (tangent) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]436 tangent->set(eval_cubic_derivative(&src[0].fX, t),
437 eval_cubic_derivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]438 }
439 if (curvature) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]440 curvature->set(eval_cubic_2ndDerivative(&src[0].fX, t),
441 eval_cubic_2ndDerivative(&src[0].fY, t));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]442 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]443}
444
445/** Cubic'(t) = At^2 + Bt + C, where
446 A = 3(-a + 3(b - c) + d)
447 B = 6(a - 2b + c)
448 C = 3(b - a)
449 Solve for t, keeping only those that fit betwee 0 < t < 1
450*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]451int SkFindCubicExtrema(SkScalar a, SkScalar b, SkScalar c, SkScalar d,
452 SkScalar tValues[2]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]453 // we divide A,B,C by 3 to simplify
454 SkScalar A = d - a + 3*(b - c);
455 SkScalar B = 2*(a - b - b + c);
456 SkScalar C = b - a;
457
458 return SkFindUnitQuadRoots(A, B, C, tValues);
459}
460
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]461static void interp_cubic_coords(const SkScalar* src, SkScalar* dst,
462 SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]463 SkScalar ab = SkScalarInterp(src[0], src[2], t);
464 SkScalar bc = SkScalarInterp(src[2], src[4], t);
465 SkScalar cd = SkScalarInterp(src[4], src[6], t);
466 SkScalar abc = SkScalarInterp(ab, bc, t);
467 SkScalar bcd = SkScalarInterp(bc, cd, t);
468 SkScalar abcd = SkScalarInterp(abc, bcd, t);
469
470 dst[0] = src[0];
471 dst[2] = ab;
472 dst[4] = abc;
473 dst[6] = abcd;
474 dst[8] = bcd;
475 dst[10] = cd;
476 dst[12] = src[6];
477}
478
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]479void SkChopCubicAt(const SkPoint src[4], SkPoint dst[7], SkScalar t) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]480 SkASSERT(t > 0 && t < SK_Scalar1);
481
482 interp_cubic_coords(&src[0].fX, &dst[0].fX, t);
483 interp_cubic_coords(&src[0].fY, &dst[0].fY, t);
484}
485
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]486/* http://code.google.com/p/skia/issues/detail?id=32
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]487
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]488 This test code would fail when we didn't check the return result of
489 valid_unit_divide in SkChopCubicAt(... tValues[], int roots). The reason is
490 that after the first chop, the parameters to valid_unit_divide are equal
491 (thanks to finite float precision and rounding in the subtracts). Thus
492 even though the 2nd tValue looks < 1.0, after we renormalize it, we end
493 up with 1.0, hence the need to check and just return the last cubic as
494 a degenerate clump of 4 points in the sampe place.
495
496 static void test_cubic() {
497 SkPoint src[4] = {
498 { 556.25000, 523.03003 },
499 { 556.23999, 522.96002 },
500 { 556.21997, 522.89001 },
501 { 556.21997, 522.82001 }
502 };
503 SkPoint dst[10];
504 SkScalar tval[] = { 0.33333334f, 0.99999994f };
505 SkChopCubicAt(src, dst, tval, 2);
506 }
507 */
508
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]509void SkChopCubicAt(const SkPoint src[4], SkPoint dst[],
510 const SkScalar tValues[], int roots) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]511#ifdef SK_DEBUG
512 {
513 for (int i = 0; i < roots - 1; i++)
514 {
515 SkASSERT(is_unit_interval(tValues[i]));
516 SkASSERT(is_unit_interval(tValues[i+1]));
517 SkASSERT(tValues[i] < tValues[i+1]);
518 }
519 }
520#endif
521
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]522 if (dst) {
523 if (roots == 0) { // nothing to chop
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]524 memcpy(dst, src, 4*sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]525 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]526 SkScalar t = tValues[0];
527 SkPoint tmp[4];
528
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]529 for (int i = 0; i < roots; i++) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]530 SkChopCubicAt(src, dst, t);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]531 if (i == roots - 1) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]532 break;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]533 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]534
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]535 dst += 3;
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]536 // have src point to the remaining cubic (after the chop)
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]537 memcpy(tmp, dst, 4 * sizeof(SkPoint));
538 src = tmp;
reed@android.com17bdc092009-08-28 20:06:54 +0000[diff] [blame]539
540 // watch out in case the renormalized t isn't in range
541 if (!valid_unit_divide(tValues[i+1] - tValues[i],
542 SK_Scalar1 - tValues[i], &t)) {
543 // if we can't, just create a degenerate cubic
544 dst[4] = dst[5] = dst[6] = src[3];
545 break;
546 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]547 }
548 }
549 }
550}
551
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]552void SkChopCubicAtHalf(const SkPoint src[4], SkPoint dst[7]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]553 SkScalar x01 = SkScalarAve(src[0].fX, src[1].fX);
554 SkScalar y01 = SkScalarAve(src[0].fY, src[1].fY);
555 SkScalar x12 = SkScalarAve(src[1].fX, src[2].fX);
556 SkScalar y12 = SkScalarAve(src[1].fY, src[2].fY);
557 SkScalar x23 = SkScalarAve(src[2].fX, src[3].fX);
558 SkScalar y23 = SkScalarAve(src[2].fY, src[3].fY);
559
560 SkScalar x012 = SkScalarAve(x01, x12);
561 SkScalar y012 = SkScalarAve(y01, y12);
562 SkScalar x123 = SkScalarAve(x12, x23);
563 SkScalar y123 = SkScalarAve(y12, y23);
564
565 dst[0] = src[0];
566 dst[1].set(x01, y01);
567 dst[2].set(x012, y012);
568 dst[3].set(SkScalarAve(x012, x123), SkScalarAve(y012, y123));
569 dst[4].set(x123, y123);
570 dst[5].set(x23, y23);
571 dst[6] = src[3];
572}
573
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]574static void flatten_double_cubic_extrema(SkScalar coords[14]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]575 coords[4] = coords[8] = coords[6];
576}
577
578/** Given 4 points on a cubic bezier, chop it into 1, 2, 3 beziers such that
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]579 the resulting beziers are monotonic in Y. This is called by the scan
580 converter. Depending on what is returned, dst[] is treated as follows:
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]581 0 dst[0..3] is the original cubic
582 1 dst[0..3] and dst[3..6] are the two new cubics
583 2 dst[0..3], dst[3..6], dst[6..9] are the three new cubics
584 If dst == null, it is ignored and only the count is returned.
585*/
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]586int SkChopCubicAtYExtrema(const SkPoint src[4], SkPoint dst[10]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]587 SkScalar tValues[2];
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]588 int roots = SkFindCubicExtrema(src[0].fY, src[1].fY, src[2].fY,
589 src[3].fY, tValues);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]590
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]591 SkChopCubicAt(src, dst, tValues, roots);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]592 if (dst && roots > 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]593 // we do some cleanup to ensure our Y extrema are flat
594 flatten_double_cubic_extrema(&dst[0].fY);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]595 if (roots == 2) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]596 flatten_double_cubic_extrema(&dst[3].fY);
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]597 }
598 }
599 return roots;
600}
601
602int SkChopCubicAtXExtrema(const SkPoint src[4], SkPoint dst[10]) {
603 SkScalar tValues[2];
604 int roots = SkFindCubicExtrema(src[0].fX, src[1].fX, src[2].fX,
605 src[3].fX, tValues);
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]606
reed@android.com68779c32009-11-18 13:47:40 +0000[diff] [blame]607 SkChopCubicAt(src, dst, tValues, roots);
608 if (dst && roots > 0) {
609 // we do some cleanup to ensure our Y extrema are flat
610 flatten_double_cubic_extrema(&dst[0].fX);
611 if (roots == 2) {
612 flatten_double_cubic_extrema(&dst[3].fX);
613 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]614 }
615 return roots;
616}
617
618/** http://www.faculty.idc.ac.il/arik/quality/appendixA.html
619
620 Inflection means that curvature is zero.
621 Curvature is [F' x F''] / [F'^3]
622 So we solve F'x X F''y - F'y X F''y == 0
623 After some canceling of the cubic term, we get
624 A = b - a
625 B = c - 2b + a
626 C = d - 3c + 3b - a
627 (BxCy - ByCx)t^2 + (AxCy - AyCx)t + AxBy - AyBx == 0
628*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]629int SkFindCubicInflections(const SkPoint src[4], SkScalar tValues[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]630 SkScalar Ax = src[1].fX - src[0].fX;
631 SkScalar Ay = src[1].fY - src[0].fY;
632 SkScalar Bx = src[2].fX - 2 * src[1].fX + src[0].fX;
633 SkScalar By = src[2].fY - 2 * src[1].fY + src[0].fY;
634 SkScalar Cx = src[3].fX + 3 * (src[1].fX - src[2].fX) - src[0].fX;
635 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]636
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]637 return SkFindUnitQuadRoots(Bx*Cy - By*Cx,
638 Ax*Cy - Ay*Cx,
639 Ax*By - Ay*Bx,
640 tValues);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]641}
642
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]643int SkChopCubicAtInflections(const SkPoint src[], SkPoint dst[10]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]644 SkScalar tValues[2];
645 int count = SkFindCubicInflections(src, tValues);
646
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]647 if (dst) {
648 if (count == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]649 memcpy(dst, src, 4 * sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]650 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]651 SkChopCubicAt(src, dst, tValues, count);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]652 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]653 }
654 return count + 1;
655}
656
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]657template <typename T> void bubble_sort(T array[], int count) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]658 for (int i = count - 1; i > 0; --i)
659 for (int j = i; j > 0; --j)
660 if (array[j] < array[j-1])
661 {
662 T tmp(array[j]);
663 array[j] = array[j-1];
664 array[j-1] = tmp;
665 }
666}
667
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]668/**
669 * Given an array and count, remove all pair-wise duplicates from the array,
670 * keeping the existing sorting, and return the new count
671 */
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]672static int collaps_duplicates(SkScalar array[], int count) {
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]673 for (int n = count; n > 1; --n) {
674 if (array[0] == array[1]) {
675 for (int i = 1; i < n; ++i) {
676 array[i - 1] = array[i];
677 }
678 count -= 1;
679 } else {
680 array += 1;
681 }
682 }
683 return count;
684}
685
686#ifdef SK_DEBUG
687
688#define TEST_COLLAPS_ENTRY(array) array, SK_ARRAY_COUNT(array)
689
690static void test_collaps_duplicates() {
691 static bool gOnce;
692 if (gOnce) { return; }
693 gOnce = true;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]694 const SkScalar src0[] = { 0 };
695 const SkScalar src1[] = { 0, 0 };
696 const SkScalar src2[] = { 0, 1 };
697 const SkScalar src3[] = { 0, 0, 0 };
698 const SkScalar src4[] = { 0, 0, 1 };
699 const SkScalar src5[] = { 0, 1, 1 };
700 const SkScalar src6[] = { 0, 1, 2 };
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]701 const struct {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]702 const SkScalar* fData;
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]703 int fCount;
704 int fCollapsedCount;
705 } data[] = {
706 { TEST_COLLAPS_ENTRY(src0), 1 },
707 { TEST_COLLAPS_ENTRY(src1), 1 },
708 { TEST_COLLAPS_ENTRY(src2), 2 },
709 { TEST_COLLAPS_ENTRY(src3), 1 },
710 { TEST_COLLAPS_ENTRY(src4), 2 },
711 { TEST_COLLAPS_ENTRY(src5), 2 },
712 { TEST_COLLAPS_ENTRY(src6), 3 },
713 };
714 for (size_t i = 0; i < SK_ARRAY_COUNT(data); ++i) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]715 SkScalar dst[3];
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]716 memcpy(dst, data[i].fData, data[i].fCount * sizeof(dst[0]));
717 int count = collaps_duplicates(dst, data[i].fCount);
718 SkASSERT(data[i].fCollapsedCount == count);
719 for (int j = 1; j < count; ++j) {
720 SkASSERT(dst[j-1] < dst[j]);
721 }
722 }
723}
724#endif
725
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]726static SkScalar SkScalarCubeRoot(SkScalar x) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]727 return SkScalarPow(x, 0.3333333f);
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]728}
729
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]730/* Solve coeff(t) == 0, returning the number of roots that
731 lie withing 0 < t < 1.
732 coeff[0]t^3 + coeff[1]t^2 + coeff[2]t + coeff[3]
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]733
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]734 Eliminates repeated roots (so that all tValues are distinct, and are always
735 in increasing order.
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]736*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]737static int solve_cubic_poly(const SkScalar coeff[4], SkScalar tValues[3]) {
738 if (SkScalarNearlyZero(coeff[0])) { // we're just a quadratic
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]739 return SkFindUnitQuadRoots(coeff[1], coeff[2], coeff[3], tValues);
740 }
741
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]742 SkScalar a, b, c, Q, R;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]743
744 {
745 SkASSERT(coeff[0] != 0);
746
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]747 SkScalar inva = SkScalarInvert(coeff[0]);
748 a = coeff[1] * inva;
749 b = coeff[2] * inva;
750 c = coeff[3] * inva;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]751 }
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]752 Q = (a*a - b*3) / 9;
753 R = (2*a*a*a - 9*a*b + 27*c) / 54;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]754
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]755 SkScalar Q3 = Q * Q * Q;
756 SkScalar R2MinusQ3 = R * R - Q3;
757 SkScalar adiv3 = a / 3;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]758
759 SkScalar* roots = tValues;
760 SkScalar r;
761
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]762 if (R2MinusQ3 < 0) { // we have 3 real roots
763 SkScalar theta = SkScalarACos(R / SkScalarSqrt(Q3));
764 SkScalar neg2RootQ = -2 * SkScalarSqrt(Q);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]765
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]766 r = neg2RootQ * SkScalarCos(theta/3) - adiv3;
767 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]768 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]769 }
770 r = neg2RootQ * SkScalarCos((theta + 2*SK_ScalarPI)/3) - adiv3;
771 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]772 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]773 }
774 r = neg2RootQ * SkScalarCos((theta - 2*SK_ScalarPI)/3) - adiv3;
775 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]776 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]777 }
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]778 SkDEBUGCODE(test_collaps_duplicates();)
779
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]780 // now sort the roots
reed@google.com7de50932012-02-29 20:59:24 +0000[diff] [blame]781 int count = (int)(roots - tValues);
782 SkASSERT((unsigned)count <= 3);
783 bubble_sort(tValues, count);
784 count = collaps_duplicates(tValues, count);
785 roots = tValues + count; // so we compute the proper count below
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]786 } else { // we have 1 real root
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]787 SkScalar A = SkScalarAbs(R) + SkScalarSqrt(R2MinusQ3);
788 A = SkScalarCubeRoot(A);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]789 if (R > 0) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]790 A = -A;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]791 }
792 if (A != 0) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]793 A += Q / A;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]794 }
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]795 r = A - adiv3;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]796 if (is_unit_interval(r)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]797 *roots++ = r;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]798 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]799 }
800
801 return (int)(roots - tValues);
802}
803
804/* Looking for F' dot F'' == 0
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]805
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]806 A = b - a
807 B = c - 2b + a
808 C = d - 3c + 3b - a
809
810 F' = 3Ct^2 + 6Bt + 3A
811 F'' = 6Ct + 6B
812
813 F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
814*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]815static void formulate_F1DotF2(const SkScalar src[], SkScalar coeff[4]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]816 SkScalar a = src[2] - src[0];
817 SkScalar b = src[4] - 2 * src[2] + src[0];
818 SkScalar c = src[6] + 3 * (src[2] - src[4]) - src[0];
819
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]820 coeff[0] = c * c;
821 coeff[1] = 3 * b * c;
822 coeff[2] = 2 * b * b + c * a;
823 coeff[3] = a * b;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]824}
825
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]826/* Looking for F' dot F'' == 0
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]827
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]828 A = b - a
829 B = c - 2b + a
830 C = d - 3c + 3b - a
831
832 F' = 3Ct^2 + 6Bt + 3A
833 F'' = 6Ct + 6B
834
835 F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
836*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]837int SkFindCubicMaxCurvature(const SkPoint src[4], SkScalar tValues[3]) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]838 SkScalar coeffX[4], coeffY[4];
839 int i;
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]840
841 formulate_F1DotF2(&src[0].fX, coeffX);
842 formulate_F1DotF2(&src[0].fY, coeffY);
843
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]844 for (i = 0; i < 4; i++) {
reed@google.comceb75262013-12-16 14:17:40 +0000[diff] [blame]845 coeffX[i] += coeffY[i];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]846 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]847
848 SkScalar t[3];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]849 int count = solve_cubic_poly(coeffX, t);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]850 int maxCount = 0;
851
852 // now remove extrema where the curvature is zero (mins)
853 // !!!! need a test for this !!!!
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]854 for (i = 0; i < count; i++) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]855 // if (not_min_curvature())
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]856 if (t[i] > 0 && t[i] < SK_Scalar1) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]857 tValues[maxCount++] = t[i];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]858 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]859 }
860 return maxCount;
861}
862
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]863int SkChopCubicAtMaxCurvature(const SkPoint src[4], SkPoint dst[13],
864 SkScalar tValues[3]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]865 SkScalar t_storage[3];
866
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]867 if (tValues == NULL) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]868 tValues = t_storage;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]869 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]870
871 int count = SkFindCubicMaxCurvature(src, tValues);
872
egdaniel@google.com63cc6e12013-07-12 20:15:34 +0000[diff] [blame]873 if (dst) {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]874 if (count == 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]875 memcpy(dst, src, 4 * sizeof(SkPoint));
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]876 } else {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]877 SkChopCubicAt(src, dst, tValues, count);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]878 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]879 }
880 return count + 1;
881}
882
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]883bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4],
884 bool* ambiguous) {
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]885 if (ambiguous) {
886 *ambiguous = false;
887 }
888
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]889 // Find the minimum and maximum y of the extrema, which are the
890 // first and last points since this cubic is monotonic
891 SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY);
892 SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY);
893
894 if (pt.fY == cubic[0].fY
895 || pt.fY < min_y
896 || pt.fY > max_y) {
897 // The query line definitely does not cross the curve
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]898 if (ambiguous) {
899 *ambiguous = (pt.fY == cubic[0].fY);
900 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]901 return false;
902 }
903
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]904 bool pt_at_extremum = (pt.fY == cubic[3].fY);
905
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]906 SkScalar min_x =
907 SkMinScalar(
908 SkMinScalar(
909 SkMinScalar(cubic[0].fX, cubic[1].fX),
910 cubic[2].fX),
911 cubic[3].fX);
912 if (pt.fX < min_x) {
913 // The query line definitely crosses the curve
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]914 if (ambiguous) {
915 *ambiguous = pt_at_extremum;
916 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]917 return true;
918 }
919
920 SkScalar max_x =
921 SkMaxScalar(
922 SkMaxScalar(
923 SkMaxScalar(cubic[0].fX, cubic[1].fX),
924 cubic[2].fX),
925 cubic[3].fX);
926 if (pt.fX > max_x) {
927 // The query line definitely does not cross the curve
928 return false;
929 }
930
931 // Do a binary search to find the parameter value which makes y as
932 // close as possible to the query point. See whether the query
933 // line's origin is to the left of the associated x coordinate.
934
935 // kMaxIter is chosen as the number of mantissa bits for a float,
936 // since there's no way we are going to get more precision by
937 // iterating more times than that.
938 const int kMaxIter = 23;
939 SkPoint eval;
940 int iter = 0;
941 SkScalar upper_t;
942 SkScalar lower_t;
943 // Need to invert direction of t parameter if cubic goes up
944 // instead of down
945 if (cubic[3].fY > cubic[0].fY) {
946 upper_t = SK_Scalar1;
commit-bot@chromium.orgdfc928c2013-11-25 19:44:07 +0000[diff] [blame]947 lower_t = 0;
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]948 } else {
commit-bot@chromium.orgdfc928c2013-11-25 19:44:07 +0000[diff] [blame]949 upper_t = 0;
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]950 lower_t = SK_Scalar1;
951 }
952 do {
953 SkScalar t = SkScalarAve(upper_t, lower_t);
954 SkEvalCubicAt(cubic, t, &eval, NULL, NULL);
955 if (pt.fY > eval.fY) {
956 lower_t = t;
957 } else {
958 upper_t = t;
959 }
960 } while (++iter < kMaxIter
961 && !SkScalarNearlyZero(eval.fY - pt.fY));
962 if (pt.fX <= eval.fX) {
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]963 if (ambiguous) {
964 *ambiguous = pt_at_extremum;
965 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]966 return true;
967 }
968 return false;
969}
970
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]971int SkNumXRayCrossingsForCubic(const SkXRay& pt,
972 const SkPoint cubic[4],
973 bool* ambiguous) {
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]974 int num_crossings = 0;
975 SkPoint monotonic_cubics[10];
976 int num_monotonic_cubics = SkChopCubicAtYExtrema(cubic, monotonic_cubics);
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]977 if (ambiguous) {
978 *ambiguous = false;
979 }
980 bool locally_ambiguous;
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]981 if (SkXRayCrossesMonotonicCubic(pt,
982 &monotonic_cubics[0],
983 &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]984 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]985 if (ambiguous) {
986 *ambiguous |= locally_ambiguous;
987 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]988 if (num_monotonic_cubics > 0)
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]989 if (SkXRayCrossesMonotonicCubic(pt,
990 &monotonic_cubics[3],
991 &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]992 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]993 if (ambiguous) {
994 *ambiguous |= locally_ambiguous;
995 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]996 if (num_monotonic_cubics > 1)
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]997 if (SkXRayCrossesMonotonicCubic(pt,
998 &monotonic_cubics[6],
999 &locally_ambiguous))
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]1000 ++num_crossings;
kbr@chromium.orgc1b53332010-07-07 22:20:35 +0000[diff] [blame]1001 if (ambiguous) {
1002 *ambiguous |= locally_ambiguous;
1003 }
reed@android.com5b4541e2010-02-05 20:41:02 +0000[diff] [blame]1004 return num_crossings;
1005}
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1006
1007///////////////////////////////////////////////////////////////////////////////
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1008
1009/* Find t value for quadratic [a, b, c] = d.
1010 Return 0 if there is no solution within [0, 1)
1011*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1012static SkScalar quad_solve(SkScalar a, SkScalar b, SkScalar c, SkScalar d) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1013 // At^2 + Bt + C = d
1014 SkScalar A = a - 2 * b + c;
1015 SkScalar B = 2 * (b - a);
1016 SkScalar C = a - d;
1017
1018 SkScalar roots[2];
1019 int count = SkFindUnitQuadRoots(A, B, C, roots);
1020
1021 SkASSERT(count <= 1);
1022 return count == 1 ? roots[0] : 0;
1023}
1024
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1025/* 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]1026 the new off-curve point and endpoint into 'dest'.
skia.committer@gmail.com6f1f1592013-07-10 07:00:58 +0000[diff] [blame]1027 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]1028 (i.e. root == 0)
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1029*/
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1030static bool truncate_last_curve(const SkPoint quad[3], SkScalar x, SkScalar y,
1031 SkPoint* dest) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1032 const SkScalar* base;
1033 SkScalar value;
1034
1035 if (SkScalarAbs(x) < SkScalarAbs(y)) {
1036 base = &quad[0].fX;
1037 value = x;
1038 } else {
1039 base = &quad[0].fY;
1040 value = y;
1041 }
1042
1043 // note: this returns 0 if it thinks value is out of range, meaning the
1044 // root might return something outside of [0, 1)
1045 SkScalar t = quad_solve(base[0], base[2], base[4], value);
1046
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1047 if (t > 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1048 SkPoint tmp[5];
1049 SkChopQuadAt(quad, tmp, t);
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1050 dest[0] = tmp[1];
robertphillips@google.coma9531cd2013-09-27 17:05:59 +0000[diff] [blame]1051 dest[1].set(x, y);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1052 return true;
1053 } else {
1054 /* t == 0 means either the value triggered a root outside of [0, 1)
1055 For our purposes, we can ignore the <= 0 roots, but we want to
1056 catch the >= 1 roots (which given our caller, will basically mean
1057 a root of 1, give-or-take numerical instability). If we are in the
1058 >= 1 case, return the existing offCurve point.
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]1059
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1060 The test below checks to see if we are close to the "end" of the
1061 curve (near base[4]). Rather than specifying a tolerance, I just
1062 check to see if value is on to the right/left of the middle point
1063 (depending on the direction/sign of the end points).
1064 */
1065 if ((base[0] < base[4] && value > base[2]) ||
1066 (base[0] > base[4] && value < base[2])) // should root have been 1
1067 {
robertphillips@google.comdd4bd432013-07-09 15:03:59 +0000[diff] [blame]1068 dest[0] = quad[1];
1069 dest[1].set(x, y);
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1070 return true;
1071 }
1072 }
1073 return false;
1074}
1075
1076static const SkPoint gQuadCirclePts[kSkBuildQuadArcStorage] = {
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1077// The mid point of the quadratic arc approximation is half way between the two
1078// control points. The float epsilon adjustment moves the on curve point out by
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]1079// two bits, distributing the convex test error between the round rect
1080// approximation and the convex cross product sign equality test.
1081#define SK_MID_RRECT_OFFSET \
1082 (SK_Scalar1 + SK_ScalarTanPIOver8 + FLT_EPSILON * 4) / 2
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1083 { SK_Scalar1, 0 },
1084 { SK_Scalar1, SK_ScalarTanPIOver8 },
1085 { SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET },
1086 { SK_ScalarTanPIOver8, SK_Scalar1 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1087
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1088 { 0, SK_Scalar1 },
1089 { -SK_ScalarTanPIOver8, SK_Scalar1 },
1090 { -SK_MID_RRECT_OFFSET, SK_MID_RRECT_OFFSET },
1091 { -SK_Scalar1, SK_ScalarTanPIOver8 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1092
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1093 { -SK_Scalar1, 0 },
1094 { -SK_Scalar1, -SK_ScalarTanPIOver8 },
1095 { -SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET },
1096 { -SK_ScalarTanPIOver8, -SK_Scalar1 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1097
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1098 { 0, -SK_Scalar1 },
1099 { SK_ScalarTanPIOver8, -SK_Scalar1 },
1100 { SK_MID_RRECT_OFFSET, -SK_MID_RRECT_OFFSET },
1101 { SK_Scalar1, -SK_ScalarTanPIOver8 },
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1102
commit-bot@chromium.org942ed4e2013-11-01 15:24:55 +0000[diff] [blame]1103 { SK_Scalar1, 0 }
1104#undef SK_MID_RRECT_OFFSET
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1105};
1106
1107int SkBuildQuadArc(const SkVector& uStart, const SkVector& uStop,
1108 SkRotationDirection dir, const SkMatrix* userMatrix,
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1109 SkPoint quadPoints[]) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1110 // rotate by x,y so that uStart is (1.0)
1111 SkScalar x = SkPoint::DotProduct(uStart, uStop);
1112 SkScalar y = SkPoint::CrossProduct(uStart, uStop);
1113
1114 SkScalar absX = SkScalarAbs(x);
1115 SkScalar absY = SkScalarAbs(y);
1116
1117 int pointCount;
1118
1119 // check for (effectively) coincident vectors
1120 // this can happen if our angle is nearly 0 or nearly 180 (y == 0)
1121 // ... we use the dot-prod to distinguish between 0 and 180 (x > 0)
1122 if (absY <= SK_ScalarNearlyZero && x > 0 &&
1123 ((y >= 0 && kCW_SkRotationDirection == dir) ||
1124 (y <= 0 && kCCW_SkRotationDirection == dir))) {
rmistry@google.com935e9f42012-08-23 18:09:54 +0000[diff] [blame]1125
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1126 // just return the start-point
1127 quadPoints[0].set(SK_Scalar1, 0);
1128 pointCount = 1;
1129 } else {
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1130 if (dir == kCCW_SkRotationDirection) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1131 y = -y;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1132 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1133 // what octant (quadratic curve) is [xy] in?
1134 int oct = 0;
1135 bool sameSign = true;
1136
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1137 if (0 == y) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1138 oct = 4; // 180
1139 SkASSERT(SkScalarAbs(x + SK_Scalar1) <= SK_ScalarNearlyZero);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1140 } else if (0 == x) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1141 SkASSERT(absY - SK_Scalar1 <= SK_ScalarNearlyZero);
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1142 oct = y > 0 ? 2 : 6; // 90 : 270
1143 } else {
1144 if (y < 0) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1145 oct += 4;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1146 }
1147 if ((x < 0) != (y < 0)) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1148 oct += 2;
1149 sameSign = false;
1150 }
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1151 if ((absX < absY) == sameSign) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1152 oct += 1;
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1153 }
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1154 }
1155
1156 int wholeCount = oct << 1;
1157 memcpy(quadPoints, gQuadCirclePts, (wholeCount + 1) * sizeof(SkPoint));
1158
1159 const SkPoint* arc = &gQuadCirclePts[wholeCount];
commit-bot@chromium.org1e314552014-02-21 12:17:34 +0000[diff] [blame]1160 if (truncate_last_curve(arc, x, y, &quadPoints[wholeCount + 1])) {
reed@android.combcd4d5a2008-12-17 15:59:43 +0000[diff] [blame]1161 wholeCount += 2;
1162 }
1163 pointCount = wholeCount + 1;
1164 }
1165
1166 // now handle counter-clockwise and the initial unitStart rotation
1167 SkMatrix matrix;
1168 matrix.setSinCos(uStart.fY, uStart.fX);
1169 if (dir == kCCW_SkRotationDirection) {
1170 matrix.preScale(SK_Scalar1, -SK_Scalar1);
1171 }
1172 if (userMatrix) {
1173 matrix.postConcat(*userMatrix);
1174 }
1175 matrix.mapPoints(quadPoints, pointCount);
1176 return pointCount;
1177}
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1178
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1179
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]1180///////////////////////////////////////////////////////////////////////////////
1181//
1182// NURB representation for conics. Helpful explanations at:
1183//
1184// http://citeseerx.ist.psu.edu/viewdoc/
1185// download?doi=10.1.1.44.5740&rep=rep1&type=ps
1186// and
1187// http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/NURBS/RB-conics.html
1188//
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1189// F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w)
1190// ------------------------------------------
1191// ((1 - t)^2 + t^2 + 2 (1 - t) t w)
1192//
1193// = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0}
1194// ------------------------------------------------
1195// {t^2 (2 - 2 w), t (-2 + 2 w), 1}
1196//
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1197
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1198static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1199 SkASSERT(src);
1200 SkASSERT(t >= 0 && t <= SK_Scalar1);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1201
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1202 SkScalar src2w = SkScalarMul(src[2], w);
1203 SkScalar C = src[0];
1204 SkScalar A = src[4] - 2 * src2w + C;
1205 SkScalar B = 2 * (src2w - C);
1206 SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1207
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1208 B = 2 * (w - SK_Scalar1);
1209 C = SK_Scalar1;
1210 A = -B;
1211 SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1212
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1213 return SkScalarDiv(numer, denom);
1214}
1215
1216// F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w)
1217//
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1218// t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w)
1219// t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w)
1220// t^0 : -2 P0 w + 2 P1 w
1221//
1222// We disregard magnitude, so we can freely ignore the denominator of F', and
1223// divide the numerator by 2
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1224//
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1225// coeff[0] for t^2
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1226// coeff[1] for t^1
1227// coeff[2] for t^0
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1228//
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]1229static void conic_deriv_coeff(const SkScalar src[],
1230 SkScalar w,
1231 SkScalar coeff[3]) {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1232 const SkScalar P20 = src[4] - src[0];
1233 const SkScalar P10 = src[2] - src[0];
1234 const SkScalar wP10 = w * P10;
1235 coeff[0] = w * P20 - P20;
1236 coeff[1] = P20 - 2 * wP10;
1237 coeff[2] = wP10;
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1238}
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1239
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1240static SkScalar conic_eval_tan(const SkScalar coord[], SkScalar w, SkScalar t) {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1241 SkScalar coeff[3];
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1242 conic_deriv_coeff(coord, w, coeff);
1243 return t * (t * coeff[0] + coeff[1]) + coeff[2];
1244}
1245
1246static bool conic_find_extrema(const SkScalar src[], SkScalar w, SkScalar* t) {
1247 SkScalar coeff[3];
1248 conic_deriv_coeff(src, w, coeff);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1249
1250 SkScalar tValues[2];
1251 int roots = SkFindUnitQuadRoots(coeff[0], coeff[1], coeff[2], tValues);
1252 SkASSERT(0 == roots || 1 == roots);
skia.committer@gmail.comcd487462013-04-17 07:00:56 +0000[diff] [blame]1253
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1254 if (1 == roots) {
1255 *t = tValues[0];
1256 return true;
1257 }
1258 return false;
1259}
reed@google.com256f3102013-04-16 21:07:27 +0000[diff] [blame]1260
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1261struct SkP3D {
1262 SkScalar fX, fY, fZ;
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1263
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1264 void set(SkScalar x, SkScalar y, SkScalar z) {
1265 fX = x; fY = y; fZ = z;
1266 }
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1267
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1268 void projectDown(SkPoint* dst) const {
1269 dst->set(fX / fZ, fY / fZ);
1270 }
1271};
1272
commit-bot@chromium.org15dd6a52014-01-28 14:36:52 +0000[diff] [blame]1273// We only interpolate one dimension at a time (the first, at +0, +3, +6).
1274static void p3d_interp(const SkScalar src[7], SkScalar dst[7], SkScalar t) {
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1275 SkScalar ab = SkScalarInterp(src[0], src[3], t);
1276 SkScalar bc = SkScalarInterp(src[3], src[6], t);
1277 dst[0] = ab;
1278 dst[3] = SkScalarInterp(ab, bc, t);
1279 dst[6] = bc;
1280}
1281
1282static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) {
1283 dst[0].set(src[0].fX * 1, src[0].fY * 1, 1);
1284 dst[1].set(src[1].fX * w, src[1].fY * w, w);
1285 dst[2].set(src[2].fX * 1, src[2].fY * 1, 1);
1286}
1287
reed@google.com4e1502a2013-05-07 20:42:35 +0000[diff] [blame]1288void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const {
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1289 SkASSERT(t >= 0 && t <= SK_Scalar1);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1290
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1291 if (pt) {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1292 pt->set(conic_eval_pos(&fPts[0].fX, fW, t),
1293 conic_eval_pos(&fPts[0].fY, fW, t));
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1294 }
reed@google.com4e1502a2013-05-07 20:42:35 +0000[diff] [blame]1295 if (tangent) {
1296 tangent->set(conic_eval_tan(&fPts[0].fX, fW, t),
1297 conic_eval_tan(&fPts[0].fY, fW, t));
1298 }
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1299}
1300
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1301void SkConic::chopAt(SkScalar t, SkConic dst[2]) const {
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1302 SkP3D tmp[3], tmp2[3];
1303
1304 ratquad_mapTo3D(fPts, fW, tmp);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1305
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1306 p3d_interp(&tmp[0].fX, &tmp2[0].fX, t);
1307 p3d_interp(&tmp[0].fY, &tmp2[0].fY, t);
1308 p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t);
skia.committer@gmail.coma43230c2013-04-13 07:01:15 +0000[diff] [blame]1309
reed@google.com0fef2ef2013-04-12 21:55:26 +0000[diff] [blame]1310 dst[0].fPts[0] = fPts[0];
1311 tmp2[0].projectDown(&dst[0].fPts[1]);
1312 tmp2[1].projectDown(&dst[0].fPts[2]); dst[1].fPts[0] = dst[0].fPts[2];
1313 tmp2[2].projectDown(&dst[1].fPts[1]);
1314 dst[1].fPts[2] = fPts[2];
1315
mike@reedtribe.org464a1532013-04-13 10:51:51 +0000[diff] [blame]1316 // to put in "standard form", where w0 and w2 are both 1, we compute the
1317 // new w1 as sqrt(w1*w1/w0*w2)
1318 // or
1319 // w1 /= sqrt(w0*w2)
1320 //
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]1321 // However, in our case, we know that for dst[0]:
1322 // w0 == 1, and for dst[1], w2 == 1
mike@reedtribe.org464a1532013-04-13 10:51:51 +0000[diff] [blame]1323 //
1324 SkScalar root = SkScalarSqrt(tmp2[1].fZ);
1325 dst[0].fW = tmp2[0].fZ / root;
1326 dst[1].fW = tmp2[2].fZ / root;
reed@google.com79975882013-04-12 19:11:10 +0000[diff] [blame]1327}
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1328
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1329static SkScalar subdivide_w_value(SkScalar w) {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1330 return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1331}
1332
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1333void SkConic::chop(SkConic dst[2]) const {
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1334 SkScalar scale = SkScalarInvert(SK_Scalar1 + fW);
1335 SkScalar p1x = fW * fPts[1].fX;
1336 SkScalar p1y = fW * fPts[1].fY;
1337 SkScalar mx = (fPts[0].fX + 2 * p1x + fPts[2].fX) * scale * SK_ScalarHalf;
1338 SkScalar my = (fPts[0].fY + 2 * p1y + fPts[2].fY) * scale * SK_ScalarHalf;
1339
1340 dst[0].fPts[0] = fPts[0];
1341 dst[0].fPts[1].set((fPts[0].fX + p1x) * scale,
1342 (fPts[0].fY + p1y) * scale);
1343 dst[0].fPts[2].set(mx, my);
1344
1345 dst[1].fPts[0].set(mx, my);
1346 dst[1].fPts[1].set((p1x + fPts[2].fX) * scale,
1347 (p1y + fPts[2].fY) * scale);
1348 dst[1].fPts[2] = fPts[2];
1349
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1350 dst[0].fW = dst[1].fW = subdivide_w_value(fW);
mike@reedtribe.org91068392013-04-14 02:40:50 +0000[diff] [blame]1351}
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1352
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1353/*
1354 * "High order approximation of conic sections by quadratic splines"
1355 * by Michael Floater, 1993
1356 */
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1357#define AS_QUAD_ERROR_SETUP \
1358 SkScalar a = fW - 1; \
1359 SkScalar k = a / (4 * (2 + a)); \
1360 SkScalar x = k * (fPts[0].fX - 2 * fPts[1].fX + fPts[2].fX); \
1361 SkScalar y = k * (fPts[0].fY - 2 * fPts[1].fY + fPts[2].fY);
1362
1363void SkConic::computeAsQuadError(SkVector* err) const {
1364 AS_QUAD_ERROR_SETUP
1365 err->set(x, y);
1366}
1367
1368bool SkConic::asQuadTol(SkScalar tol) const {
1369 AS_QUAD_ERROR_SETUP
1370 return (x * x + y * y) <= tol * tol;
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1371}
1372
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1373int SkConic::computeQuadPOW2(SkScalar tol) const {
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1374 AS_QUAD_ERROR_SETUP
1375 SkScalar error = SkScalarSqrt(x * x + y * y) - tol;
1376
1377 if (error <= 0) {
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1378 return 0;
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1379 }
mike@reedtribe.orgdc5176e2013-04-27 18:23:16 +0000[diff] [blame]1380 uint32_t ierr = (uint32_t)error;
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1381 return (34 - SkCLZ(ierr)) >> 1;
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1382}
1383
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1384static SkPoint* subdivide(const SkConic& src, SkPoint pts[], int level) {
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1385 SkASSERT(level >= 0);
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1386
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1387 if (0 == level) {
1388 memcpy(pts, &src.fPts[1], 2 * sizeof(SkPoint));
1389 return pts + 2;
1390 } else {
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1391 SkConic dst[2];
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1392 src.chop(dst);
1393 --level;
1394 pts = subdivide(dst[0], pts, level);
1395 return subdivide(dst[1], pts, level);
1396 }
1397}
1398
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1399int SkConic::chopIntoQuadsPOW2(SkPoint pts[], int pow2) const {
mike@reedtribe.org3661c442013-04-30 02:14:58 +0000[diff] [blame]1400 SkASSERT(pow2 >= 0);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1401 *pts = fPts[0];
reed@google.com901641b2013-04-15 15:23:38 +0000[diff] [blame]1402 SkDEBUGCODE(SkPoint* endPts =) subdivide(*this, pts + 1, pow2);
mike@reedtribe.org6c125bd2013-04-15 15:20:52 +0000[diff] [blame]1403 SkASSERT(endPts - pts == (2 * (1 << pow2) + 1));
1404 return 1 << pow2;
1405}
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1406
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1407bool SkConic::findXExtrema(SkScalar* t) const {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1408 return conic_find_extrema(&fPts[0].fX, fW, t);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1409}
1410
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1411bool SkConic::findYExtrema(SkScalar* t) const {
mike@reedtribe.org3f0cf542013-05-08 01:55:49 +0000[diff] [blame]1412 return conic_find_extrema(&fPts[0].fY, fW, t);
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1413}
1414
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1415bool SkConic::chopAtXExtrema(SkConic dst[2]) const {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1416 SkScalar t;
1417 if (this->findXExtrema(&t)) {
1418 this->chopAt(t, dst);
1419 // now clean-up the middle, since we know t was meant to be at
1420 // an X-extrema
1421 SkScalar value = dst[0].fPts[2].fX;
1422 dst[0].fPts[1].fX = value;
1423 dst[1].fPts[0].fX = value;
1424 dst[1].fPts[1].fX = value;
1425 return true;
1426 }
1427 return false;
1428}
1429
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1430bool SkConic::chopAtYExtrema(SkConic dst[2]) const {
mike@reedtribe.org472a49c2013-04-17 01:21:01 +0000[diff] [blame]1431 SkScalar t;
1432 if (this->findYExtrema(&t)) {
1433 this->chopAt(t, dst);
1434 // now clean-up the middle, since we know t was meant to be at
1435 // an Y-extrema
1436 SkScalar value = dst[0].fPts[2].fY;
1437 dst[0].fPts[1].fY = value;
1438 dst[1].fPts[0].fY = value;
1439 dst[1].fPts[1].fY = value;
1440 return true;
1441 }
1442 return false;
1443}
1444
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1445void SkConic::computeTightBounds(SkRect* bounds) const {
mike@reedtribe.orgc7325912013-04-17 02:25:33 +0000[diff] [blame]1446 SkPoint pts[4];
1447 pts[0] = fPts[0];
1448 pts[1] = fPts[2];
1449 int count = 2;
1450
1451 SkScalar t;
1452 if (this->findXExtrema(&t)) {
1453 this->evalAt(t, &pts[count++]);
1454 }
1455 if (this->findYExtrema(&t)) {
1456 this->evalAt(t, &pts[count++]);
1457 }
1458 bounds->set(pts, count);
1459}
1460
mike@reedtribe.org27a0a562013-04-26 00:58:29 +0000[diff] [blame]1461void SkConic::computeFastBounds(SkRect* bounds) const {
mike@reedtribe.orgc7325912013-04-17 02:25:33 +0000[diff] [blame]1462 bounds->set(fPts, 3);
1463}
commit-bot@chromium.org4a0370d2014-02-21 19:49:10 +0000[diff] [blame]1464
1465bool SkConic::findMaxCurvature(SkScalar* t) const {
1466 // TODO: Implement me
1467 return false;
1468}