1 /*
2 * Copyright 2011 Google Inc.
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
8 #include "src/gpu/ganesh/geometry/GrPathUtils.h"
9
10 #include "include/core/SkMatrix.h"
11 #include "include/core/SkRect.h"
12 #include "include/private/base/SkAssert.h"
13 #include "include/private/base/SkFloatingPoint.h"
14 #include "src/core/SkGeometry.h"
15 #include "src/core/SkPathEnums.h"
16 #include "src/core/SkPointPriv.h"
17 #include "src/gpu/tessellate/WangsFormula.h"
18
19 #include <algorithm>
20
21 using namespace skia_private;
22
23 static const SkScalar kMinCurveTol = 0.0001f;
24
tolerance_to_wangs_precision(float srcTol)25 static float tolerance_to_wangs_precision(float srcTol) {
26 // You should have called scaleToleranceToSrc, which guarantees this
27 SkASSERT(srcTol >= kMinCurveTol);
28
29 // The GrPathUtil API defines tolerance as the max distance the linear segment can be from
30 // the real curve. Wang's formula guarantees the linear segments will be within 1/precision
31 // of the true curve, so precision = 1/srcTol
32 return 1.f / srcTol;
33 }
34
max_bezier_vertices(uint32_t chopCount)35 uint32_t max_bezier_vertices(uint32_t chopCount) {
36 static constexpr uint32_t kMaxChopsPerCurve = 10;
37 static_assert((1 << kMaxChopsPerCurve) == GrPathUtils::kMaxPointsPerCurve);
38 return 1 << std::min(chopCount, kMaxChopsPerCurve);
39 }
40
scaleToleranceToSrc(SkScalar devTol,const SkMatrix & viewM,const SkRect & pathBounds)41 SkScalar GrPathUtils::scaleToleranceToSrc(SkScalar devTol,
42 const SkMatrix& viewM,
43 const SkRect& pathBounds) {
44 // In order to tesselate the path we get a bound on how much the matrix can
45 // scale when mapping to screen coordinates.
46 SkScalar stretch = viewM.getMaxScale();
47
48 if (stretch < 0) {
49 // take worst case mapRadius amoung four corners.
50 // (less than perfect)
51 for (int i = 0; i < 4; ++i) {
52 SkMatrix mat;
53 mat.setTranslate((i % 2) ? pathBounds.fLeft : pathBounds.fRight,
54 (i < 2) ? pathBounds.fTop : pathBounds.fBottom);
55 mat.postConcat(viewM);
56 stretch = std::max(stretch, mat.mapRadius(SK_Scalar1));
57 }
58 }
59 SkScalar srcTol = 0;
60 if (stretch <= 0) {
61 // We have degenerate bounds or some degenerate matrix. Thus we set the tolerance to be the
62 // max of the path pathBounds width and height.
63 srcTol = std::max(pathBounds.width(), pathBounds.height());
64 } else {
65 srcTol = devTol / stretch;
66 }
67 if (srcTol < kMinCurveTol) {
68 srcTol = kMinCurveTol;
69 }
70 return srcTol;
71 }
72
quadraticPointCount(const SkPoint points[],SkScalar tol)73 uint32_t GrPathUtils::quadraticPointCount(const SkPoint points[], SkScalar tol) {
74 return max_bezier_vertices(skgpu::wangs_formula::quadratic_log2(
75 tolerance_to_wangs_precision(tol), points));
76 }
77
generateQuadraticPoints(const SkPoint & p0,const SkPoint & p1,const SkPoint & p2,SkScalar tolSqd,SkPoint ** points,uint32_t pointsLeft)78 uint32_t GrPathUtils::generateQuadraticPoints(const SkPoint& p0,
79 const SkPoint& p1,
80 const SkPoint& p2,
81 SkScalar tolSqd,
82 SkPoint** points,
83 uint32_t pointsLeft) {
84 if (pointsLeft < 2 ||
85 (SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p2)) < tolSqd) {
86 (*points)[0] = p2;
87 *points += 1;
88 return 1;
89 }
90
91 SkPoint q[] = {
92 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
93 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
94 };
95 SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
96
97 pointsLeft >>= 1;
98 uint32_t a = generateQuadraticPoints(p0, q[0], r, tolSqd, points, pointsLeft);
99 uint32_t b = generateQuadraticPoints(r, q[1], p2, tolSqd, points, pointsLeft);
100 return a + b;
101 }
102
cubicPointCount(const SkPoint points[],SkScalar tol)103 uint32_t GrPathUtils::cubicPointCount(const SkPoint points[], SkScalar tol) {
104 return max_bezier_vertices(skgpu::wangs_formula::cubic_log2(
105 tolerance_to_wangs_precision(tol), points));
106 }
107
generateCubicPoints(const SkPoint & p0,const SkPoint & p1,const SkPoint & p2,const SkPoint & p3,SkScalar tolSqd,SkPoint ** points,uint32_t pointsLeft)108 uint32_t GrPathUtils::generateCubicPoints(const SkPoint& p0,
109 const SkPoint& p1,
110 const SkPoint& p2,
111 const SkPoint& p3,
112 SkScalar tolSqd,
113 SkPoint** points,
114 uint32_t pointsLeft) {
115 if (pointsLeft < 2 ||
116 (SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p3) < tolSqd &&
117 SkPointPriv::DistanceToLineSegmentBetweenSqd(p2, p0, p3) < tolSqd)) {
118 (*points)[0] = p3;
119 *points += 1;
120 return 1;
121 }
122 SkPoint q[] = {
123 { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
124 { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
125 { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
126 };
127 SkPoint r[] = {
128 { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
129 { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
130 };
131 SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
132 pointsLeft >>= 1;
133 uint32_t a = generateCubicPoints(p0, q[0], r[0], s, tolSqd, points, pointsLeft);
134 uint32_t b = generateCubicPoints(s, r[1], q[2], p3, tolSqd, points, pointsLeft);
135 return a + b;
136 }
137
set(const SkPoint qPts[3])138 void GrPathUtils::QuadUVMatrix::set(const SkPoint qPts[3]) {
139 // We want M such that M * xy_pt = uv_pt
140 // We know M * control_pts = [0 1/2 1]
141 // [0 0 1]
142 // [1 1 1]
143 // And control_pts = [x0 x1 x2]
144 // [y0 y1 y2]
145 // [1 1 1 ]
146 // We invert the control pt matrix and post concat to both sides to get M.
147 // Using the known form of the control point matrix and the result, we can
148 // optimize and improve precision.
149
150 double x0 = qPts[0].fX;
151 double y0 = qPts[0].fY;
152 double x1 = qPts[1].fX;
153 double y1 = qPts[1].fY;
154 double x2 = qPts[2].fX;
155 double y2 = qPts[2].fY;
156
157 // pre-calculate some adjugate matrix factors for determinant
158 double a2 = x1*y2-x2*y1;
159 double a5 = x2*y0-x0*y2;
160 double a8 = x0*y1-x1*y0;
161 double det = a2 + a5 + a8;
162
163 if (!SkIsFinite(det)
164 || SkScalarNearlyZero((float)det, SK_ScalarNearlyZero * SK_ScalarNearlyZero)) {
165 // The quad is degenerate. Hopefully this is rare. Find the pts that are
166 // farthest apart to compute a line (unless it is really a pt).
167 SkScalar maxD = SkPointPriv::DistanceToSqd(qPts[0], qPts[1]);
168 int maxEdge = 0;
169 SkScalar d = SkPointPriv::DistanceToSqd(qPts[1], qPts[2]);
170 if (d > maxD) {
171 maxD = d;
172 maxEdge = 1;
173 }
174 d = SkPointPriv::DistanceToSqd(qPts[2], qPts[0]);
175 if (d > maxD) {
176 maxD = d;
177 maxEdge = 2;
178 }
179 // We could have a tolerance here, not sure if it would improve anything
180 if (maxD > 0) {
181 // Set the matrix to give (u = 0, v = distance_to_line)
182 SkVector lineVec = qPts[(maxEdge + 1)%3] - qPts[maxEdge];
183 // when looking from the point 0 down the line we want positive
184 // distances to be to the left. This matches the non-degenerate
185 // case.
186 lineVec = SkPointPriv::MakeOrthog(lineVec, SkPointPriv::kLeft_Side);
187 // first row
188 fM[0] = 0;
189 fM[1] = 0;
190 fM[2] = 0;
191 // second row
192 fM[3] = lineVec.fX;
193 fM[4] = lineVec.fY;
194 fM[5] = -lineVec.dot(qPts[maxEdge]);
195 } else {
196 // It's a point. It should cover zero area. Just set the matrix such
197 // that (u, v) will always be far away from the quad.
198 fM[0] = 0; fM[1] = 0; fM[2] = 100.f;
199 fM[3] = 0; fM[4] = 0; fM[5] = 100.f;
200 }
201 } else {
202 double scale = 1.0/det;
203
204 // compute adjugate matrix
205 double a3, a4, a6, a7;
206 a3 = y2-y0;
207 a4 = x0-x2;
208
209 a6 = y0-y1;
210 a7 = x1-x0;
211
212 // this performs the uv_pts*adjugate(control_pts) multiply,
213 // then does the scale by 1/det afterwards to improve precision
214 fM[0] = (float)((0.5*a3 + a6)*scale);
215 fM[1] = (float)((0.5*a4 + a7)*scale);
216 fM[2] = (float)((0.5*a5 + a8)*scale);
217 fM[3] = (float)(a6*scale);
218 fM[4] = (float)(a7*scale);
219 fM[5] = (float)(a8*scale);
220 }
221 }
222
223 ////////////////////////////////////////////////////////////////////////////////
224
225 // k = (y2 - y0, x0 - x2, x2*y0 - x0*y2)
226 // l = (y1 - y0, x0 - x1, x1*y0 - x0*y1) * 2*w
227 // m = (y2 - y1, x1 - x2, x2*y1 - x1*y2) * 2*w
getConicKLM(const SkPoint p[3],const SkScalar weight,SkMatrix * out)228 void GrPathUtils::getConicKLM(const SkPoint p[3], const SkScalar weight, SkMatrix* out) {
229 SkMatrix& klm = *out;
230 const SkScalar w2 = 2.f * weight;
231 klm[0] = p[2].fY - p[0].fY;
232 klm[1] = p[0].fX - p[2].fX;
233 klm[2] = p[2].fX * p[0].fY - p[0].fX * p[2].fY;
234
235 klm[3] = w2 * (p[1].fY - p[0].fY);
236 klm[4] = w2 * (p[0].fX - p[1].fX);
237 klm[5] = w2 * (p[1].fX * p[0].fY - p[0].fX * p[1].fY);
238
239 klm[6] = w2 * (p[2].fY - p[1].fY);
240 klm[7] = w2 * (p[1].fX - p[2].fX);
241 klm[8] = w2 * (p[2].fX * p[1].fY - p[1].fX * p[2].fY);
242
243 // scale the max absolute value of coeffs to 10
244 SkScalar scale = 0.f;
245 for (int i = 0; i < 9; ++i) {
246 scale = std::max(scale, SkScalarAbs(klm[i]));
247 }
248 SkASSERT(scale > 0.f);
249 scale = 10.f / scale;
250 for (int i = 0; i < 9; ++i) {
251 klm[i] *= scale;
252 }
253 }
254
255 ////////////////////////////////////////////////////////////////////////////////
256
257 namespace {
258
259 // a is the first control point of the cubic.
260 // ab is the vector from a to the second control point.
261 // dc is the vector from the fourth to the third control point.
262 // d is the fourth control point.
263 // p is the candidate quadratic control point.
264 // this assumes that the cubic doesn't inflect and is simple
is_point_within_cubic_tangents(const SkPoint & a,const SkVector & ab,const SkVector & dc,const SkPoint & d,SkPathFirstDirection dir,const SkPoint p)265 bool is_point_within_cubic_tangents(const SkPoint& a,
266 const SkVector& ab,
267 const SkVector& dc,
268 const SkPoint& d,
269 SkPathFirstDirection dir,
270 const SkPoint p) {
271 SkVector ap = p - a;
272 SkScalar apXab = ap.cross(ab);
273 if (SkPathFirstDirection::kCW == dir) {
274 if (apXab > 0) {
275 return false;
276 }
277 } else {
278 SkASSERT(SkPathFirstDirection::kCCW == dir);
279 if (apXab < 0) {
280 return false;
281 }
282 }
283
284 SkVector dp = p - d;
285 SkScalar dpXdc = dp.cross(dc);
286 if (SkPathFirstDirection::kCW == dir) {
287 if (dpXdc < 0) {
288 return false;
289 }
290 } else {
291 SkASSERT(SkPathFirstDirection::kCCW == dir);
292 if (dpXdc > 0) {
293 return false;
294 }
295 }
296 return true;
297 }
298
convert_noninflect_cubic_to_quads(const SkPoint p[4],SkScalar toleranceSqd,TArray<SkPoint,true> * quads,int sublevel=0,bool preserveFirstTangent=true,bool preserveLastTangent=true)299 void convert_noninflect_cubic_to_quads(const SkPoint p[4],
300 SkScalar toleranceSqd,
301 TArray<SkPoint, true>* quads,
302 int sublevel = 0,
303 bool preserveFirstTangent = true,
304 bool preserveLastTangent = true) {
305 // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is
306 // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1].
307 SkVector ab = p[1] - p[0];
308 SkVector dc = p[2] - p[3];
309
310 if (SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero) {
311 if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) {
312 SkPoint* degQuad = quads->push_back_n(3);
313 degQuad[0] = p[0];
314 degQuad[1] = p[0];
315 degQuad[2] = p[3];
316 return;
317 }
318 ab = p[2] - p[0];
319 }
320 if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) {
321 dc = p[1] - p[3];
322 }
323
324 static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2;
325 static const int kMaxSubdivs = 10;
326
327 ab.scale(kLengthScale);
328 dc.scale(kLengthScale);
329
330 // c0 and c1 are extrapolations along vectors ab and dc.
331 SkPoint c0 = p[0] + ab;
332 SkPoint c1 = p[3] + dc;
333
334 SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : SkPointPriv::DistanceToSqd(c0, c1);
335 if (dSqd < toleranceSqd) {
336 SkPoint newC;
337 if (preserveFirstTangent == preserveLastTangent) {
338 // We used to force a split when both tangents need to be preserved and c0 != c1.
339 // This introduced a large performance regression for tiny paths for no noticeable
340 // quality improvement. However, we aren't quite fulfilling our contract of guaranteeing
341 // the two tangent vectors and this could introduce a missed pixel in
342 // AAHairlinePathRenderer.
343 newC = (c0 + c1) * 0.5f;
344 } else if (preserveFirstTangent) {
345 newC = c0;
346 } else {
347 newC = c1;
348 }
349
350 SkPoint* pts = quads->push_back_n(3);
351 pts[0] = p[0];
352 pts[1] = newC;
353 pts[2] = p[3];
354 return;
355 }
356 SkPoint choppedPts[7];
357 SkChopCubicAtHalf(p, choppedPts);
358 convert_noninflect_cubic_to_quads(
359 choppedPts + 0, toleranceSqd, quads, sublevel + 1, preserveFirstTangent, false);
360 convert_noninflect_cubic_to_quads(
361 choppedPts + 3, toleranceSqd, quads, sublevel + 1, false, preserveLastTangent);
362 }
363
convert_noninflect_cubic_to_quads_with_constraint(const SkPoint p[4],SkScalar toleranceSqd,SkPathFirstDirection dir,TArray<SkPoint,true> * quads,int sublevel=0)364 void convert_noninflect_cubic_to_quads_with_constraint(const SkPoint p[4],
365 SkScalar toleranceSqd,
366 SkPathFirstDirection dir,
367 TArray<SkPoint, true>* quads,
368 int sublevel = 0) {
369 // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is
370 // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1].
371
372 SkVector ab = p[1] - p[0];
373 SkVector dc = p[2] - p[3];
374
375 if (SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero) {
376 if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) {
377 SkPoint* degQuad = quads->push_back_n(3);
378 degQuad[0] = p[0];
379 degQuad[1] = p[0];
380 degQuad[2] = p[3];
381 return;
382 }
383 ab = p[2] - p[0];
384 }
385 if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) {
386 dc = p[1] - p[3];
387 }
388
389 // When the ab and cd tangents are degenerate or nearly parallel with vector from d to a the
390 // constraint that the quad point falls between the tangents becomes hard to enforce and we are
391 // likely to hit the max subdivision count. However, in this case the cubic is approaching a
392 // line and the accuracy of the quad point isn't so important. We check if the two middle cubic
393 // control points are very close to the baseline vector. If so then we just pick quadratic
394 // points on the control polygon.
395
396 SkVector da = p[0] - p[3];
397 bool doQuads = SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero ||
398 SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero;
399 if (!doQuads) {
400 SkScalar invDALengthSqd = SkPointPriv::LengthSqd(da);
401 if (invDALengthSqd > SK_ScalarNearlyZero) {
402 invDALengthSqd = SkScalarInvert(invDALengthSqd);
403 // cross(ab, da)^2/length(da)^2 == sqd distance from b to line from d to a.
404 // same goes for point c using vector cd.
405 SkScalar detABSqd = ab.cross(da);
406 detABSqd = SkScalarSquare(detABSqd);
407 SkScalar detDCSqd = dc.cross(da);
408 detDCSqd = SkScalarSquare(detDCSqd);
409 if (detABSqd * invDALengthSqd < toleranceSqd &&
410 detDCSqd * invDALengthSqd < toleranceSqd) {
411 doQuads = true;
412 }
413 }
414 }
415 if (doQuads) {
416 SkPoint b = p[0] + ab;
417 SkPoint c = p[3] + dc;
418 SkPoint mid = b + c;
419 mid.scale(SK_ScalarHalf);
420 // Insert two quadratics to cover the case when ab points away from d and/or dc
421 // points away from a.
422 if (SkVector::DotProduct(da, dc) < 0 || SkVector::DotProduct(ab, da) > 0) {
423 SkPoint* qpts = quads->push_back_n(6);
424 qpts[0] = p[0];
425 qpts[1] = b;
426 qpts[2] = mid;
427 qpts[3] = mid;
428 qpts[4] = c;
429 qpts[5] = p[3];
430 } else {
431 SkPoint* qpts = quads->push_back_n(3);
432 qpts[0] = p[0];
433 qpts[1] = mid;
434 qpts[2] = p[3];
435 }
436 return;
437 }
438
439 static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2;
440 static const int kMaxSubdivs = 10;
441
442 ab.scale(kLengthScale);
443 dc.scale(kLengthScale);
444
445 // c0 and c1 are extrapolations along vectors ab and dc.
446 SkVector c0 = p[0] + ab;
447 SkVector c1 = p[3] + dc;
448
449 SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : SkPointPriv::DistanceToSqd(c0, c1);
450 if (dSqd < toleranceSqd) {
451 SkPoint cAvg = (c0 + c1) * 0.5f;
452 bool subdivide = false;
453
454 if (!is_point_within_cubic_tangents(p[0], ab, dc, p[3], dir, cAvg)) {
455 // choose a new cAvg that is the intersection of the two tangent lines.
456 ab = SkPointPriv::MakeOrthog(ab);
457 SkScalar z0 = -ab.dot(p[0]);
458 dc = SkPointPriv::MakeOrthog(dc);
459 SkScalar z1 = -dc.dot(p[3]);
460 cAvg.fX = ab.fY * z1 - z0 * dc.fY;
461 cAvg.fY = z0 * dc.fX - ab.fX * z1;
462 SkScalar z = ab.fX * dc.fY - ab.fY * dc.fX;
463 z = sk_ieee_float_divide(1.0f, z);
464 cAvg.fX *= z;
465 cAvg.fY *= z;
466 if (sublevel <= kMaxSubdivs) {
467 SkScalar d0Sqd = SkPointPriv::DistanceToSqd(c0, cAvg);
468 SkScalar d1Sqd = SkPointPriv::DistanceToSqd(c1, cAvg);
469 // We need to subdivide if d0 + d1 > tolerance but we have the sqd values. We know
470 // the distances and tolerance can't be negative.
471 // (d0 + d1)^2 > toleranceSqd
472 // d0Sqd + 2*d0*d1 + d1Sqd > toleranceSqd
473 SkScalar d0d1 = SkScalarSqrt(d0Sqd * d1Sqd);
474 subdivide = 2 * d0d1 + d0Sqd + d1Sqd > toleranceSqd;
475 }
476 }
477 if (!subdivide) {
478 SkPoint* pts = quads->push_back_n(3);
479 pts[0] = p[0];
480 pts[1] = cAvg;
481 pts[2] = p[3];
482 return;
483 }
484 }
485 SkPoint choppedPts[7];
486 SkChopCubicAtHalf(p, choppedPts);
487 convert_noninflect_cubic_to_quads_with_constraint(
488 choppedPts + 0, toleranceSqd, dir, quads, sublevel + 1);
489 convert_noninflect_cubic_to_quads_with_constraint(
490 choppedPts + 3, toleranceSqd, dir, quads, sublevel + 1);
491 }
492 } // namespace
493
convertCubicToQuads(const SkPoint p[4],SkScalar tolScale,TArray<SkPoint,true> * quads)494 void GrPathUtils::convertCubicToQuads(const SkPoint p[4],
495 SkScalar tolScale,
496 TArray<SkPoint, true>* quads) {
497 if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) {
498 return;
499 }
500 if (!SkIsFinite(tolScale)) {
501 return;
502 }
503 SkPoint chopped[10];
504 int count = SkChopCubicAtInflections(p, chopped);
505
506 const SkScalar tolSqd = SkScalarSquare(tolScale);
507
508 for (int i = 0; i < count; ++i) {
509 SkPoint* cubic = chopped + 3*i;
510 convert_noninflect_cubic_to_quads(cubic, tolSqd, quads);
511 }
512 }
513
convertCubicToQuadsConstrainToTangents(const SkPoint p[4],SkScalar tolScale,SkPathFirstDirection dir,TArray<SkPoint,true> * quads)514 void GrPathUtils::convertCubicToQuadsConstrainToTangents(const SkPoint p[4],
515 SkScalar tolScale,
516 SkPathFirstDirection dir,
517 TArray<SkPoint, true>* quads) {
518 if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) {
519 return;
520 }
521 if (!SkIsFinite(tolScale)) {
522 return;
523 }
524 SkPoint chopped[10];
525 int count = SkChopCubicAtInflections(p, chopped);
526
527 const SkScalar tolSqd = SkScalarSquare(tolScale);
528
529 for (int i = 0; i < count; ++i) {
530 SkPoint* cubic = chopped + 3*i;
531 convert_noninflect_cubic_to_quads_with_constraint(cubic, tolSqd, dir, quads);
532 }
533 }
534