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1 /*
2  * Copyright 2020 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 "include/utils/SkRandom.h"
9 #include "src/core/SkGeometry.h"
10 #include "src/gpu/tessellate/WangsFormula.h"
11 #include "tests/Test.h"
12 
13 namespace skgpu {
14 
15 constexpr static float kPrecision = 4;  // 1/4 pixel max error.
16 
17 const SkPoint kSerp[4] = {
18         {285.625f, 499.687f}, {411.625f, 808.188f}, {1064.62f, 135.688f}, {1042.63f, 585.187f}};
19 
20 const SkPoint kLoop[4] = {
21         {635.625f, 614.687f}, {171.625f, 236.188f}, {1064.62f, 135.688f}, {516.625f, 570.187f}};
22 
23 const SkPoint kQuad[4] = {
24         {460.625f, 557.187f}, {707.121f, 209.688f}, {779.628f, 577.687f}};
25 
wangs_formula_quadratic_reference_impl(float precision,const SkPoint p[3])26 static float wangs_formula_quadratic_reference_impl(float precision, const SkPoint p[3]) {
27     float k = (2 * 1) / 8.f * precision;
28     return sqrtf(k * (p[0] - p[1]*2 + p[2]).length());
29 }
30 
wangs_formula_cubic_reference_impl(float precision,const SkPoint p[4])31 static float wangs_formula_cubic_reference_impl(float precision, const SkPoint p[4]) {
32     float k = (3 * 2) / 8.f * precision;
33     return sqrtf(k * std::max((p[0] - p[1]*2 + p[2]).length(),
34                               (p[1] - p[2]*2 + p[3]).length()));
35 }
36 
37 // Returns number of segments for linearized quadratic rational. This is an analogue
38 // to Wang's formula, taken from:
39 //
40 //   J. Zheng, T. Sederberg. "Estimating Tessellation Parameter Intervals for
41 //   Rational Curves and Surfaces." ACM Transactions on Graphics 19(1). 2000.
42 // See Thm 3, Corollary 1.
43 //
44 // Input points should be in projected space.
wangs_formula_conic_reference_impl(float precision,const SkPoint P[3],const float w)45 static float wangs_formula_conic_reference_impl(float precision,
46                                                 const SkPoint P[3],
47                                                 const float w) {
48     // Compute center of bounding box in projected space
49     float min_x = P[0].fX, max_x = min_x,
50           min_y = P[0].fY, max_y = min_y;
51     for (int i = 1; i < 3; i++) {
52         min_x = std::min(min_x, P[i].fX);
53         max_x = std::max(max_x, P[i].fX);
54         min_y = std::min(min_y, P[i].fY);
55         max_y = std::max(max_y, P[i].fY);
56     }
57     const SkPoint C = SkPoint::Make(0.5f * (min_x + max_x), 0.5f * (min_y + max_y));
58 
59     // Translate control points and compute max length
60     SkPoint tP[3] = {P[0] - C, P[1] - C, P[2] - C};
61     float max_len = 0;
62     for (int i = 0; i < 3; i++) {
63         max_len = std::max(max_len, tP[i].length());
64     }
65     SkASSERT(max_len > 0);
66 
67     // Compute delta = parametric step size of linearization
68     const float eps = 1 / precision;
69     const float r_minus_eps = std::max(0.f, max_len - eps);
70     const float min_w = std::min(w, 1.f);
71     const float numer = 4 * min_w * eps;
72     const float denom =
73             (tP[2] - tP[1] * 2 * w + tP[0]).length() + r_minus_eps * std::abs(1 - 2 * w + 1);
74     const float delta = sqrtf(numer / denom);
75 
76     // Return corresponding num segments in the interval [tmin,tmax]
77     constexpr float tmin = 0, tmax = 1;
78     SkASSERT(delta > 0);
79     return (tmax - tmin) / delta;
80 }
81 
for_random_matrices(SkRandom * rand,std::function<void (const SkMatrix &)> f)82 static void for_random_matrices(SkRandom* rand, std::function<void(const SkMatrix&)> f) {
83     SkMatrix m;
84     m.setIdentity();
85     f(m);
86 
87     for (int i = -10; i <= 30; ++i) {
88         for (int j = -10; j <= 30; ++j) {
89             m.setScaleX(std::ldexp(1 + rand->nextF(), i));
90             m.setSkewX(0);
91             m.setSkewY(0);
92             m.setScaleY(std::ldexp(1 + rand->nextF(), j));
93             f(m);
94 
95             m.setScaleX(std::ldexp(1 + rand->nextF(), i));
96             m.setSkewX(std::ldexp(1 + rand->nextF(), (j + i) / 2));
97             m.setSkewY(std::ldexp(1 + rand->nextF(), (j + i) / 2));
98             m.setScaleY(std::ldexp(1 + rand->nextF(), j));
99             f(m);
100         }
101     }
102 }
103 
for_random_beziers(int numPoints,SkRandom * rand,std::function<void (const SkPoint[])> f,int maxExponent=30)104 static void for_random_beziers(int numPoints, SkRandom* rand,
105                                std::function<void(const SkPoint[])> f,
106                                int maxExponent = 30) {
107     SkASSERT(numPoints <= 4);
108     SkPoint pts[4];
109     for (int i = -10; i <= maxExponent; ++i) {
110         for (int j = 0; j < numPoints; ++j) {
111             pts[j].set(std::ldexp(1 + rand->nextF(), i), std::ldexp(1 + rand->nextF(), i));
112         }
113         f(pts);
114     }
115 }
116 
117 // Ensure the optimized "*_log2" versions return the same value as ceil(std::log2(f)).
DEF_TEST(wangs_formula_log2,r)118 DEF_TEST(wangs_formula_log2, r) {
119     // Constructs a cubic such that the 'length' term in wang's formula == term.
120     //
121     //     f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
122     //                             abs(p1 - p2*2 + p3))));
123     auto setupCubicLengthTerm = [](int seed, SkPoint pts[], float term) {
124         memset(pts, 0, sizeof(SkPoint) * 4);
125 
126         SkPoint term2d = (seed & 1) ?
127                 SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
128         seed >>= 1;
129 
130         if (seed & 1) {
131             term2d.fX = -term2d.fX;
132         }
133         seed >>= 1;
134 
135         if (seed & 1) {
136             std::swap(term2d.fX, term2d.fY);
137         }
138         seed >>= 1;
139 
140         switch (seed % 4) {
141             case 0:
142                 pts[0] = term2d;
143                 pts[3] = term2d * .75f;
144                 return;
145             case 1:
146                 pts[1] = term2d * -.5f;
147                 return;
148             case 2:
149                 pts[1] = term2d * -.5f;
150                 return;
151             case 3:
152                 pts[3] = term2d;
153                 pts[0] = term2d * .75f;
154                 return;
155         }
156     };
157 
158     // Constructs a quadratic such that the 'length' term in wang's formula == term.
159     //
160     //     f = sqrt(k * length(p0 - p1*2 + p2));
161     auto setupQuadraticLengthTerm = [](int seed, SkPoint pts[], float term) {
162         memset(pts, 0, sizeof(SkPoint) * 3);
163 
164         SkPoint term2d = (seed & 1) ?
165                 SkPoint::Make(term, 0) : SkPoint::Make(.5f, std::sqrt(3)/2) * term;
166         seed >>= 1;
167 
168         if (seed & 1) {
169             term2d.fX = -term2d.fX;
170         }
171         seed >>= 1;
172 
173         if (seed & 1) {
174             std::swap(term2d.fX, term2d.fY);
175         }
176         seed >>= 1;
177 
178         switch (seed % 3) {
179             case 0:
180                 pts[0] = term2d;
181                 return;
182             case 1:
183                 pts[1] = term2d * -.5f;
184                 return;
185             case 2:
186                 pts[2] = term2d;
187                 return;
188         }
189     };
190 
191     // wangs_formula_cubic and wangs_formula_quadratic both use rsqrt instead of sqrt for speed.
192     // Linearization is all approximate anyway, so as long as we are within ~1/2 tessellation
193     // segment of the reference value we are good enough.
194     constexpr static float kTessellationTolerance = 1/128.f;
195 
196     for (int level = 0; level < 30; ++level) {
197         float epsilon = std::ldexp(SK_ScalarNearlyZero, level * 2);
198         SkPoint pts[4];
199 
200         {
201             // Test cubic boundaries.
202             //     f = sqrt(k * length(max(abs(p0 - p1*2 + p2),
203             //                             abs(p1 - p2*2 + p3))));
204             constexpr static float k = (3 * 2) / (8 * (1.f/kPrecision));
205             float x = std::ldexp(1, level * 2) / k;
206             setupCubicLengthTerm(level << 1, pts, x - epsilon);
207             float referenceValue = wangs_formula_cubic_reference_impl(kPrecision, pts);
208             REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level);
209             float c = wangs_formula::cubic(kPrecision, pts);
210             REPORTER_ASSERT(r, SkScalarNearlyEqual(c/referenceValue, 1, kTessellationTolerance));
211             REPORTER_ASSERT(r, wangs_formula::cubic_log2(kPrecision, pts) == level);
212             setupCubicLengthTerm(level << 1, pts, x + epsilon);
213             referenceValue = wangs_formula_cubic_reference_impl(kPrecision, pts);
214             REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level + 1);
215             c = wangs_formula::cubic(kPrecision, pts);
216             REPORTER_ASSERT(r, SkScalarNearlyEqual(c/referenceValue, 1, kTessellationTolerance));
217             REPORTER_ASSERT(r, wangs_formula::cubic_log2(kPrecision, pts) == level + 1);
218         }
219 
220         {
221             // Test quadratic boundaries.
222             //     f = std::sqrt(k * Length(p0 - p1*2 + p2));
223             constexpr static float k = 2 / (8 * (1.f/kPrecision));
224             float x = std::ldexp(1, level * 2) / k;
225             setupQuadraticLengthTerm(level << 1, pts, x - epsilon);
226             float referenceValue = wangs_formula_quadratic_reference_impl(kPrecision, pts);
227             REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level);
228             float q = wangs_formula::quadratic(kPrecision, pts);
229             REPORTER_ASSERT(r, SkScalarNearlyEqual(q/referenceValue, 1, kTessellationTolerance));
230             REPORTER_ASSERT(r, wangs_formula::quadratic_log2(kPrecision, pts) == level);
231             setupQuadraticLengthTerm(level << 1, pts, x + epsilon);
232             referenceValue = wangs_formula_quadratic_reference_impl(kPrecision, pts);
233             REPORTER_ASSERT(r, std::ceil(std::log2(referenceValue)) == level+1);
234             q = wangs_formula::quadratic(kPrecision, pts);
235             REPORTER_ASSERT(r, SkScalarNearlyEqual(q/referenceValue, 1, kTessellationTolerance));
236             REPORTER_ASSERT(r, wangs_formula::quadratic_log2(kPrecision, pts) == level + 1);
237         }
238     }
239 
240     auto check_cubic_log2 = [&](const SkPoint* pts) {
241         float f = std::max(1.f, wangs_formula_cubic_reference_impl(kPrecision, pts));
242         int f_log2 = wangs_formula::cubic_log2(kPrecision, pts);
243         REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
244         float c = std::max(1.f, wangs_formula::cubic(kPrecision, pts));
245         REPORTER_ASSERT(r, SkScalarNearlyEqual(c/f, 1, kTessellationTolerance));
246     };
247 
248     auto check_quadratic_log2 = [&](const SkPoint* pts) {
249         float f = std::max(1.f, wangs_formula_quadratic_reference_impl(kPrecision, pts));
250         int f_log2 = wangs_formula::quadratic_log2(kPrecision, pts);
251         REPORTER_ASSERT(r, SkScalarCeilToInt(std::log2(f)) == f_log2);
252         float q = std::max(1.f, wangs_formula::quadratic(kPrecision, pts));
253         REPORTER_ASSERT(r, SkScalarNearlyEqual(q/f, 1, kTessellationTolerance));
254     };
255 
256     SkRandom rand;
257 
258     for_random_matrices(&rand, [&](const SkMatrix& m) {
259         SkPoint pts[4];
260         m.mapPoints(pts, kSerp, 4);
261         check_cubic_log2(pts);
262 
263         m.mapPoints(pts, kLoop, 4);
264         check_cubic_log2(pts);
265 
266         m.mapPoints(pts, kQuad, 3);
267         check_quadratic_log2(pts);
268     });
269 
270     for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
271         check_cubic_log2(pts);
272     });
273 
274     for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
275         check_quadratic_log2(pts);
276     });
277 }
278 
279 // Ensure using transformations gives the same result as pre-transforming all points.
DEF_TEST(wangs_formula_vectorXforms,r)280 DEF_TEST(wangs_formula_vectorXforms, r) {
281     auto check_cubic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m){
282         SkPoint ptsXformed[4];
283         m.mapPoints(ptsXformed, pts, 4);
284         int expected = wangs_formula::cubic_log2(kPrecision, ptsXformed);
285         int actual = wangs_formula::cubic_log2(kPrecision, pts, wangs_formula::VectorXform(m));
286         REPORTER_ASSERT(r, actual == expected);
287     };
288 
289     auto check_quadratic_log2_with_transform = [&](const SkPoint* pts, const SkMatrix& m) {
290         SkPoint ptsXformed[3];
291         m.mapPoints(ptsXformed, pts, 3);
292         int expected = wangs_formula::quadratic_log2(kPrecision, ptsXformed);
293         int actual = wangs_formula::quadratic_log2(kPrecision, pts, wangs_formula::VectorXform(m));
294         REPORTER_ASSERT(r, actual == expected);
295     };
296 
297     SkRandom rand;
298 
299     for_random_matrices(&rand, [&](const SkMatrix& m) {
300         check_cubic_log2_with_transform(kSerp, m);
301         check_cubic_log2_with_transform(kLoop, m);
302         check_quadratic_log2_with_transform(kQuad, m);
303 
304         for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
305             check_cubic_log2_with_transform(pts, m);
306         });
307 
308         for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
309             check_quadratic_log2_with_transform(pts, m);
310         });
311     });
312 }
313 
DEF_TEST(wangs_formula_worst_case_cubic,r)314 DEF_TEST(wangs_formula_worst_case_cubic, r) {
315     {
316         SkPoint worstP[] = {{0,0}, {100,100}, {0,0}, {0,0}};
317         REPORTER_ASSERT(r, wangs_formula::worst_case_cubic(kPrecision, 100, 100) ==
318                            wangs_formula_cubic_reference_impl(kPrecision, worstP));
319         REPORTER_ASSERT(r, wangs_formula::worst_case_cubic_log2(kPrecision, 100, 100) ==
320                            wangs_formula::cubic_log2(kPrecision, worstP));
321     }
322     {
323         SkPoint worstP[] = {{100,100}, {100,100}, {200,200}, {100,100}};
324         REPORTER_ASSERT(r, wangs_formula::worst_case_cubic(kPrecision, 100, 100) ==
325                            wangs_formula_cubic_reference_impl(kPrecision, worstP));
326         REPORTER_ASSERT(r, wangs_formula::worst_case_cubic_log2(kPrecision, 100, 100) ==
327                            wangs_formula::cubic_log2(kPrecision, worstP));
328     }
329     auto check_worst_case_cubic = [&](const SkPoint* pts) {
330         SkRect bbox;
331         bbox.setBoundsNoCheck(pts, 4);
332         float worst = wangs_formula::worst_case_cubic(kPrecision, bbox.width(), bbox.height());
333         int worst_log2 = wangs_formula::worst_case_cubic_log2(kPrecision, bbox.width(),
334                                                                bbox.height());
335         float actual = wangs_formula_cubic_reference_impl(kPrecision, pts);
336         REPORTER_ASSERT(r, worst >= actual);
337         REPORTER_ASSERT(r, std::ceil(std::log2(std::max(1.f, worst))) == worst_log2);
338     };
339     SkRandom rand;
340     for (int i = 0; i < 100; ++i) {
341         for_random_beziers(4, &rand, [&](const SkPoint pts[]) {
342             check_worst_case_cubic(pts);
343         });
344     }
345     // Make sure overflow saturates at infinity (not NaN).
346     constexpr static float inf = std::numeric_limits<float>::infinity();
347     REPORTER_ASSERT(r, wangs_formula::worst_case_cubic_pow4(kPrecision, inf, inf) == inf);
348     REPORTER_ASSERT(r, wangs_formula::worst_case_cubic(kPrecision, inf, inf) == inf);
349 }
350 
351 // Ensure Wang's formula for quads produces max error within tolerance.
DEF_TEST(wangs_formula_quad_within_tol,r)352 DEF_TEST(wangs_formula_quad_within_tol, r) {
353     // Wang's formula and the quad math starts to lose precision with very large
354     // coordinate values, so limit the magnitude a bit to prevent test failures
355     // due to loss of precision.
356     constexpr int maxExponent = 15;
357     SkRandom rand;
358     for_random_beziers(3, &rand, [&r](const SkPoint pts[]) {
359         const int nsegs = static_cast<int>(
360                 std::ceil(wangs_formula_quadratic_reference_impl(kPrecision, pts)));
361 
362         const float tdelta = 1.f / nsegs;
363         for (int j = 0; j < nsegs; ++j) {
364             const float tmin = j * tdelta, tmax = (j + 1) * tdelta;
365 
366             // Get section of quad in [tmin,tmax]
367             const SkPoint* sectionPts;
368             SkPoint tmp0[5];
369             SkPoint tmp1[5];
370             if (tmin == 0) {
371                 if (tmax == 1) {
372                     sectionPts = pts;
373                 } else {
374                     SkChopQuadAt(pts, tmp0, tmax);
375                     sectionPts = tmp0;
376                 }
377             } else {
378                 SkChopQuadAt(pts, tmp0, tmin);
379                 if (tmax == 1) {
380                     sectionPts = tmp0 + 2;
381                 } else {
382                     SkChopQuadAt(tmp0 + 2, tmp1, (tmax - tmin) / (1 - tmin));
383                     sectionPts = tmp1;
384                 }
385             }
386 
387             // For quads, max distance from baseline is always at t=0.5.
388             SkPoint p;
389             p = SkEvalQuadAt(sectionPts, 0.5f);
390 
391             // Get distance of p to baseline
392             const SkPoint n = {sectionPts[2].fY - sectionPts[0].fY,
393                                sectionPts[0].fX - sectionPts[2].fX};
394             const float d = std::abs((p - sectionPts[0]).dot(n)) / n.length();
395 
396             // Check distance is within specified tolerance
397             REPORTER_ASSERT(r, d <= (1.f / kPrecision) + SK_ScalarNearlyZero);
398         }
399     }, maxExponent);
400 }
401 
402 // Ensure the specialized version for rational quads reduces to regular Wang's
403 // formula when all weights are equal to one
DEF_TEST(wangs_formula_rational_quad_reduces,r)404 DEF_TEST(wangs_formula_rational_quad_reduces, r) {
405     constexpr static float kTessellationTolerance = 1 / 128.f;
406 
407     SkRandom rand;
408     for (int i = 0; i < 100; ++i) {
409         for_random_beziers(3, &rand, [&r](const SkPoint pts[]) {
410             const float rational_nsegs = wangs_formula::conic(kPrecision, pts, 1.f);
411             const float integral_nsegs = wangs_formula_quadratic_reference_impl(kPrecision, pts);
412             REPORTER_ASSERT(
413                     r, SkScalarNearlyEqual(rational_nsegs, integral_nsegs, kTessellationTolerance));
414         });
415     }
416 }
417 
418 // Ensure the rational quad version (used for conics) produces max error within tolerance.
DEF_TEST(wangs_formula_conic_within_tol,r)419 DEF_TEST(wangs_formula_conic_within_tol, r) {
420     constexpr int maxExponent = 24;
421 
422     // Single-precision functions in SkConic/SkGeometry lose too much accuracy with
423     // large-magnitude curves and large weights for this test to pass.
424     using Sk2d = skvx::Vec<2, double>;
425     const auto eval_conic = [](const SkPoint pts[3], float w, float t) -> Sk2d {
426         const auto eval = [](Sk2d A, Sk2d B, Sk2d C, float t) -> Sk2d {
427             return (A * t + B) * t + C;
428         };
429 
430         const Sk2d p0 = {pts[0].fX, pts[0].fY};
431         const Sk2d p1 = {pts[1].fX, pts[1].fY};
432         const Sk2d p1w = p1 * w;
433         const Sk2d p2 = {pts[2].fX, pts[2].fY};
434         Sk2d numer = eval(p2 - p1w * 2 + p0, (p1w - p0) * 2, p0, t);
435 
436         Sk2d denomC = {1, 1};
437         Sk2d denomB = {2 * (w - 1), 2 * (w - 1)};
438         Sk2d denomA = {-2 * (w - 1), -2 * (w - 1)};
439         Sk2d denom = eval(denomA, denomB, denomC, t);
440         return numer / denom;
441     };
442 
443     const auto dot = [](const Sk2d& a, const Sk2d& b) -> double {
444         return a[0] * b[0] + a[1] * b[1];
445     };
446 
447     const auto length = [](const Sk2d& p) -> double { return sqrt(p[0] * p[0] + p[1] * p[1]); };
448 
449     SkRandom rand;
450     for (int i = -10; i <= 10; ++i) {
451         const float w = std::ldexp(1 + rand.nextF(), i);
452         for_random_beziers(
453                 3, &rand,
454                 [&](const SkPoint pts[]) {
455                     const int nsegs = SkScalarCeilToInt(wangs_formula::conic(kPrecision, pts, w));
456 
457                     const float tdelta = 1.f / nsegs;
458                     for (int j = 0; j < nsegs; ++j) {
459                         const float tmin = j * tdelta, tmax = (j + 1) * tdelta,
460                                     tmid = 0.5f * (tmin + tmax);
461 
462                         Sk2d p0, p1, p2;
463                         p0 = eval_conic(pts, w, tmin);
464                         p1 = eval_conic(pts, w, tmid);
465                         p2 = eval_conic(pts, w, tmax);
466 
467                         // Get distance of p1 to baseline (p0, p2).
468                         const Sk2d n = {p2[1] - p0[1], p0[0] - p2[0]};
469                         SkASSERT(length(n) != 0);
470                         const double d = std::abs(dot(p1 - p0, n)) / length(n);
471 
472                         // Check distance is within tolerance
473                         REPORTER_ASSERT(r, d <= (1.0 / kPrecision) + SK_ScalarNearlyZero);
474                     }
475                 },
476                 maxExponent);
477     }
478 }
479 
480 // Ensure the vectorized conic version equals the reference implementation
DEF_TEST(wangs_formula_conic_matches_reference,r)481 DEF_TEST(wangs_formula_conic_matches_reference, r) {
482     SkRandom rand;
483     for (int i = -10; i <= 10; ++i) {
484         const float w = std::ldexp(1 + rand.nextF(), i);
485         for_random_beziers(3, &rand, [&r, w](const SkPoint pts[]) {
486             const float ref_nsegs = wangs_formula_conic_reference_impl(kPrecision, pts, w);
487             const float nsegs = wangs_formula::conic(kPrecision, pts, w);
488 
489             // Because the Gr version may implement the math differently for performance,
490             // allow different slack in the comparison based on the rough scale of the answer.
491             const float cmpThresh = ref_nsegs * (1.f / (1 << 20));
492             REPORTER_ASSERT(r, SkScalarNearlyEqual(ref_nsegs, nsegs, cmpThresh));
493         });
494     }
495 }
496 
497 // Ensure using transformations gives the same result as pre-transforming all points.
DEF_TEST(wangs_formula_conic_vectorXforms,r)498 DEF_TEST(wangs_formula_conic_vectorXforms, r) {
499     auto check_conic_with_transform = [&](const SkPoint* pts, float w, const SkMatrix& m) {
500         SkPoint ptsXformed[3];
501         m.mapPoints(ptsXformed, pts, 3);
502         float expected = wangs_formula::conic(kPrecision, ptsXformed, w);
503         float actual = wangs_formula::conic(kPrecision, pts, w, wangs_formula::VectorXform(m));
504         REPORTER_ASSERT(r, SkScalarNearlyEqual(actual, expected));
505     };
506 
507     SkRandom rand;
508     for (int i = -10; i <= 10; ++i) {
509         const float w = std::ldexp(1 + rand.nextF(), i);
510         for_random_beziers(3, &rand, [&](const SkPoint pts[]) {
511             check_conic_with_transform(pts, w, SkMatrix::I());
512             check_conic_with_transform(
513                     pts, w, SkMatrix::Scale(rand.nextRangeF(-10, 10), rand.nextRangeF(-10, 10)));
514 
515             // Random 2x2 matrix
516             SkMatrix m;
517             m.setScaleX(rand.nextRangeF(-10, 10));
518             m.setSkewX(rand.nextRangeF(-10, 10));
519             m.setSkewY(rand.nextRangeF(-10, 10));
520             m.setScaleY(rand.nextRangeF(-10, 10));
521             check_conic_with_transform(pts, w, m);
522         });
523     }
524 }
525 
526 }  // namespace skgpu
527