1 /*
2 * Copyright 2014 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 "SkPatchUtils.h"
9
10 #include "SkColorData.h"
11 #include "SkGeometry.h"
12 #include "SkPM4f.h"
13
14 namespace {
15 enum CubicCtrlPts {
16 kTopP0_CubicCtrlPts = 0,
17 kTopP1_CubicCtrlPts = 1,
18 kTopP2_CubicCtrlPts = 2,
19 kTopP3_CubicCtrlPts = 3,
20
21 kRightP0_CubicCtrlPts = 3,
22 kRightP1_CubicCtrlPts = 4,
23 kRightP2_CubicCtrlPts = 5,
24 kRightP3_CubicCtrlPts = 6,
25
26 kBottomP0_CubicCtrlPts = 9,
27 kBottomP1_CubicCtrlPts = 8,
28 kBottomP2_CubicCtrlPts = 7,
29 kBottomP3_CubicCtrlPts = 6,
30
31 kLeftP0_CubicCtrlPts = 0,
32 kLeftP1_CubicCtrlPts = 11,
33 kLeftP2_CubicCtrlPts = 10,
34 kLeftP3_CubicCtrlPts = 9,
35 };
36
37 // Enum for corner also clockwise.
38 enum Corner {
39 kTopLeft_Corner = 0,
40 kTopRight_Corner,
41 kBottomRight_Corner,
42 kBottomLeft_Corner
43 };
44 }
45
46 /**
47 * Evaluator to sample the values of a cubic bezier using forward differences.
48 * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
49 * adding precalculated values.
50 * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
51 * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
52 * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After
53 * obtaining this value (mh) we could just add this constant step to our first sampled point
54 * to compute the next one.
55 *
56 * For the cubic case the first difference gives as a result a quadratic polynomial to which we can
57 * apply again forward differences and get linear function to which we can apply again forward
58 * differences to get a constant difference. This is why we keep an array of size 4, the 0th
59 * position keeps the sampled value while the next ones keep the quadratic, linear and constant
60 * difference values.
61 */
62
63 class FwDCubicEvaluator {
64
65 public:
66
67 /**
68 * Receives the 4 control points of the cubic bezier.
69 */
70
FwDCubicEvaluator(const SkPoint points[4])71 explicit FwDCubicEvaluator(const SkPoint points[4])
72 : fCoefs(points) {
73 memcpy(fPoints, points, 4 * sizeof(SkPoint));
74
75 this->restart(1);
76 }
77
78 /**
79 * Restarts the forward differences evaluator to the first value of t = 0.
80 */
restart(int divisions)81 void restart(int divisions) {
82 fDivisions = divisions;
83 fCurrent = 0;
84 fMax = fDivisions + 1;
85 Sk2s h = Sk2s(1.f / fDivisions);
86 Sk2s h2 = h * h;
87 Sk2s h3 = h2 * h;
88 Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3;
89 fFwDiff[3] = to_point(fwDiff3);
90 fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2);
91 fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h);
92 fFwDiff[0] = to_point(fCoefs.fD);
93 }
94
95 /**
96 * Check if the evaluator is still within the range of 0<=t<=1
97 */
done() const98 bool done() const {
99 return fCurrent > fMax;
100 }
101
102 /**
103 * Call next to obtain the SkPoint sampled and move to the next one.
104 */
next()105 SkPoint next() {
106 SkPoint point = fFwDiff[0];
107 fFwDiff[0] += fFwDiff[1];
108 fFwDiff[1] += fFwDiff[2];
109 fFwDiff[2] += fFwDiff[3];
110 fCurrent++;
111 return point;
112 }
113
getCtrlPoints() const114 const SkPoint* getCtrlPoints() const {
115 return fPoints;
116 }
117
118 private:
119 SkCubicCoeff fCoefs;
120 int fMax, fCurrent, fDivisions;
121 SkPoint fFwDiff[4], fPoints[4];
122 };
123
124 ////////////////////////////////////////////////////////////////////////////////
125
126 // size in pixels of each partition per axis, adjust this knob
127 static const int kPartitionSize = 10;
128
129 /**
130 * Calculate the approximate arc length given a bezier curve's control points.
131 */
approx_arc_length(SkPoint * points,int count)132 static SkScalar approx_arc_length(SkPoint* points, int count) {
133 if (count < 2) {
134 return 0;
135 }
136 SkScalar arcLength = 0;
137 for (int i = 0; i < count - 1; i++) {
138 arcLength += SkPoint::Distance(points[i], points[i + 1]);
139 }
140 return arcLength;
141 }
142
bilerp(SkScalar tx,SkScalar ty,SkScalar c00,SkScalar c10,SkScalar c01,SkScalar c11)143 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
144 SkScalar c11) {
145 SkScalar a = c00 * (1.f - tx) + c10 * tx;
146 SkScalar b = c01 * (1.f - tx) + c11 * tx;
147 return a * (1.f - ty) + b * ty;
148 }
149
bilerp(SkScalar tx,SkScalar ty,const Sk4f & c00,const Sk4f & c10,const Sk4f & c01,const Sk4f & c11)150 static Sk4f bilerp(SkScalar tx, SkScalar ty,
151 const Sk4f& c00, const Sk4f& c10, const Sk4f& c01, const Sk4f& c11) {
152 Sk4f a = c00 * (1.f - tx) + c10 * tx;
153 Sk4f b = c01 * (1.f - tx) + c11 * tx;
154 return a * (1.f - ty) + b * ty;
155 }
156
GetLevelOfDetail(const SkPoint cubics[12],const SkMatrix * matrix)157 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
158
159 // Approximate length of each cubic.
160 SkPoint pts[kNumPtsCubic];
161 SkPatchUtils::GetTopCubic(cubics, pts);
162 matrix->mapPoints(pts, kNumPtsCubic);
163 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
164
165 SkPatchUtils::GetBottomCubic(cubics, pts);
166 matrix->mapPoints(pts, kNumPtsCubic);
167 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
168
169 SkPatchUtils::GetLeftCubic(cubics, pts);
170 matrix->mapPoints(pts, kNumPtsCubic);
171 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
172
173 SkPatchUtils::GetRightCubic(cubics, pts);
174 matrix->mapPoints(pts, kNumPtsCubic);
175 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
176
177 // Level of detail per axis, based on the larger side between top and bottom or left and right
178 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
179 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
180
181 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
182 }
183
GetTopCubic(const SkPoint cubics[12],SkPoint points[4])184 void SkPatchUtils::GetTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
185 points[0] = cubics[kTopP0_CubicCtrlPts];
186 points[1] = cubics[kTopP1_CubicCtrlPts];
187 points[2] = cubics[kTopP2_CubicCtrlPts];
188 points[3] = cubics[kTopP3_CubicCtrlPts];
189 }
190
GetBottomCubic(const SkPoint cubics[12],SkPoint points[4])191 void SkPatchUtils::GetBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
192 points[0] = cubics[kBottomP0_CubicCtrlPts];
193 points[1] = cubics[kBottomP1_CubicCtrlPts];
194 points[2] = cubics[kBottomP2_CubicCtrlPts];
195 points[3] = cubics[kBottomP3_CubicCtrlPts];
196 }
197
GetLeftCubic(const SkPoint cubics[12],SkPoint points[4])198 void SkPatchUtils::GetLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
199 points[0] = cubics[kLeftP0_CubicCtrlPts];
200 points[1] = cubics[kLeftP1_CubicCtrlPts];
201 points[2] = cubics[kLeftP2_CubicCtrlPts];
202 points[3] = cubics[kLeftP3_CubicCtrlPts];
203 }
204
GetRightCubic(const SkPoint cubics[12],SkPoint points[4])205 void SkPatchUtils::GetRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
206 points[0] = cubics[kRightP0_CubicCtrlPts];
207 points[1] = cubics[kRightP1_CubicCtrlPts];
208 points[2] = cubics[kRightP2_CubicCtrlPts];
209 points[3] = cubics[kRightP3_CubicCtrlPts];
210 }
211
212 #include "SkPM4fPriv.h"
213 #include "SkColorSpaceXform.h"
214
215 struct SkRGBAf {
216 float fVec[4];
217
From4fSkRGBAf218 static SkRGBAf From4f(const Sk4f& x) {
219 SkRGBAf c;
220 x.store(c.fVec);
221 return c;
222 }
223
FromBGRA32SkRGBAf224 static SkRGBAf FromBGRA32(SkColor c) {
225 return From4f(swizzle_rb(SkNx_cast<float>(Sk4b::Load(&c)) * (1/255.0f)));
226 }
227
to4fSkRGBAf228 Sk4f to4f() const {
229 return Sk4f::Load(fVec);
230 }
231
toBGRA32SkRGBAf232 SkColor toBGRA32() const {
233 SkColor color;
234 SkNx_cast<uint8_t>(swizzle_rb(this->to4f()) * Sk4f(255) + Sk4f(0.5f)).store(&color);
235 return color;
236 }
237
premulSkRGBAf238 SkRGBAf premul() const {
239 float a = fVec[3];
240 return From4f(this->to4f() * Sk4f(a, a, a, 1));
241 }
242
unpremulSkRGBAf243 SkRGBAf unpremul() const {
244 float a = fVec[3];
245 float inv = a ? 1/a : 0;
246 return From4f(this->to4f() * Sk4f(inv, inv, inv, 1));
247 }
248 };
249
skcolor_to_linear(SkRGBAf dst[],const SkColor src[],int count,SkColorSpace * cs,bool doPremul)250 static void skcolor_to_linear(SkRGBAf dst[], const SkColor src[], int count, SkColorSpace* cs,
251 bool doPremul) {
252 if (cs) {
253 auto srcCS = SkColorSpace::MakeSRGB();
254 auto dstCS = cs->makeLinearGamma();
255 auto op = doPremul ? SkColorSpaceXform::kPremul_AlphaOp
256 : SkColorSpaceXform::kPreserve_AlphaOp;
257 SkColorSpaceXform::Apply(dstCS.get(), SkColorSpaceXform::kRGBA_F32_ColorFormat, dst,
258 srcCS.get(), SkColorSpaceXform::kBGRA_8888_ColorFormat, src,
259 count, op);
260 } else {
261 for (int i = 0; i < count; ++i) {
262 dst[i] = SkRGBAf::FromBGRA32(src[i]);
263 if (doPremul) {
264 dst[i] = dst[i].premul();
265 }
266 }
267 }
268 }
269
linear_to_skcolor(SkColor dst[],const SkRGBAf src[],int count,SkColorSpace * cs)270 static void linear_to_skcolor(SkColor dst[], const SkRGBAf src[], int count, SkColorSpace* cs) {
271 if (cs) {
272 auto srcCS = cs->makeLinearGamma();
273 auto dstCS = SkColorSpace::MakeSRGB();
274 SkColorSpaceXform::Apply(dstCS.get(), SkColorSpaceXform::kBGRA_8888_ColorFormat, dst,
275 srcCS.get(), SkColorSpaceXform::kRGBA_F32_ColorFormat, src,
276 count, SkColorSpaceXform::kPreserve_AlphaOp);
277 } else {
278 for (int i = 0; i < count; ++i) {
279 dst[i] = src[i].toBGRA32();
280 }
281 }
282 }
283
unpremul(SkRGBAf array[],int count)284 static void unpremul(SkRGBAf array[], int count) {
285 for (int i = 0; i < count; ++i) {
286 array[i] = array[i].unpremul();
287 }
288 }
289
MakeVertices(const SkPoint cubics[12],const SkColor srcColors[4],const SkPoint srcTexCoords[4],int lodX,int lodY,bool interpColorsLinearly)290 sk_sp<SkVertices> SkPatchUtils::MakeVertices(const SkPoint cubics[12], const SkColor srcColors[4],
291 const SkPoint srcTexCoords[4], int lodX, int lodY,
292 bool interpColorsLinearly) {
293 if (lodX < 1 || lodY < 1 || nullptr == cubics) {
294 return nullptr;
295 }
296
297 // check for overflow in multiplication
298 const int64_t lodX64 = (lodX + 1),
299 lodY64 = (lodY + 1),
300 mult64 = lodX64 * lodY64;
301 if (mult64 > SK_MaxS32) {
302 return nullptr;
303 }
304
305 int vertexCount = SkToS32(mult64);
306 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
307 // more than 60000 indices. To accomplish that we resize the LOD and vertex count
308 if (vertexCount > 10000 || lodX > 200 || lodY > 200) {
309 float weightX = static_cast<float>(lodX) / (lodX + lodY);
310 float weightY = static_cast<float>(lodY) / (lodX + lodY);
311
312 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
313 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
314 lodX = static_cast<int>(weightX * 200);
315 lodY = static_cast<int>(weightY * 200);
316 vertexCount = (lodX + 1) * (lodY + 1);
317 }
318 const int indexCount = lodX * lodY * 6;
319 uint32_t flags = 0;
320 if (srcTexCoords) {
321 flags |= SkVertices::kHasTexCoords_BuilderFlag;
322 }
323 if (srcColors) {
324 flags |= SkVertices::kHasColors_BuilderFlag;
325 }
326
327 SkSTArenaAlloc<2048> alloc;
328 SkRGBAf* cornerColors = srcColors ? alloc.makeArray<SkRGBAf>(4) : nullptr;
329 SkRGBAf* tmpColors = srcColors ? alloc.makeArray<SkRGBAf>(vertexCount) : nullptr;
330 auto convertCS = interpColorsLinearly ? SkColorSpace::MakeSRGB() : nullptr;
331
332 SkVertices::Builder builder(SkVertices::kTriangles_VertexMode, vertexCount, indexCount, flags);
333 SkPoint* pos = builder.positions();
334 SkPoint* texs = builder.texCoords();
335 uint16_t* indices = builder.indices();
336 bool is_opaque = false;
337
338 /*
339 * 1. Should we offer this as a runtime choice, as we do in gradients?
340 * 2. Since drawing the vertices wants premul, shoudl we extend SkVertices to store
341 * premul colors (as floats, w/ a colorspace)?
342 */
343 bool doPremul = true;
344 if (cornerColors) {
345 SkColor c = ~0;
346 for (int i = 0; i < kNumCorners; i++) {
347 c &= srcColors[i];
348 }
349 is_opaque = (SkColorGetA(c) == 0xFF);
350 if (is_opaque) {
351 doPremul = false; // no need
352 }
353
354 skcolor_to_linear(cornerColors, srcColors, kNumCorners, convertCS.get(), doPremul);
355 }
356
357 SkPoint pts[kNumPtsCubic];
358 SkPatchUtils::GetBottomCubic(cubics, pts);
359 FwDCubicEvaluator fBottom(pts);
360 SkPatchUtils::GetTopCubic(cubics, pts);
361 FwDCubicEvaluator fTop(pts);
362 SkPatchUtils::GetLeftCubic(cubics, pts);
363 FwDCubicEvaluator fLeft(pts);
364 SkPatchUtils::GetRightCubic(cubics, pts);
365 FwDCubicEvaluator fRight(pts);
366
367 fBottom.restart(lodX);
368 fTop.restart(lodX);
369
370 SkScalar u = 0.0f;
371 int stride = lodY + 1;
372 for (int x = 0; x <= lodX; x++) {
373 SkPoint bottom = fBottom.next(), top = fTop.next();
374 fLeft.restart(lodY);
375 fRight.restart(lodY);
376 SkScalar v = 0.f;
377 for (int y = 0; y <= lodY; y++) {
378 int dataIndex = x * (lodY + 1) + y;
379
380 SkPoint left = fLeft.next(), right = fRight.next();
381
382 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
383 (1.0f - v) * top.y() + v * bottom.y());
384 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
385 (1.0f - u) * left.y() + u * right.y());
386 SkPoint s2 = SkPoint::Make(
387 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
388 + u * fTop.getCtrlPoints()[3].x())
389 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
390 + u * fBottom.getCtrlPoints()[3].x()),
391 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
392 + u * fTop.getCtrlPoints()[3].y())
393 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
394 + u * fBottom.getCtrlPoints()[3].y()));
395 pos[dataIndex] = s0 + s1 - s2;
396
397 if (cornerColors) {
398 bilerp(u, v, cornerColors[kTopLeft_Corner].to4f(),
399 cornerColors[kTopRight_Corner].to4f(),
400 cornerColors[kBottomLeft_Corner].to4f(),
401 cornerColors[kBottomRight_Corner].to4f()).store(tmpColors[dataIndex].fVec);
402 if (is_opaque) {
403 tmpColors[dataIndex].fVec[3] = 1;
404 }
405 }
406
407 if (texs) {
408 texs[dataIndex] = SkPoint::Make(bilerp(u, v, srcTexCoords[kTopLeft_Corner].x(),
409 srcTexCoords[kTopRight_Corner].x(),
410 srcTexCoords[kBottomLeft_Corner].x(),
411 srcTexCoords[kBottomRight_Corner].x()),
412 bilerp(u, v, srcTexCoords[kTopLeft_Corner].y(),
413 srcTexCoords[kTopRight_Corner].y(),
414 srcTexCoords[kBottomLeft_Corner].y(),
415 srcTexCoords[kBottomRight_Corner].y()));
416
417 }
418
419 if(x < lodX && y < lodY) {
420 int i = 6 * (x * lodY + y);
421 indices[i] = x * stride + y;
422 indices[i + 1] = x * stride + 1 + y;
423 indices[i + 2] = (x + 1) * stride + 1 + y;
424 indices[i + 3] = indices[i];
425 indices[i + 4] = indices[i + 2];
426 indices[i + 5] = (x + 1) * stride + y;
427 }
428 v = SkScalarClampMax(v + 1.f / lodY, 1);
429 }
430 u = SkScalarClampMax(u + 1.f / lodX, 1);
431 }
432
433 if (tmpColors) {
434 if (doPremul) {
435 unpremul(tmpColors, vertexCount);
436 }
437 linear_to_skcolor(builder.colors(), tmpColors, vertexCount, convertCS.get());
438 }
439 return builder.detach();
440 }
441