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 "src/utils/SkPatchUtils.h"
9
10 #include "include/private/SkColorData.h"
11 #include "include/private/SkTo.h"
12 #include "src/core/SkArenaAlloc.h"
13 #include "src/core/SkColorSpacePriv.h"
14 #include "src/core/SkConvertPixels.h"
15 #include "src/core/SkGeometry.h"
16
17 namespace {
18 enum CubicCtrlPts {
19 kTopP0_CubicCtrlPts = 0,
20 kTopP1_CubicCtrlPts = 1,
21 kTopP2_CubicCtrlPts = 2,
22 kTopP3_CubicCtrlPts = 3,
23
24 kRightP0_CubicCtrlPts = 3,
25 kRightP1_CubicCtrlPts = 4,
26 kRightP2_CubicCtrlPts = 5,
27 kRightP3_CubicCtrlPts = 6,
28
29 kBottomP0_CubicCtrlPts = 9,
30 kBottomP1_CubicCtrlPts = 8,
31 kBottomP2_CubicCtrlPts = 7,
32 kBottomP3_CubicCtrlPts = 6,
33
34 kLeftP0_CubicCtrlPts = 0,
35 kLeftP1_CubicCtrlPts = 11,
36 kLeftP2_CubicCtrlPts = 10,
37 kLeftP3_CubicCtrlPts = 9,
38 };
39
40 // Enum for corner also clockwise.
41 enum Corner {
42 kTopLeft_Corner = 0,
43 kTopRight_Corner,
44 kBottomRight_Corner,
45 kBottomLeft_Corner
46 };
47 }
48
49 /**
50 * Evaluator to sample the values of a cubic bezier using forward differences.
51 * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
52 * adding precalculated values.
53 * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
54 * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
55 * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After
56 * obtaining this value (mh) we could just add this constant step to our first sampled point
57 * to compute the next one.
58 *
59 * For the cubic case the first difference gives as a result a quadratic polynomial to which we can
60 * apply again forward differences and get linear function to which we can apply again forward
61 * differences to get a constant difference. This is why we keep an array of size 4, the 0th
62 * position keeps the sampled value while the next ones keep the quadratic, linear and constant
63 * difference values.
64 */
65
66 class FwDCubicEvaluator {
67
68 public:
69
70 /**
71 * Receives the 4 control points of the cubic bezier.
72 */
73
FwDCubicEvaluator(const SkPoint points[4])74 explicit FwDCubicEvaluator(const SkPoint points[4])
75 : fCoefs(points) {
76 memcpy(fPoints, points, 4 * sizeof(SkPoint));
77
78 this->restart(1);
79 }
80
81 /**
82 * Restarts the forward differences evaluator to the first value of t = 0.
83 */
restart(int divisions)84 void restart(int divisions) {
85 fDivisions = divisions;
86 fCurrent = 0;
87 fMax = fDivisions + 1;
88 Sk2s h = Sk2s(1.f / fDivisions);
89 Sk2s h2 = h * h;
90 Sk2s h3 = h2 * h;
91 Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3;
92 fFwDiff[3] = to_point(fwDiff3);
93 fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2);
94 fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h);
95 fFwDiff[0] = to_point(fCoefs.fD);
96 }
97
98 /**
99 * Check if the evaluator is still within the range of 0<=t<=1
100 */
done() const101 bool done() const {
102 return fCurrent > fMax;
103 }
104
105 /**
106 * Call next to obtain the SkPoint sampled and move to the next one.
107 */
next()108 SkPoint next() {
109 SkPoint point = fFwDiff[0];
110 fFwDiff[0] += fFwDiff[1];
111 fFwDiff[1] += fFwDiff[2];
112 fFwDiff[2] += fFwDiff[3];
113 fCurrent++;
114 return point;
115 }
116
getCtrlPoints() const117 const SkPoint* getCtrlPoints() const {
118 return fPoints;
119 }
120
121 private:
122 SkCubicCoeff fCoefs;
123 int fMax, fCurrent, fDivisions;
124 SkPoint fFwDiff[4], fPoints[4];
125 };
126
127 ////////////////////////////////////////////////////////////////////////////////
128
129 // size in pixels of each partition per axis, adjust this knob
130 static const int kPartitionSize = 10;
131
132 /**
133 * Calculate the approximate arc length given a bezier curve's control points.
134 * Returns -1 if bad calc (i.e. non-finite)
135 */
approx_arc_length(const SkPoint points[],int count)136 static SkScalar approx_arc_length(const SkPoint points[], int count) {
137 if (count < 2) {
138 return 0;
139 }
140 SkScalar arcLength = 0;
141 for (int i = 0; i < count - 1; i++) {
142 arcLength += SkPoint::Distance(points[i], points[i + 1]);
143 }
144 return SkScalarIsFinite(arcLength) ? arcLength : -1;
145 }
146
bilerp(SkScalar tx,SkScalar ty,SkScalar c00,SkScalar c10,SkScalar c01,SkScalar c11)147 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
148 SkScalar c11) {
149 SkScalar a = c00 * (1.f - tx) + c10 * tx;
150 SkScalar b = c01 * (1.f - tx) + c11 * tx;
151 return a * (1.f - ty) + b * ty;
152 }
153
bilerp(SkScalar tx,SkScalar ty,const Sk4f & c00,const Sk4f & c10,const Sk4f & c01,const Sk4f & c11)154 static Sk4f bilerp(SkScalar tx, SkScalar ty,
155 const Sk4f& c00, const Sk4f& c10, const Sk4f& c01, const Sk4f& c11) {
156 Sk4f a = c00 * (1.f - tx) + c10 * tx;
157 Sk4f b = c01 * (1.f - tx) + c11 * tx;
158 return a * (1.f - ty) + b * ty;
159 }
160
GetLevelOfDetail(const SkPoint cubics[12],const SkMatrix * matrix)161 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
162 // Approximate length of each cubic.
163 SkPoint pts[kNumPtsCubic];
164 SkPatchUtils::GetTopCubic(cubics, pts);
165 matrix->mapPoints(pts, kNumPtsCubic);
166 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
167
168 SkPatchUtils::GetBottomCubic(cubics, pts);
169 matrix->mapPoints(pts, kNumPtsCubic);
170 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
171
172 SkPatchUtils::GetLeftCubic(cubics, pts);
173 matrix->mapPoints(pts, kNumPtsCubic);
174 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
175
176 SkPatchUtils::GetRightCubic(cubics, pts);
177 matrix->mapPoints(pts, kNumPtsCubic);
178 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
179
180 if (topLength < 0 || bottomLength < 0 || leftLength < 0 || rightLength < 0) {
181 return {0, 0}; // negative length is a sentinel for bad length (i.e. non-finite)
182 }
183
184 // Level of detail per axis, based on the larger side between top and bottom or left and right
185 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
186 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
187
188 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
189 }
190
GetTopCubic(const SkPoint cubics[12],SkPoint points[4])191 void SkPatchUtils::GetTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
192 points[0] = cubics[kTopP0_CubicCtrlPts];
193 points[1] = cubics[kTopP1_CubicCtrlPts];
194 points[2] = cubics[kTopP2_CubicCtrlPts];
195 points[3] = cubics[kTopP3_CubicCtrlPts];
196 }
197
GetBottomCubic(const SkPoint cubics[12],SkPoint points[4])198 void SkPatchUtils::GetBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
199 points[0] = cubics[kBottomP0_CubicCtrlPts];
200 points[1] = cubics[kBottomP1_CubicCtrlPts];
201 points[2] = cubics[kBottomP2_CubicCtrlPts];
202 points[3] = cubics[kBottomP3_CubicCtrlPts];
203 }
204
GetLeftCubic(const SkPoint cubics[12],SkPoint points[4])205 void SkPatchUtils::GetLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
206 points[0] = cubics[kLeftP0_CubicCtrlPts];
207 points[1] = cubics[kLeftP1_CubicCtrlPts];
208 points[2] = cubics[kLeftP2_CubicCtrlPts];
209 points[3] = cubics[kLeftP3_CubicCtrlPts];
210 }
211
GetRightCubic(const SkPoint cubics[12],SkPoint points[4])212 void SkPatchUtils::GetRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
213 points[0] = cubics[kRightP0_CubicCtrlPts];
214 points[1] = cubics[kRightP1_CubicCtrlPts];
215 points[2] = cubics[kRightP2_CubicCtrlPts];
216 points[3] = cubics[kRightP3_CubicCtrlPts];
217 }
218
skcolor_to_float(SkPMColor4f * dst,const SkColor * src,int count,SkColorSpace * dstCS)219 static void skcolor_to_float(SkPMColor4f* dst, const SkColor* src, int count, SkColorSpace* dstCS) {
220 SkImageInfo srcInfo = SkImageInfo::Make(count, 1, kBGRA_8888_SkColorType,
221 kUnpremul_SkAlphaType, SkColorSpace::MakeSRGB());
222 SkImageInfo dstInfo = SkImageInfo::Make(count, 1, kRGBA_F32_SkColorType,
223 kPremul_SkAlphaType, sk_ref_sp(dstCS));
224 SkConvertPixels(dstInfo, dst, 0, srcInfo, src, 0);
225 }
226
float_to_skcolor(SkColor * dst,const SkPMColor4f * src,int count,SkColorSpace * srcCS)227 static void float_to_skcolor(SkColor* dst, const SkPMColor4f* src, int count, SkColorSpace* srcCS) {
228 SkImageInfo srcInfo = SkImageInfo::Make(count, 1, kRGBA_F32_SkColorType,
229 kPremul_SkAlphaType, sk_ref_sp(srcCS));
230 SkImageInfo dstInfo = SkImageInfo::Make(count, 1, kBGRA_8888_SkColorType,
231 kUnpremul_SkAlphaType, SkColorSpace::MakeSRGB());
232 SkConvertPixels(dstInfo, dst, 0, srcInfo, src, 0);
233 }
234
MakeVertices(const SkPoint cubics[12],const SkColor srcColors[4],const SkPoint srcTexCoords[4],int lodX,int lodY,SkColorSpace * colorSpace)235 sk_sp<SkVertices> SkPatchUtils::MakeVertices(const SkPoint cubics[12], const SkColor srcColors[4],
236 const SkPoint srcTexCoords[4], int lodX, int lodY,
237 SkColorSpace* colorSpace) {
238 if (lodX < 1 || lodY < 1 || nullptr == cubics) {
239 return nullptr;
240 }
241
242 // check for overflow in multiplication
243 const int64_t lodX64 = (lodX + 1),
244 lodY64 = (lodY + 1),
245 mult64 = lodX64 * lodY64;
246 if (mult64 > SK_MaxS32) {
247 return nullptr;
248 }
249
250 // Treat null interpolation space as sRGB.
251 if (!colorSpace) {
252 colorSpace = sk_srgb_singleton();
253 }
254
255 int vertexCount = SkToS32(mult64);
256 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
257 // more than 60000 indices. To accomplish that we resize the LOD and vertex count
258 if (vertexCount > 10000 || lodX > 200 || lodY > 200) {
259 float weightX = static_cast<float>(lodX) / (lodX + lodY);
260 float weightY = static_cast<float>(lodY) / (lodX + lodY);
261
262 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
263 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
264 // Need a min of 1 since we later divide by lod
265 lodX = std::max(1, sk_float_floor2int_no_saturate(weightX * 200));
266 lodY = std::max(1, sk_float_floor2int_no_saturate(weightY * 200));
267 vertexCount = (lodX + 1) * (lodY + 1);
268 }
269 const int indexCount = lodX * lodY * 6;
270 uint32_t flags = 0;
271 if (srcTexCoords) {
272 flags |= SkVertices::kHasTexCoords_BuilderFlag;
273 }
274 if (srcColors) {
275 flags |= SkVertices::kHasColors_BuilderFlag;
276 }
277
278 SkSTArenaAlloc<2048> alloc;
279 SkPMColor4f* cornerColors = srcColors ? alloc.makeArray<SkPMColor4f>(4) : nullptr;
280 SkPMColor4f* tmpColors = srcColors ? alloc.makeArray<SkPMColor4f>(vertexCount) : nullptr;
281
282 SkVertices::Builder builder(SkVertices::kTriangles_VertexMode, vertexCount, indexCount, flags);
283 SkPoint* pos = builder.positions();
284 SkPoint* texs = builder.texCoords();
285 uint16_t* indices = builder.indices();
286
287 if (cornerColors) {
288 skcolor_to_float(cornerColors, srcColors, kNumCorners, colorSpace);
289 }
290
291 SkPoint pts[kNumPtsCubic];
292 SkPatchUtils::GetBottomCubic(cubics, pts);
293 FwDCubicEvaluator fBottom(pts);
294 SkPatchUtils::GetTopCubic(cubics, pts);
295 FwDCubicEvaluator fTop(pts);
296 SkPatchUtils::GetLeftCubic(cubics, pts);
297 FwDCubicEvaluator fLeft(pts);
298 SkPatchUtils::GetRightCubic(cubics, pts);
299 FwDCubicEvaluator fRight(pts);
300
301 fBottom.restart(lodX);
302 fTop.restart(lodX);
303
304 SkScalar u = 0.0f;
305 int stride = lodY + 1;
306 for (int x = 0; x <= lodX; x++) {
307 SkPoint bottom = fBottom.next(), top = fTop.next();
308 fLeft.restart(lodY);
309 fRight.restart(lodY);
310 SkScalar v = 0.f;
311 for (int y = 0; y <= lodY; y++) {
312 int dataIndex = x * (lodY + 1) + y;
313
314 SkPoint left = fLeft.next(), right = fRight.next();
315
316 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
317 (1.0f - v) * top.y() + v * bottom.y());
318 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
319 (1.0f - u) * left.y() + u * right.y());
320 SkPoint s2 = SkPoint::Make(
321 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
322 + u * fTop.getCtrlPoints()[3].x())
323 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
324 + u * fBottom.getCtrlPoints()[3].x()),
325 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
326 + u * fTop.getCtrlPoints()[3].y())
327 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
328 + u * fBottom.getCtrlPoints()[3].y()));
329 pos[dataIndex] = s0 + s1 - s2;
330
331 if (cornerColors) {
332 bilerp(u, v, Sk4f::Load(cornerColors[kTopLeft_Corner].vec()),
333 Sk4f::Load(cornerColors[kTopRight_Corner].vec()),
334 Sk4f::Load(cornerColors[kBottomLeft_Corner].vec()),
335 Sk4f::Load(cornerColors[kBottomRight_Corner].vec()))
336 .store(tmpColors[dataIndex].vec());
337 }
338
339 if (texs) {
340 texs[dataIndex] = SkPoint::Make(bilerp(u, v, srcTexCoords[kTopLeft_Corner].x(),
341 srcTexCoords[kTopRight_Corner].x(),
342 srcTexCoords[kBottomLeft_Corner].x(),
343 srcTexCoords[kBottomRight_Corner].x()),
344 bilerp(u, v, srcTexCoords[kTopLeft_Corner].y(),
345 srcTexCoords[kTopRight_Corner].y(),
346 srcTexCoords[kBottomLeft_Corner].y(),
347 srcTexCoords[kBottomRight_Corner].y()));
348
349 }
350
351 if(x < lodX && y < lodY) {
352 int i = 6 * (x * lodY + y);
353 indices[i] = x * stride + y;
354 indices[i + 1] = x * stride + 1 + y;
355 indices[i + 2] = (x + 1) * stride + 1 + y;
356 indices[i + 3] = indices[i];
357 indices[i + 4] = indices[i + 2];
358 indices[i + 5] = (x + 1) * stride + y;
359 }
360 v = SkScalarClampMax(v + 1.f / lodY, 1);
361 }
362 u = SkScalarClampMax(u + 1.f / lodX, 1);
363 }
364
365 if (tmpColors) {
366 float_to_skcolor(builder.colors(), tmpColors, vertexCount, colorSpace);
367 }
368 return builder.detach();
369 }
370