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 "SkColorPriv.h"
11 #include "SkGeometry.h"
12
13 /**
14 * Evaluator to sample the values of a cubic bezier using forward differences.
15 * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
16 * adding precalculated values.
17 * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
18 * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
19 * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After
20 * obtaining this value (mh) we could just add this constant step to our first sampled point
21 * to compute the next one.
22 *
23 * For the cubic case the first difference gives as a result a quadratic polynomial to which we can
24 * apply again forward differences and get linear function to which we can apply again forward
25 * differences to get a constant difference. This is why we keep an array of size 4, the 0th
26 * position keeps the sampled value while the next ones keep the quadratic, linear and constant
27 * difference values.
28 */
29
30 class FwDCubicEvaluator {
31
32 public:
FwDCubicEvaluator()33 FwDCubicEvaluator()
34 : fMax(0)
35 , fCurrent(0)
36 , fDivisions(0) {
37 memset(fPoints, 0, 4 * sizeof(SkPoint));
38 memset(fPoints, 0, 4 * sizeof(SkPoint));
39 memset(fPoints, 0, 4 * sizeof(SkPoint));
40 }
41
42 /**
43 * Receives the 4 control points of the cubic bezier.
44 */
FwDCubicEvaluator(SkPoint a,SkPoint b,SkPoint c,SkPoint d)45 FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) {
46 fPoints[0] = a;
47 fPoints[1] = b;
48 fPoints[2] = c;
49 fPoints[3] = d;
50
51 SkCubicToCoeff(fPoints, fCoefs);
52
53 this->restart(1);
54 }
55
FwDCubicEvaluator(const SkPoint points[4])56 explicit FwDCubicEvaluator(const SkPoint points[4]) {
57 memcpy(fPoints, points, 4 * sizeof(SkPoint));
58
59 SkCubicToCoeff(fPoints, fCoefs);
60
61 this->restart(1);
62 }
63
64 /**
65 * Restarts the forward differences evaluator to the first value of t = 0.
66 */
restart(int divisions)67 void restart(int divisions) {
68 fDivisions = divisions;
69 SkScalar h = 1.f / fDivisions;
70 fCurrent = 0;
71 fMax = fDivisions + 1;
72 fFwDiff[0] = fCoefs[3];
73 SkScalar h2 = h * h;
74 SkScalar h3 = h2 * h;
75
76 fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
77 fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
78 fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
79 fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
80 fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
81 }
82
83 /**
84 * Check if the evaluator is still within the range of 0<=t<=1
85 */
done() const86 bool done() const {
87 return fCurrent > fMax;
88 }
89
90 /**
91 * Call next to obtain the SkPoint sampled and move to the next one.
92 */
next()93 SkPoint next() {
94 SkPoint point = fFwDiff[0];
95 fFwDiff[0] += fFwDiff[1];
96 fFwDiff[1] += fFwDiff[2];
97 fFwDiff[2] += fFwDiff[3];
98 fCurrent++;
99 return point;
100 }
101
getCtrlPoints() const102 const SkPoint* getCtrlPoints() const {
103 return fPoints;
104 }
105
106 private:
107 int fMax, fCurrent, fDivisions;
108 SkPoint fFwDiff[4], fCoefs[4], fPoints[4];
109 };
110
111 ////////////////////////////////////////////////////////////////////////////////
112
113 // size in pixels of each partition per axis, adjust this knob
114 static const int kPartitionSize = 10;
115
116 /**
117 * Calculate the approximate arc length given a bezier curve's control points.
118 */
approx_arc_length(SkPoint * points,int count)119 static SkScalar approx_arc_length(SkPoint* points, int count) {
120 if (count < 2) {
121 return 0;
122 }
123 SkScalar arcLength = 0;
124 for (int i = 0; i < count - 1; i++) {
125 arcLength += SkPoint::Distance(points[i], points[i + 1]);
126 }
127 return arcLength;
128 }
129
bilerp(SkScalar tx,SkScalar ty,SkScalar c00,SkScalar c10,SkScalar c01,SkScalar c11)130 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
131 SkScalar c11) {
132 SkScalar a = c00 * (1.f - tx) + c10 * tx;
133 SkScalar b = c01 * (1.f - tx) + c11 * tx;
134 return a * (1.f - ty) + b * ty;
135 }
136
GetLevelOfDetail(const SkPoint cubics[12],const SkMatrix * matrix)137 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
138
139 // Approximate length of each cubic.
140 SkPoint pts[kNumPtsCubic];
141 SkPatchUtils::getTopCubic(cubics, pts);
142 matrix->mapPoints(pts, kNumPtsCubic);
143 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
144
145 SkPatchUtils::getBottomCubic(cubics, pts);
146 matrix->mapPoints(pts, kNumPtsCubic);
147 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
148
149 SkPatchUtils::getLeftCubic(cubics, pts);
150 matrix->mapPoints(pts, kNumPtsCubic);
151 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
152
153 SkPatchUtils::getRightCubic(cubics, pts);
154 matrix->mapPoints(pts, kNumPtsCubic);
155 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
156
157 // Level of detail per axis, based on the larger side between top and bottom or left and right
158 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
159 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
160
161 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
162 }
163
getTopCubic(const SkPoint cubics[12],SkPoint points[4])164 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
165 points[0] = cubics[kTopP0_CubicCtrlPts];
166 points[1] = cubics[kTopP1_CubicCtrlPts];
167 points[2] = cubics[kTopP2_CubicCtrlPts];
168 points[3] = cubics[kTopP3_CubicCtrlPts];
169 }
170
getBottomCubic(const SkPoint cubics[12],SkPoint points[4])171 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
172 points[0] = cubics[kBottomP0_CubicCtrlPts];
173 points[1] = cubics[kBottomP1_CubicCtrlPts];
174 points[2] = cubics[kBottomP2_CubicCtrlPts];
175 points[3] = cubics[kBottomP3_CubicCtrlPts];
176 }
177
getLeftCubic(const SkPoint cubics[12],SkPoint points[4])178 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
179 points[0] = cubics[kLeftP0_CubicCtrlPts];
180 points[1] = cubics[kLeftP1_CubicCtrlPts];
181 points[2] = cubics[kLeftP2_CubicCtrlPts];
182 points[3] = cubics[kLeftP3_CubicCtrlPts];
183 }
184
getRightCubic(const SkPoint cubics[12],SkPoint points[4])185 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
186 points[0] = cubics[kRightP0_CubicCtrlPts];
187 points[1] = cubics[kRightP1_CubicCtrlPts];
188 points[2] = cubics[kRightP2_CubicCtrlPts];
189 points[3] = cubics[kRightP3_CubicCtrlPts];
190 }
191
getVertexData(SkPatchUtils::VertexData * data,const SkPoint cubics[12],const SkColor colors[4],const SkPoint texCoords[4],int lodX,int lodY)192 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
193 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
194 if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) {
195 return false;
196 }
197
198 // check for overflow in multiplication
199 const int64_t lodX64 = (lodX + 1),
200 lodY64 = (lodY + 1),
201 mult64 = lodX64 * lodY64;
202 if (mult64 > SK_MaxS32) {
203 return false;
204 }
205 data->fVertexCount = SkToS32(mult64);
206
207 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
208 // more than 60000 indices. To accomplish that we resize the LOD and vertex count
209 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) {
210 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY);
211 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY);
212
213 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
214 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
215 lodX = static_cast<int>(weightX * 200);
216 lodY = static_cast<int>(weightY * 200);
217 data->fVertexCount = (lodX + 1) * (lodY + 1);
218 }
219 data->fIndexCount = lodX * lodY * 6;
220
221 data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
222 data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);
223
224 // if colors is not null then create array for colors
225 SkPMColor colorsPM[kNumCorners];
226 if (colors) {
227 // premultiply colors to avoid color bleeding.
228 for (int i = 0; i < kNumCorners; i++) {
229 colorsPM[i] = SkPreMultiplyColor(colors[i]);
230 }
231 data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
232 }
233
234 // if texture coordinates are not null then create array for them
235 if (texCoords) {
236 data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
237 }
238
239 SkPoint pts[kNumPtsCubic];
240 SkPatchUtils::getBottomCubic(cubics, pts);
241 FwDCubicEvaluator fBottom(pts);
242 SkPatchUtils::getTopCubic(cubics, pts);
243 FwDCubicEvaluator fTop(pts);
244 SkPatchUtils::getLeftCubic(cubics, pts);
245 FwDCubicEvaluator fLeft(pts);
246 SkPatchUtils::getRightCubic(cubics, pts);
247 FwDCubicEvaluator fRight(pts);
248
249 fBottom.restart(lodX);
250 fTop.restart(lodX);
251
252 SkScalar u = 0.0f;
253 int stride = lodY + 1;
254 for (int x = 0; x <= lodX; x++) {
255 SkPoint bottom = fBottom.next(), top = fTop.next();
256 fLeft.restart(lodY);
257 fRight.restart(lodY);
258 SkScalar v = 0.f;
259 for (int y = 0; y <= lodY; y++) {
260 int dataIndex = x * (lodY + 1) + y;
261
262 SkPoint left = fLeft.next(), right = fRight.next();
263
264 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
265 (1.0f - v) * top.y() + v * bottom.y());
266 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
267 (1.0f - u) * left.y() + u * right.y());
268 SkPoint s2 = SkPoint::Make(
269 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
270 + u * fTop.getCtrlPoints()[3].x())
271 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
272 + u * fBottom.getCtrlPoints()[3].x()),
273 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
274 + u * fTop.getCtrlPoints()[3].y())
275 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
276 + u * fBottom.getCtrlPoints()[3].y()));
277 data->fPoints[dataIndex] = s0 + s1 - s2;
278
279 if (colors) {
280 uint8_t a = uint8_t(bilerp(u, v,
281 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
282 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
283 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
284 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
285 uint8_t r = uint8_t(bilerp(u, v,
286 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
287 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
288 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
289 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
290 uint8_t g = uint8_t(bilerp(u, v,
291 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
292 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
293 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
294 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
295 uint8_t b = uint8_t(bilerp(u, v,
296 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
297 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
298 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
299 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
300 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
301 }
302
303 if (texCoords) {
304 data->fTexCoords[dataIndex] = SkPoint::Make(
305 bilerp(u, v, texCoords[kTopLeft_Corner].x(),
306 texCoords[kTopRight_Corner].x(),
307 texCoords[kBottomLeft_Corner].x(),
308 texCoords[kBottomRight_Corner].x()),
309 bilerp(u, v, texCoords[kTopLeft_Corner].y(),
310 texCoords[kTopRight_Corner].y(),
311 texCoords[kBottomLeft_Corner].y(),
312 texCoords[kBottomRight_Corner].y()));
313
314 }
315
316 if(x < lodX && y < lodY) {
317 int i = 6 * (x * lodY + y);
318 data->fIndices[i] = x * stride + y;
319 data->fIndices[i + 1] = x * stride + 1 + y;
320 data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
321 data->fIndices[i + 3] = data->fIndices[i];
322 data->fIndices[i + 4] = data->fIndices[i + 2];
323 data->fIndices[i + 5] = (x + 1) * stride + y;
324 }
325 v = SkScalarClampMax(v + 1.f / lodY, 1);
326 }
327 u = SkScalarClampMax(u + 1.f / lodX, 1);
328 }
329 return true;
330
331 }
332