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 SkScalar cx[4], cy[4];
52 SkGetCubicCoeff(fPoints, cx, cy);
53 fCoefs[0].set(cx[0], cy[0]);
54 fCoefs[1].set(cx[1], cy[1]);
55 fCoefs[2].set(cx[2], cy[2]);
56 fCoefs[3].set(cx[3], cy[3]);
57
58 this->restart(1);
59 }
60
FwDCubicEvaluator(const SkPoint points[4])61 explicit FwDCubicEvaluator(const SkPoint points[4]) {
62 memcpy(fPoints, points, 4 * sizeof(SkPoint));
63
64 SkScalar cx[4], cy[4];
65 SkGetCubicCoeff(fPoints, cx, cy);
66 fCoefs[0].set(cx[0], cy[0]);
67 fCoefs[1].set(cx[1], cy[1]);
68 fCoefs[2].set(cx[2], cy[2]);
69 fCoefs[3].set(cx[3], cy[3]);
70
71 this->restart(1);
72 }
73
74 /**
75 * Restarts the forward differences evaluator to the first value of t = 0.
76 */
restart(int divisions)77 void restart(int divisions) {
78 fDivisions = divisions;
79 SkScalar h = 1.f / fDivisions;
80 fCurrent = 0;
81 fMax = fDivisions + 1;
82 fFwDiff[0] = fCoefs[3];
83 SkScalar h2 = h * h;
84 SkScalar h3 = h2 * h;
85
86 fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
87 fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
88 fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
89 fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
90 fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
91 }
92
93 /**
94 * Check if the evaluator is still within the range of 0<=t<=1
95 */
done() const96 bool done() const {
97 return fCurrent > fMax;
98 }
99
100 /**
101 * Call next to obtain the SkPoint sampled and move to the next one.
102 */
next()103 SkPoint next() {
104 SkPoint point = fFwDiff[0];
105 fFwDiff[0] += fFwDiff[1];
106 fFwDiff[1] += fFwDiff[2];
107 fFwDiff[2] += fFwDiff[3];
108 fCurrent++;
109 return point;
110 }
111
getCtrlPoints() const112 const SkPoint* getCtrlPoints() const {
113 return fPoints;
114 }
115
116 private:
117 int fMax, fCurrent, fDivisions;
118 SkPoint fFwDiff[4], fCoefs[4], fPoints[4];
119 };
120
121 ////////////////////////////////////////////////////////////////////////////////
122
123 // size in pixels of each partition per axis, adjust this knob
124 static const int kPartitionSize = 10;
125
126 /**
127 * Calculate the approximate arc length given a bezier curve's control points.
128 */
approx_arc_length(SkPoint * points,int count)129 static SkScalar approx_arc_length(SkPoint* points, int count) {
130 if (count < 2) {
131 return 0;
132 }
133 SkScalar arcLength = 0;
134 for (int i = 0; i < count - 1; i++) {
135 arcLength += SkPoint::Distance(points[i], points[i + 1]);
136 }
137 return arcLength;
138 }
139
bilerp(SkScalar tx,SkScalar ty,SkScalar c00,SkScalar c10,SkScalar c01,SkScalar c11)140 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
141 SkScalar c11) {
142 SkScalar a = c00 * (1.f - tx) + c10 * tx;
143 SkScalar b = c01 * (1.f - tx) + c11 * tx;
144 return a * (1.f - ty) + b * ty;
145 }
146
GetLevelOfDetail(const SkPoint cubics[12],const SkMatrix * matrix)147 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
148
149 // Approximate length of each cubic.
150 SkPoint pts[kNumPtsCubic];
151 SkPatchUtils::getTopCubic(cubics, pts);
152 matrix->mapPoints(pts, kNumPtsCubic);
153 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
154
155 SkPatchUtils::getBottomCubic(cubics, pts);
156 matrix->mapPoints(pts, kNumPtsCubic);
157 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
158
159 SkPatchUtils::getLeftCubic(cubics, pts);
160 matrix->mapPoints(pts, kNumPtsCubic);
161 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
162
163 SkPatchUtils::getRightCubic(cubics, pts);
164 matrix->mapPoints(pts, kNumPtsCubic);
165 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
166
167 // Level of detail per axis, based on the larger side between top and bottom or left and right
168 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
169 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
170
171 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
172 }
173
getTopCubic(const SkPoint cubics[12],SkPoint points[4])174 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
175 points[0] = cubics[kTopP0_CubicCtrlPts];
176 points[1] = cubics[kTopP1_CubicCtrlPts];
177 points[2] = cubics[kTopP2_CubicCtrlPts];
178 points[3] = cubics[kTopP3_CubicCtrlPts];
179 }
180
getBottomCubic(const SkPoint cubics[12],SkPoint points[4])181 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
182 points[0] = cubics[kBottomP0_CubicCtrlPts];
183 points[1] = cubics[kBottomP1_CubicCtrlPts];
184 points[2] = cubics[kBottomP2_CubicCtrlPts];
185 points[3] = cubics[kBottomP3_CubicCtrlPts];
186 }
187
getLeftCubic(const SkPoint cubics[12],SkPoint points[4])188 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
189 points[0] = cubics[kLeftP0_CubicCtrlPts];
190 points[1] = cubics[kLeftP1_CubicCtrlPts];
191 points[2] = cubics[kLeftP2_CubicCtrlPts];
192 points[3] = cubics[kLeftP3_CubicCtrlPts];
193 }
194
getRightCubic(const SkPoint cubics[12],SkPoint points[4])195 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
196 points[0] = cubics[kRightP0_CubicCtrlPts];
197 points[1] = cubics[kRightP1_CubicCtrlPts];
198 points[2] = cubics[kRightP2_CubicCtrlPts];
199 points[3] = cubics[kRightP3_CubicCtrlPts];
200 }
201
getVertexData(SkPatchUtils::VertexData * data,const SkPoint cubics[12],const SkColor colors[4],const SkPoint texCoords[4],int lodX,int lodY)202 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
203 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
204 if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) {
205 return false;
206 }
207
208 // check for overflow in multiplication
209 const int64_t lodX64 = (lodX + 1),
210 lodY64 = (lodY + 1),
211 mult64 = lodX64 * lodY64;
212 if (mult64 > SK_MaxS32) {
213 return false;
214 }
215 data->fVertexCount = SkToS32(mult64);
216
217 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
218 // more than 60000 indices. To accomplish that we resize the LOD and vertex count
219 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) {
220 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY);
221 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY);
222
223 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
224 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
225 lodX = static_cast<int>(weightX * 200);
226 lodY = static_cast<int>(weightY * 200);
227 data->fVertexCount = (lodX + 1) * (lodY + 1);
228 }
229 data->fIndexCount = lodX * lodY * 6;
230
231 data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
232 data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);
233
234 // if colors is not null then create array for colors
235 SkPMColor colorsPM[kNumCorners];
236 if (colors) {
237 // premultiply colors to avoid color bleeding.
238 for (int i = 0; i < kNumCorners; i++) {
239 colorsPM[i] = SkPreMultiplyColor(colors[i]);
240 }
241 data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
242 }
243
244 // if texture coordinates are not null then create array for them
245 if (texCoords) {
246 data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
247 }
248
249 SkPoint pts[kNumPtsCubic];
250 SkPatchUtils::getBottomCubic(cubics, pts);
251 FwDCubicEvaluator fBottom(pts);
252 SkPatchUtils::getTopCubic(cubics, pts);
253 FwDCubicEvaluator fTop(pts);
254 SkPatchUtils::getLeftCubic(cubics, pts);
255 FwDCubicEvaluator fLeft(pts);
256 SkPatchUtils::getRightCubic(cubics, pts);
257 FwDCubicEvaluator fRight(pts);
258
259 fBottom.restart(lodX);
260 fTop.restart(lodX);
261
262 SkScalar u = 0.0f;
263 int stride = lodY + 1;
264 for (int x = 0; x <= lodX; x++) {
265 SkPoint bottom = fBottom.next(), top = fTop.next();
266 fLeft.restart(lodY);
267 fRight.restart(lodY);
268 SkScalar v = 0.f;
269 for (int y = 0; y <= lodY; y++) {
270 int dataIndex = x * (lodY + 1) + y;
271
272 SkPoint left = fLeft.next(), right = fRight.next();
273
274 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
275 (1.0f - v) * top.y() + v * bottom.y());
276 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
277 (1.0f - u) * left.y() + u * right.y());
278 SkPoint s2 = SkPoint::Make(
279 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
280 + u * fTop.getCtrlPoints()[3].x())
281 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
282 + u * fBottom.getCtrlPoints()[3].x()),
283 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
284 + u * fTop.getCtrlPoints()[3].y())
285 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
286 + u * fBottom.getCtrlPoints()[3].y()));
287 data->fPoints[dataIndex] = s0 + s1 - s2;
288
289 if (colors) {
290 uint8_t a = uint8_t(bilerp(u, v,
291 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
292 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
293 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
294 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
295 uint8_t r = uint8_t(bilerp(u, v,
296 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
297 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
298 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
299 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
300 uint8_t g = uint8_t(bilerp(u, v,
301 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
302 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
303 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
304 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
305 uint8_t b = uint8_t(bilerp(u, v,
306 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
307 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
308 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
309 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
310 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
311 }
312
313 if (texCoords) {
314 data->fTexCoords[dataIndex] = SkPoint::Make(
315 bilerp(u, v, texCoords[kTopLeft_Corner].x(),
316 texCoords[kTopRight_Corner].x(),
317 texCoords[kBottomLeft_Corner].x(),
318 texCoords[kBottomRight_Corner].x()),
319 bilerp(u, v, texCoords[kTopLeft_Corner].y(),
320 texCoords[kTopRight_Corner].y(),
321 texCoords[kBottomLeft_Corner].y(),
322 texCoords[kBottomRight_Corner].y()));
323
324 }
325
326 if(x < lodX && y < lodY) {
327 int i = 6 * (x * lodY + y);
328 data->fIndices[i] = x * stride + y;
329 data->fIndices[i + 1] = x * stride + 1 + y;
330 data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
331 data->fIndices[i + 3] = data->fIndices[i];
332 data->fIndices[i + 4] = data->fIndices[i + 2];
333 data->fIndices[i + 5] = (x + 1) * stride + y;
334 }
335 v = SkScalarClampMax(v + 1.f / lodY, 1);
336 }
337 u = SkScalarClampMax(u + 1.f / lodX, 1);
338 }
339 return true;
340
341 }
342