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:
33
34 /**
35 * Receives the 4 control points of the cubic bezier.
36 */
37
FwDCubicEvaluator(const SkPoint points[4])38 explicit FwDCubicEvaluator(const SkPoint points[4])
39 : fCoefs(points) {
40 memcpy(fPoints, points, 4 * sizeof(SkPoint));
41
42 this->restart(1);
43 }
44
45 /**
46 * Restarts the forward differences evaluator to the first value of t = 0.
47 */
restart(int divisions)48 void restart(int divisions) {
49 fDivisions = divisions;
50 fCurrent = 0;
51 fMax = fDivisions + 1;
52 Sk2s h = Sk2s(1.f / fDivisions);
53 Sk2s h2 = h * h;
54 Sk2s h3 = h2 * h;
55 Sk2s fwDiff3 = Sk2s(6) * fCoefs.fA * h3;
56 fFwDiff[3] = to_point(fwDiff3);
57 fFwDiff[2] = to_point(fwDiff3 + times_2(fCoefs.fB) * h2);
58 fFwDiff[1] = to_point(fCoefs.fA * h3 + fCoefs.fB * h2 + fCoefs.fC * h);
59 fFwDiff[0] = to_point(fCoefs.fD);
60 }
61
62 /**
63 * Check if the evaluator is still within the range of 0<=t<=1
64 */
done() const65 bool done() const {
66 return fCurrent > fMax;
67 }
68
69 /**
70 * Call next to obtain the SkPoint sampled and move to the next one.
71 */
next()72 SkPoint next() {
73 SkPoint point = fFwDiff[0];
74 fFwDiff[0] += fFwDiff[1];
75 fFwDiff[1] += fFwDiff[2];
76 fFwDiff[2] += fFwDiff[3];
77 fCurrent++;
78 return point;
79 }
80
getCtrlPoints() const81 const SkPoint* getCtrlPoints() const {
82 return fPoints;
83 }
84
85 private:
86 SkCubicCoeff fCoefs;
87 int fMax, fCurrent, fDivisions;
88 SkPoint fFwDiff[4], fPoints[4];
89 };
90
91 ////////////////////////////////////////////////////////////////////////////////
92
93 // size in pixels of each partition per axis, adjust this knob
94 static const int kPartitionSize = 10;
95
96 /**
97 * Calculate the approximate arc length given a bezier curve's control points.
98 */
approx_arc_length(SkPoint * points,int count)99 static SkScalar approx_arc_length(SkPoint* points, int count) {
100 if (count < 2) {
101 return 0;
102 }
103 SkScalar arcLength = 0;
104 for (int i = 0; i < count - 1; i++) {
105 arcLength += SkPoint::Distance(points[i], points[i + 1]);
106 }
107 return arcLength;
108 }
109
bilerp(SkScalar tx,SkScalar ty,SkScalar c00,SkScalar c10,SkScalar c01,SkScalar c11)110 static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
111 SkScalar c11) {
112 SkScalar a = c00 * (1.f - tx) + c10 * tx;
113 SkScalar b = c01 * (1.f - tx) + c11 * tx;
114 return a * (1.f - ty) + b * ty;
115 }
116
GetLevelOfDetail(const SkPoint cubics[12],const SkMatrix * matrix)117 SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
118
119 // Approximate length of each cubic.
120 SkPoint pts[kNumPtsCubic];
121 SkPatchUtils::getTopCubic(cubics, pts);
122 matrix->mapPoints(pts, kNumPtsCubic);
123 SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
124
125 SkPatchUtils::getBottomCubic(cubics, pts);
126 matrix->mapPoints(pts, kNumPtsCubic);
127 SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
128
129 SkPatchUtils::getLeftCubic(cubics, pts);
130 matrix->mapPoints(pts, kNumPtsCubic);
131 SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
132
133 SkPatchUtils::getRightCubic(cubics, pts);
134 matrix->mapPoints(pts, kNumPtsCubic);
135 SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
136
137 // Level of detail per axis, based on the larger side between top and bottom or left and right
138 int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
139 int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
140
141 return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
142 }
143
getTopCubic(const SkPoint cubics[12],SkPoint points[4])144 void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
145 points[0] = cubics[kTopP0_CubicCtrlPts];
146 points[1] = cubics[kTopP1_CubicCtrlPts];
147 points[2] = cubics[kTopP2_CubicCtrlPts];
148 points[3] = cubics[kTopP3_CubicCtrlPts];
149 }
150
getBottomCubic(const SkPoint cubics[12],SkPoint points[4])151 void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
152 points[0] = cubics[kBottomP0_CubicCtrlPts];
153 points[1] = cubics[kBottomP1_CubicCtrlPts];
154 points[2] = cubics[kBottomP2_CubicCtrlPts];
155 points[3] = cubics[kBottomP3_CubicCtrlPts];
156 }
157
getLeftCubic(const SkPoint cubics[12],SkPoint points[4])158 void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
159 points[0] = cubics[kLeftP0_CubicCtrlPts];
160 points[1] = cubics[kLeftP1_CubicCtrlPts];
161 points[2] = cubics[kLeftP2_CubicCtrlPts];
162 points[3] = cubics[kLeftP3_CubicCtrlPts];
163 }
164
getRightCubic(const SkPoint cubics[12],SkPoint points[4])165 void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
166 points[0] = cubics[kRightP0_CubicCtrlPts];
167 points[1] = cubics[kRightP1_CubicCtrlPts];
168 points[2] = cubics[kRightP2_CubicCtrlPts];
169 points[3] = cubics[kRightP3_CubicCtrlPts];
170 }
171
getVertexData(SkPatchUtils::VertexData * data,const SkPoint cubics[12],const SkColor colors[4],const SkPoint texCoords[4],int lodX,int lodY)172 bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
173 const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
174 if (lodX < 1 || lodY < 1 || nullptr == cubics || nullptr == data) {
175 return false;
176 }
177
178 // check for overflow in multiplication
179 const int64_t lodX64 = (lodX + 1),
180 lodY64 = (lodY + 1),
181 mult64 = lodX64 * lodY64;
182 if (mult64 > SK_MaxS32) {
183 return false;
184 }
185 data->fVertexCount = SkToS32(mult64);
186
187 // it is recommended to generate draw calls of no more than 65536 indices, so we never generate
188 // more than 60000 indices. To accomplish that we resize the LOD and vertex count
189 if (data->fVertexCount > 10000 || lodX > 200 || lodY > 200) {
190 SkScalar weightX = static_cast<SkScalar>(lodX) / (lodX + lodY);
191 SkScalar weightY = static_cast<SkScalar>(lodY) / (lodX + lodY);
192
193 // 200 comes from the 100 * 2 which is the max value of vertices because of the limit of
194 // 60000 indices ( sqrt(60000 / 6) that comes from data->fIndexCount = lodX * lodY * 6)
195 lodX = static_cast<int>(weightX * 200);
196 lodY = static_cast<int>(weightY * 200);
197 data->fVertexCount = (lodX + 1) * (lodY + 1);
198 }
199 data->fIndexCount = lodX * lodY * 6;
200
201 data->fPoints = new SkPoint[data->fVertexCount];
202 data->fIndices = new uint16_t[data->fIndexCount];
203
204 // if colors is not null then create array for colors
205 SkPMColor colorsPM[kNumCorners];
206 if (colors) {
207 // premultiply colors to avoid color bleeding.
208 for (int i = 0; i < kNumCorners; i++) {
209 colorsPM[i] = SkPreMultiplyColor(colors[i]);
210 }
211 data->fColors = new uint32_t[data->fVertexCount];
212 }
213
214 // if texture coordinates are not null then create array for them
215 if (texCoords) {
216 data->fTexCoords = new SkPoint[data->fVertexCount];
217 }
218
219 SkPoint pts[kNumPtsCubic];
220 SkPatchUtils::getBottomCubic(cubics, pts);
221 FwDCubicEvaluator fBottom(pts);
222 SkPatchUtils::getTopCubic(cubics, pts);
223 FwDCubicEvaluator fTop(pts);
224 SkPatchUtils::getLeftCubic(cubics, pts);
225 FwDCubicEvaluator fLeft(pts);
226 SkPatchUtils::getRightCubic(cubics, pts);
227 FwDCubicEvaluator fRight(pts);
228
229 fBottom.restart(lodX);
230 fTop.restart(lodX);
231
232 SkScalar u = 0.0f;
233 int stride = lodY + 1;
234 for (int x = 0; x <= lodX; x++) {
235 SkPoint bottom = fBottom.next(), top = fTop.next();
236 fLeft.restart(lodY);
237 fRight.restart(lodY);
238 SkScalar v = 0.f;
239 for (int y = 0; y <= lodY; y++) {
240 int dataIndex = x * (lodY + 1) + y;
241
242 SkPoint left = fLeft.next(), right = fRight.next();
243
244 SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
245 (1.0f - v) * top.y() + v * bottom.y());
246 SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
247 (1.0f - u) * left.y() + u * right.y());
248 SkPoint s2 = SkPoint::Make(
249 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
250 + u * fTop.getCtrlPoints()[3].x())
251 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
252 + u * fBottom.getCtrlPoints()[3].x()),
253 (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
254 + u * fTop.getCtrlPoints()[3].y())
255 + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
256 + u * fBottom.getCtrlPoints()[3].y()));
257 data->fPoints[dataIndex] = s0 + s1 - s2;
258
259 if (colors) {
260 uint8_t a = uint8_t(bilerp(u, v,
261 SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
262 SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
263 SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
264 SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
265 uint8_t r = uint8_t(bilerp(u, v,
266 SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
267 SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
268 SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
269 SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
270 uint8_t g = uint8_t(bilerp(u, v,
271 SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
272 SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
273 SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
274 SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
275 uint8_t b = uint8_t(bilerp(u, v,
276 SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
277 SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
278 SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
279 SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
280 data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
281 }
282
283 if (texCoords) {
284 data->fTexCoords[dataIndex] = SkPoint::Make(
285 bilerp(u, v, texCoords[kTopLeft_Corner].x(),
286 texCoords[kTopRight_Corner].x(),
287 texCoords[kBottomLeft_Corner].x(),
288 texCoords[kBottomRight_Corner].x()),
289 bilerp(u, v, texCoords[kTopLeft_Corner].y(),
290 texCoords[kTopRight_Corner].y(),
291 texCoords[kBottomLeft_Corner].y(),
292 texCoords[kBottomRight_Corner].y()));
293
294 }
295
296 if(x < lodX && y < lodY) {
297 int i = 6 * (x * lodY + y);
298 data->fIndices[i] = x * stride + y;
299 data->fIndices[i + 1] = x * stride + 1 + y;
300 data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
301 data->fIndices[i + 3] = data->fIndices[i];
302 data->fIndices[i + 4] = data->fIndices[i + 2];
303 data->fIndices[i + 5] = (x + 1) * stride + y;
304 }
305 v = SkScalarClampMax(v + 1.f / lodY, 1);
306 }
307 u = SkScalarClampMax(u + 1.f / lodX, 1);
308 }
309 return true;
310
311 }
312