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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