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| 1 /* | 1 /* | 
| 2  * Copyright 2006 The Android Open Source Project | 2  * Copyright 2006 The Android Open Source Project | 
| 3  * | 3  * | 
| 4  * Use of this source code is governed by a BSD-style license that can be | 4  * Use of this source code is governed by a BSD-style license that can be | 
| 5  * found in the LICENSE file. | 5  * found in the LICENSE file. | 
| 6  */ | 6  */ | 
| 7 | 7 | 
| 8 #include "SkGeometry.h" | 8 #include "SkGeometry.h" | 
| 9 #include "SkMatrix.h" | 9 #include "SkMatrix.h" | 
| 10 #include "SkNx.h" | 10 #include "SkNx.h" | 
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| 1139 // | 1139 // | 
| 1140 // F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) | 1140 // F = (A (1 - t)^2 + C t^2 + 2 B (1 - t) t w) | 
| 1141 //     ------------------------------------------ | 1141 //     ------------------------------------------ | 
| 1142 //         ((1 - t)^2 + t^2 + 2 (1 - t) t w) | 1142 //         ((1 - t)^2 + t^2 + 2 (1 - t) t w) | 
| 1143 // | 1143 // | 
| 1144 //   = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} | 1144 //   = {t^2 (P0 + P2 - 2 P1 w), t (-2 P0 + 2 P1 w), P0} | 
| 1145 //     ------------------------------------------------ | 1145 //     ------------------------------------------------ | 
| 1146 //             {t^2 (2 - 2 w), t (-2 + 2 w), 1} | 1146 //             {t^2 (2 - 2 w), t (-2 + 2 w), 1} | 
| 1147 // | 1147 // | 
| 1148 | 1148 | 
| 1149 static SkScalar conic_eval_pos(const SkScalar src[], SkScalar w, SkScalar t) { |  | 
| 1150     SkASSERT(src); |  | 
| 1151     SkASSERT(t >= 0 && t <= SK_Scalar1); |  | 
| 1152 |  | 
| 1153     SkScalar    src2w = SkScalarMul(src[2], w); |  | 
| 1154     SkScalar    C = src[0]; |  | 
| 1155     SkScalar    A = src[4] - 2 * src2w + C; |  | 
| 1156     SkScalar    B = 2 * (src2w - C); |  | 
| 1157     SkScalar numer = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |  | 
| 1158 |  | 
| 1159     B = 2 * (w - SK_Scalar1); |  | 
| 1160     C = SK_Scalar1; |  | 
| 1161     A = -B; |  | 
| 1162     SkScalar denom = SkScalarMulAdd(SkScalarMulAdd(A, t, B), t, C); |  | 
| 1163 |  | 
| 1164     return numer / denom; |  | 
| 1165 } |  | 
| 1166 |  | 
| 1167 // F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) | 1149 // F' = 2 (C t (1 + t (-1 + w)) - A (-1 + t) (t (-1 + w) - w) + B (1 - 2 t) w) | 
| 1168 // | 1150 // | 
| 1169 //  t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) | 1151 //  t^2 : (2 P0 - 2 P2 - 2 P0 w + 2 P2 w) | 
| 1170 //  t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) | 1152 //  t^1 : (-2 P0 + 2 P2 + 4 P0 w - 4 P1 w) | 
| 1171 //  t^0 : -2 P0 w + 2 P1 w | 1153 //  t^0 : -2 P0 w + 2 P1 w | 
| 1172 // | 1154 // | 
| 1173 //  We disregard magnitude, so we can freely ignore the denominator of F', and | 1155 //  We disregard magnitude, so we can freely ignore the denominator of F', and | 
| 1174 //  divide the numerator by 2 | 1156 //  divide the numerator by 2 | 
| 1175 // | 1157 // | 
| 1176 //    coeff[0] for t^2 | 1158 //    coeff[0] for t^2 | 
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| 1223     dst[3] = SkScalarInterp(ab, bc, t); | 1205     dst[3] = SkScalarInterp(ab, bc, t); | 
| 1224     dst[6] = bc; | 1206     dst[6] = bc; | 
| 1225 } | 1207 } | 
| 1226 | 1208 | 
| 1227 static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { | 1209 static void ratquad_mapTo3D(const SkPoint src[3], SkScalar w, SkP3D dst[]) { | 
| 1228     dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); | 1210     dst[0].set(src[0].fX * 1, src[0].fY * 1, 1); | 
| 1229     dst[1].set(src[1].fX * w, src[1].fY * w, w); | 1211     dst[1].set(src[1].fX * w, src[1].fY * w, w); | 
| 1230     dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); | 1212     dst[2].set(src[2].fX * 1, src[2].fY * 1, 1); | 
| 1231 } | 1213 } | 
| 1232 | 1214 | 
| 1233 void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { |  | 
| 1234     SkASSERT(t >= 0 && t <= SK_Scalar1); |  | 
| 1235 |  | 
| 1236     if (pt) { |  | 
| 1237         pt->set(conic_eval_pos(&fPts[0].fX, fW, t), |  | 
| 1238                 conic_eval_pos(&fPts[0].fY, fW, t)); |  | 
| 1239     } |  | 
| 1240     if (tangent) { |  | 
| 1241         *tangent = evalTangentAt(t); |  | 
| 1242     } |  | 
| 1243 } |  | 
| 1244 |  | 
| 1245 void SkConic::chopAt(SkScalar t, SkConic dst[2]) const { | 1215 void SkConic::chopAt(SkScalar t, SkConic dst[2]) const { | 
| 1246     SkP3D tmp[3], tmp2[3]; | 1216     SkP3D tmp[3], tmp2[3]; | 
| 1247 | 1217 | 
| 1248     ratquad_mapTo3D(fPts, fW, tmp); | 1218     ratquad_mapTo3D(fPts, fW, tmp); | 
| 1249 | 1219 | 
| 1250     p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); | 1220     p3d_interp(&tmp[0].fX, &tmp2[0].fX, t); | 
| 1251     p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); | 1221     p3d_interp(&tmp[0].fY, &tmp2[0].fY, t); | 
| 1252     p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); | 1222     p3d_interp(&tmp[0].fZ, &tmp2[0].fZ, t); | 
| 1253 | 1223 | 
| 1254     dst[0].fPts[0] = fPts[0]; | 1224     dst[0].fPts[0] = fPts[0]; | 
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| 1310     Sk2s p20 = p2 - p0; | 1280     Sk2s p20 = p2 - p0; | 
| 1311     Sk2s p10 = p1 - p0; | 1281     Sk2s p10 = p1 - p0; | 
| 1312 | 1282 | 
| 1313     Sk2s C = ww * p10; | 1283     Sk2s C = ww * p10; | 
| 1314     Sk2s A = ww * p20 - p20; | 1284     Sk2s A = ww * p20 - p20; | 
| 1315     Sk2s B = p20 - C - C; | 1285     Sk2s B = p20 - C - C; | 
| 1316 | 1286 | 
| 1317     return to_vector(quad_poly_eval(A, B, C, Sk2s(t))); | 1287     return to_vector(quad_poly_eval(A, B, C, Sk2s(t))); | 
| 1318 } | 1288 } | 
| 1319 | 1289 | 
|  | 1290 void SkConic::evalAt(SkScalar t, SkPoint* pt, SkVector* tangent) const { | 
|  | 1291     SkASSERT(t >= 0 && t <= SK_Scalar1); | 
|  | 1292 | 
|  | 1293     if (pt) { | 
|  | 1294         *pt = this->evalAt(t); | 
|  | 1295     } | 
|  | 1296     if (tangent) { | 
|  | 1297         *tangent = this->evalTangentAt(t); | 
|  | 1298     } | 
|  | 1299 } | 
|  | 1300 | 
| 1320 static SkScalar subdivide_w_value(SkScalar w) { | 1301 static SkScalar subdivide_w_value(SkScalar w) { | 
| 1321     return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); | 1302     return SkScalarSqrt(SK_ScalarHalf + w * SK_ScalarHalf); | 
| 1322 } | 1303 } | 
| 1323 | 1304 | 
| 1324 static Sk2s twice(const Sk2s& value) { | 1305 static Sk2s twice(const Sk2s& value) { | 
| 1325     return value + value; | 1306     return value + value; | 
| 1326 } | 1307 } | 
| 1327 | 1308 | 
| 1328 void SkConic::chop(SkConic * SK_RESTRICT dst) const { | 1309 void SkConic::chop(SkConic * SK_RESTRICT dst) const { | 
| 1329     Sk2s scale = Sk2s(SkScalarInvert(SK_Scalar1 + fW)); | 1310     Sk2s scale = Sk2s(SkScalarInvert(SK_Scalar1 + fW)); | 
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| 1590         matrix.preScale(SK_Scalar1, -SK_Scalar1); | 1571         matrix.preScale(SK_Scalar1, -SK_Scalar1); | 
| 1591     } | 1572     } | 
| 1592     if (userMatrix) { | 1573     if (userMatrix) { | 
| 1593         matrix.postConcat(*userMatrix); | 1574         matrix.postConcat(*userMatrix); | 
| 1594     } | 1575     } | 
| 1595     for (int i = 0; i < conicCount; ++i) { | 1576     for (int i = 0; i < conicCount; ++i) { | 
| 1596         matrix.mapPoints(dst[i].fPts, 3); | 1577         matrix.mapPoints(dst[i].fPts, 3); | 
| 1597     } | 1578     } | 
| 1598     return conicCount; | 1579     return conicCount; | 
| 1599 } | 1580 } | 
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