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| 1 // Copyright 2012 The Chromium Authors. All rights reserved. | |
| 2 // Use of this source code is governed by a BSD-style license that can be | |
| 3 // found in the LICENSE file. | |
| 4 | |
| 5 #include "cc/base/math_util.h" | |
| 6 | |
| 7 #include <algorithm> | |
| 8 #include <cmath> | |
| 9 #include <limits> | |
| 10 | |
| 11 #include "base/trace_event/trace_event_argument.h" | |
| 12 #include "base/values.h" | |
| 13 #include "ui/gfx/geometry/quad_f.h" | |
| 14 #include "ui/gfx/geometry/rect.h" | |
| 15 #include "ui/gfx/geometry/rect_conversions.h" | |
| 16 #include "ui/gfx/geometry/rect_f.h" | |
| 17 #include "ui/gfx/geometry/vector2d_f.h" | |
| 18 #include "ui/gfx/transform.h" | |
| 19 | |
| 20 namespace cc { | |
| 21 | |
| 22 const double MathUtil::kPiDouble = 3.14159265358979323846; | |
| 23 const float MathUtil::kPiFloat = 3.14159265358979323846f; | |
| 24 | |
| 25 static HomogeneousCoordinate ProjectHomogeneousPoint( | |
| 26 const gfx::Transform& transform, | |
| 27 const gfx::PointF& p) { | |
| 28 // In this case, the layer we are trying to project onto is perpendicular to | |
| 29 // ray (point p and z-axis direction) that we are trying to project. This | |
| 30 // happens when the layer is rotated so that it is infinitesimally thin, or | |
| 31 // when it is co-planar with the camera origin -- i.e. when the layer is | |
| 32 // invisible anyway. | |
| 33 if (!transform.matrix().get(2, 2)) | |
| 34 return HomogeneousCoordinate(0.0, 0.0, 0.0, 1.0); | |
| 35 | |
| 36 SkMScalar z = -(transform.matrix().get(2, 0) * p.x() + | |
| 37 transform.matrix().get(2, 1) * p.y() + | |
| 38 transform.matrix().get(2, 3)) / | |
| 39 transform.matrix().get(2, 2); | |
| 40 HomogeneousCoordinate result(p.x(), p.y(), z, 1.0); | |
| 41 transform.matrix().mapMScalars(result.vec, result.vec); | |
| 42 return result; | |
| 43 } | |
| 44 | |
| 45 static HomogeneousCoordinate ProjectHomogeneousPoint( | |
| 46 const gfx::Transform& transform, | |
| 47 const gfx::PointF& p, | |
| 48 bool* clipped) { | |
| 49 HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p); | |
| 50 *clipped = h.w() <= 0; | |
| 51 return h; | |
| 52 } | |
| 53 | |
| 54 static HomogeneousCoordinate MapHomogeneousPoint( | |
| 55 const gfx::Transform& transform, | |
| 56 const gfx::Point3F& p) { | |
| 57 HomogeneousCoordinate result(p.x(), p.y(), p.z(), 1.0); | |
| 58 transform.matrix().mapMScalars(result.vec, result.vec); | |
| 59 return result; | |
| 60 } | |
| 61 | |
| 62 static HomogeneousCoordinate ComputeClippedPointForEdge( | |
| 63 const HomogeneousCoordinate& h1, | |
| 64 const HomogeneousCoordinate& h2) { | |
| 65 // Points h1 and h2 form a line in 4d, and any point on that line can be | |
| 66 // represented as an interpolation between h1 and h2: | |
| 67 // p = (1-t) h1 + (t) h2 | |
| 68 // | |
| 69 // We want to compute point p such that p.w == epsilon, where epsilon is a | |
| 70 // small non-zero number. (but the smaller the number is, the higher the risk | |
| 71 // of overflow) | |
| 72 // To do this, we solve for t in the following equation: | |
| 73 // p.w = epsilon = (1-t) * h1.w + (t) * h2.w | |
| 74 // | |
| 75 // Once paramter t is known, the rest of p can be computed via | |
| 76 // p = (1-t) h1 + (t) h2. | |
| 77 | |
| 78 // Technically this is a special case of the following assertion, but its a | |
| 79 // good idea to keep it an explicit sanity check here. | |
| 80 DCHECK_NE(h2.w(), h1.w()); | |
| 81 // Exactly one of h1 or h2 (but not both) must be on the negative side of the | |
| 82 // w plane when this is called. | |
| 83 DCHECK(h1.ShouldBeClipped() ^ h2.ShouldBeClipped()); | |
| 84 | |
| 85 // ...or any positive non-zero small epsilon | |
| 86 SkMScalar w = 0.00001f; | |
| 87 SkMScalar t = (w - h1.w()) / (h2.w() - h1.w()); | |
| 88 | |
| 89 SkMScalar x = (SK_MScalar1 - t) * h1.x() + t * h2.x(); | |
| 90 SkMScalar y = (SK_MScalar1 - t) * h1.y() + t * h2.y(); | |
| 91 SkMScalar z = (SK_MScalar1 - t) * h1.z() + t * h2.z(); | |
| 92 | |
| 93 return HomogeneousCoordinate(x, y, z, w); | |
| 94 } | |
| 95 | |
| 96 static inline void ExpandBoundsToIncludePoint(float* xmin, | |
| 97 float* xmax, | |
| 98 float* ymin, | |
| 99 float* ymax, | |
| 100 const gfx::PointF& p) { | |
| 101 *xmin = std::min(p.x(), *xmin); | |
| 102 *xmax = std::max(p.x(), *xmax); | |
| 103 *ymin = std::min(p.y(), *ymin); | |
| 104 *ymax = std::max(p.y(), *ymax); | |
| 105 } | |
| 106 | |
| 107 static inline void AddVertexToClippedQuad(const gfx::PointF& new_vertex, | |
| 108 gfx::PointF clipped_quad[8], | |
| 109 int* num_vertices_in_clipped_quad) { | |
| 110 clipped_quad[*num_vertices_in_clipped_quad] = new_vertex; | |
| 111 (*num_vertices_in_clipped_quad)++; | |
| 112 } | |
| 113 | |
| 114 static inline void AddVertexToClippedQuad3d(const gfx::Point3F& new_vertex, | |
| 115 gfx::Point3F clipped_quad[8], | |
| 116 int* num_vertices_in_clipped_quad) { | |
| 117 clipped_quad[*num_vertices_in_clipped_quad] = new_vertex; | |
| 118 (*num_vertices_in_clipped_quad)++; | |
| 119 } | |
| 120 | |
| 121 gfx::Rect MathUtil::MapEnclosingClippedRect(const gfx::Transform& transform, | |
| 122 const gfx::Rect& src_rect) { | |
| 123 if (transform.IsIdentityOrIntegerTranslation()) { | |
| 124 gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), | |
| 125 static_cast<int>(transform.matrix().getFloat(1, 3))); | |
| 126 return src_rect + offset; | |
| 127 } | |
| 128 return gfx::ToEnclosingRect(MapClippedRect(transform, gfx::RectF(src_rect))); | |
| 129 } | |
| 130 | |
| 131 gfx::RectF MathUtil::MapClippedRect(const gfx::Transform& transform, | |
| 132 const gfx::RectF& src_rect) { | |
| 133 if (transform.IsIdentityOrTranslation()) { | |
| 134 gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), | |
| 135 transform.matrix().getFloat(1, 3)); | |
| 136 return src_rect + offset; | |
| 137 } | |
| 138 | |
| 139 // Apply the transform, but retain the result in homogeneous coordinates. | |
| 140 | |
| 141 SkMScalar quad[4 * 2]; // input: 4 x 2D points | |
| 142 quad[0] = src_rect.x(); | |
| 143 quad[1] = src_rect.y(); | |
| 144 quad[2] = src_rect.right(); | |
| 145 quad[3] = src_rect.y(); | |
| 146 quad[4] = src_rect.right(); | |
| 147 quad[5] = src_rect.bottom(); | |
| 148 quad[6] = src_rect.x(); | |
| 149 quad[7] = src_rect.bottom(); | |
| 150 | |
| 151 SkMScalar result[4 * 4]; // output: 4 x 4D homogeneous points | |
| 152 transform.matrix().map2(quad, 4, result); | |
| 153 | |
| 154 HomogeneousCoordinate hc0(result[0], result[1], result[2], result[3]); | |
| 155 HomogeneousCoordinate hc1(result[4], result[5], result[6], result[7]); | |
| 156 HomogeneousCoordinate hc2(result[8], result[9], result[10], result[11]); | |
| 157 HomogeneousCoordinate hc3(result[12], result[13], result[14], result[15]); | |
| 158 return ComputeEnclosingClippedRect(hc0, hc1, hc2, hc3); | |
| 159 } | |
| 160 | |
| 161 gfx::Rect MathUtil::ProjectEnclosingClippedRect(const gfx::Transform& transform, | |
| 162 const gfx::Rect& src_rect) { | |
| 163 if (transform.IsIdentityOrIntegerTranslation()) { | |
| 164 gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), | |
| 165 static_cast<int>(transform.matrix().getFloat(1, 3))); | |
| 166 return src_rect + offset; | |
| 167 } | |
| 168 return gfx::ToEnclosingRect( | |
| 169 ProjectClippedRect(transform, gfx::RectF(src_rect))); | |
| 170 } | |
| 171 | |
| 172 gfx::RectF MathUtil::ProjectClippedRect(const gfx::Transform& transform, | |
| 173 const gfx::RectF& src_rect) { | |
| 174 if (transform.IsIdentityOrTranslation()) { | |
| 175 gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), | |
| 176 transform.matrix().getFloat(1, 3)); | |
| 177 return src_rect + offset; | |
| 178 } | |
| 179 | |
| 180 // Perform the projection, but retain the result in homogeneous coordinates. | |
| 181 gfx::QuadF q = gfx::QuadF(src_rect); | |
| 182 HomogeneousCoordinate h1 = ProjectHomogeneousPoint(transform, q.p1()); | |
| 183 HomogeneousCoordinate h2 = ProjectHomogeneousPoint(transform, q.p2()); | |
| 184 HomogeneousCoordinate h3 = ProjectHomogeneousPoint(transform, q.p3()); | |
| 185 HomogeneousCoordinate h4 = ProjectHomogeneousPoint(transform, q.p4()); | |
| 186 | |
| 187 return ComputeEnclosingClippedRect(h1, h2, h3, h4); | |
| 188 } | |
| 189 | |
| 190 gfx::Rect MathUtil::MapEnclosedRectWith2dAxisAlignedTransform( | |
| 191 const gfx::Transform& transform, | |
| 192 const gfx::Rect& rect) { | |
| 193 DCHECK(transform.Preserves2dAxisAlignment()); | |
| 194 | |
| 195 if (transform.IsIdentityOrIntegerTranslation()) { | |
| 196 gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), | |
| 197 static_cast<int>(transform.matrix().getFloat(1, 3))); | |
| 198 return rect + offset; | |
| 199 } | |
| 200 if (transform.IsIdentityOrTranslation()) { | |
| 201 gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), | |
| 202 transform.matrix().getFloat(1, 3)); | |
| 203 return gfx::ToEnclosedRect(rect + offset); | |
| 204 } | |
| 205 | |
| 206 SkMScalar quad[2 * 2]; // input: 2 x 2D points | |
| 207 quad[0] = rect.x(); | |
| 208 quad[1] = rect.y(); | |
| 209 quad[2] = rect.right(); | |
| 210 quad[3] = rect.bottom(); | |
| 211 | |
| 212 SkMScalar result[4 * 2]; // output: 2 x 4D homogeneous points | |
| 213 transform.matrix().map2(quad, 2, result); | |
| 214 | |
| 215 HomogeneousCoordinate hc0(result[0], result[1], result[2], result[3]); | |
| 216 HomogeneousCoordinate hc1(result[4], result[5], result[6], result[7]); | |
| 217 DCHECK(!hc0.ShouldBeClipped()); | |
| 218 DCHECK(!hc1.ShouldBeClipped()); | |
| 219 | |
| 220 gfx::PointF top_left(hc0.CartesianPoint2d()); | |
| 221 gfx::PointF bottom_right(hc1.CartesianPoint2d()); | |
| 222 return gfx::ToEnclosedRect(gfx::BoundingRect(top_left, bottom_right)); | |
| 223 } | |
| 224 | |
| 225 void MathUtil::MapClippedQuad(const gfx::Transform& transform, | |
| 226 const gfx::QuadF& src_quad, | |
| 227 gfx::PointF clipped_quad[8], | |
| 228 int* num_vertices_in_clipped_quad) { | |
| 229 HomogeneousCoordinate h1 = | |
| 230 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p1())); | |
| 231 HomogeneousCoordinate h2 = | |
| 232 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p2())); | |
| 233 HomogeneousCoordinate h3 = | |
| 234 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p3())); | |
| 235 HomogeneousCoordinate h4 = | |
| 236 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p4())); | |
| 237 | |
| 238 // The order of adding the vertices to the array is chosen so that | |
| 239 // clockwise / counter-clockwise orientation is retained. | |
| 240 | |
| 241 *num_vertices_in_clipped_quad = 0; | |
| 242 | |
| 243 if (!h1.ShouldBeClipped()) { | |
| 244 AddVertexToClippedQuad( | |
| 245 h1.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 246 } | |
| 247 | |
| 248 if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) { | |
| 249 AddVertexToClippedQuad( | |
| 250 ComputeClippedPointForEdge(h1, h2).CartesianPoint2d(), | |
| 251 clipped_quad, | |
| 252 num_vertices_in_clipped_quad); | |
| 253 } | |
| 254 | |
| 255 if (!h2.ShouldBeClipped()) { | |
| 256 AddVertexToClippedQuad( | |
| 257 h2.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 258 } | |
| 259 | |
| 260 if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) { | |
| 261 AddVertexToClippedQuad( | |
| 262 ComputeClippedPointForEdge(h2, h3).CartesianPoint2d(), | |
| 263 clipped_quad, | |
| 264 num_vertices_in_clipped_quad); | |
| 265 } | |
| 266 | |
| 267 if (!h3.ShouldBeClipped()) { | |
| 268 AddVertexToClippedQuad( | |
| 269 h3.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 270 } | |
| 271 | |
| 272 if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) { | |
| 273 AddVertexToClippedQuad( | |
| 274 ComputeClippedPointForEdge(h3, h4).CartesianPoint2d(), | |
| 275 clipped_quad, | |
| 276 num_vertices_in_clipped_quad); | |
| 277 } | |
| 278 | |
| 279 if (!h4.ShouldBeClipped()) { | |
| 280 AddVertexToClippedQuad( | |
| 281 h4.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 282 } | |
| 283 | |
| 284 if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) { | |
| 285 AddVertexToClippedQuad( | |
| 286 ComputeClippedPointForEdge(h4, h1).CartesianPoint2d(), | |
| 287 clipped_quad, | |
| 288 num_vertices_in_clipped_quad); | |
| 289 } | |
| 290 | |
| 291 DCHECK_LE(*num_vertices_in_clipped_quad, 8); | |
| 292 } | |
| 293 | |
| 294 bool MathUtil::MapClippedQuad3d(const gfx::Transform& transform, | |
| 295 const gfx::QuadF& src_quad, | |
| 296 gfx::Point3F clipped_quad[8], | |
| 297 int* num_vertices_in_clipped_quad) { | |
| 298 HomogeneousCoordinate h1 = | |
| 299 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p1())); | |
| 300 HomogeneousCoordinate h2 = | |
| 301 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p2())); | |
| 302 HomogeneousCoordinate h3 = | |
| 303 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p3())); | |
| 304 HomogeneousCoordinate h4 = | |
| 305 MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p4())); | |
| 306 | |
| 307 // The order of adding the vertices to the array is chosen so that | |
| 308 // clockwise / counter-clockwise orientation is retained. | |
| 309 | |
| 310 *num_vertices_in_clipped_quad = 0; | |
| 311 | |
| 312 if (!h1.ShouldBeClipped()) { | |
| 313 AddVertexToClippedQuad3d( | |
| 314 h1.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 315 } | |
| 316 | |
| 317 if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) { | |
| 318 AddVertexToClippedQuad3d( | |
| 319 ComputeClippedPointForEdge(h1, h2).CartesianPoint3d(), | |
| 320 clipped_quad, | |
| 321 num_vertices_in_clipped_quad); | |
| 322 } | |
| 323 | |
| 324 if (!h2.ShouldBeClipped()) { | |
| 325 AddVertexToClippedQuad3d( | |
| 326 h2.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 327 } | |
| 328 | |
| 329 if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) { | |
| 330 AddVertexToClippedQuad3d( | |
| 331 ComputeClippedPointForEdge(h2, h3).CartesianPoint3d(), | |
| 332 clipped_quad, | |
| 333 num_vertices_in_clipped_quad); | |
| 334 } | |
| 335 | |
| 336 if (!h3.ShouldBeClipped()) { | |
| 337 AddVertexToClippedQuad3d( | |
| 338 h3.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 339 } | |
| 340 | |
| 341 if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) { | |
| 342 AddVertexToClippedQuad3d( | |
| 343 ComputeClippedPointForEdge(h3, h4).CartesianPoint3d(), | |
| 344 clipped_quad, | |
| 345 num_vertices_in_clipped_quad); | |
| 346 } | |
| 347 | |
| 348 if (!h4.ShouldBeClipped()) { | |
| 349 AddVertexToClippedQuad3d( | |
| 350 h4.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); | |
| 351 } | |
| 352 | |
| 353 if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) { | |
| 354 AddVertexToClippedQuad3d( | |
| 355 ComputeClippedPointForEdge(h4, h1).CartesianPoint3d(), | |
| 356 clipped_quad, | |
| 357 num_vertices_in_clipped_quad); | |
| 358 } | |
| 359 | |
| 360 DCHECK_LE(*num_vertices_in_clipped_quad, 8); | |
| 361 return (*num_vertices_in_clipped_quad >= 4); | |
| 362 } | |
| 363 | |
| 364 gfx::RectF MathUtil::ComputeEnclosingRectOfVertices( | |
| 365 const gfx::PointF vertices[], | |
| 366 int num_vertices) { | |
| 367 if (num_vertices < 2) | |
| 368 return gfx::RectF(); | |
| 369 | |
| 370 float xmin = std::numeric_limits<float>::max(); | |
| 371 float xmax = -std::numeric_limits<float>::max(); | |
| 372 float ymin = std::numeric_limits<float>::max(); | |
| 373 float ymax = -std::numeric_limits<float>::max(); | |
| 374 | |
| 375 for (int i = 0; i < num_vertices; ++i) | |
| 376 ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, vertices[i]); | |
| 377 | |
| 378 return gfx::RectF(gfx::PointF(xmin, ymin), | |
| 379 gfx::SizeF(xmax - xmin, ymax - ymin)); | |
| 380 } | |
| 381 | |
| 382 gfx::RectF MathUtil::ComputeEnclosingClippedRect( | |
| 383 const HomogeneousCoordinate& h1, | |
| 384 const HomogeneousCoordinate& h2, | |
| 385 const HomogeneousCoordinate& h3, | |
| 386 const HomogeneousCoordinate& h4) { | |
| 387 // This function performs clipping as necessary and computes the enclosing 2d | |
| 388 // gfx::RectF of the vertices. Doing these two steps simultaneously allows us | |
| 389 // to avoid the overhead of storing an unknown number of clipped vertices. | |
| 390 | |
| 391 // If no vertices on the quad are clipped, then we can simply return the | |
| 392 // enclosing rect directly. | |
| 393 bool something_clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() || | |
| 394 h3.ShouldBeClipped() || h4.ShouldBeClipped(); | |
| 395 if (!something_clipped) { | |
| 396 gfx::QuadF mapped_quad = gfx::QuadF(h1.CartesianPoint2d(), | |
| 397 h2.CartesianPoint2d(), | |
| 398 h3.CartesianPoint2d(), | |
| 399 h4.CartesianPoint2d()); | |
| 400 return mapped_quad.BoundingBox(); | |
| 401 } | |
| 402 | |
| 403 bool everything_clipped = h1.ShouldBeClipped() && h2.ShouldBeClipped() && | |
| 404 h3.ShouldBeClipped() && h4.ShouldBeClipped(); | |
| 405 if (everything_clipped) | |
| 406 return gfx::RectF(); | |
| 407 | |
| 408 float xmin = std::numeric_limits<float>::max(); | |
| 409 float xmax = -std::numeric_limits<float>::max(); | |
| 410 float ymin = std::numeric_limits<float>::max(); | |
| 411 float ymax = -std::numeric_limits<float>::max(); | |
| 412 | |
| 413 if (!h1.ShouldBeClipped()) | |
| 414 ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, | |
| 415 h1.CartesianPoint2d()); | |
| 416 | |
| 417 if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) | |
| 418 ExpandBoundsToIncludePoint(&xmin, | |
| 419 &xmax, | |
| 420 &ymin, | |
| 421 &ymax, | |
| 422 ComputeClippedPointForEdge(h1, h2) | |
| 423 .CartesianPoint2d()); | |
| 424 | |
| 425 if (!h2.ShouldBeClipped()) | |
| 426 ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, | |
| 427 h2.CartesianPoint2d()); | |
| 428 | |
| 429 if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) | |
| 430 ExpandBoundsToIncludePoint(&xmin, | |
| 431 &xmax, | |
| 432 &ymin, | |
| 433 &ymax, | |
| 434 ComputeClippedPointForEdge(h2, h3) | |
| 435 .CartesianPoint2d()); | |
| 436 | |
| 437 if (!h3.ShouldBeClipped()) | |
| 438 ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, | |
| 439 h3.CartesianPoint2d()); | |
| 440 | |
| 441 if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) | |
| 442 ExpandBoundsToIncludePoint(&xmin, | |
| 443 &xmax, | |
| 444 &ymin, | |
| 445 &ymax, | |
| 446 ComputeClippedPointForEdge(h3, h4) | |
| 447 .CartesianPoint2d()); | |
| 448 | |
| 449 if (!h4.ShouldBeClipped()) | |
| 450 ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, | |
| 451 h4.CartesianPoint2d()); | |
| 452 | |
| 453 if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) | |
| 454 ExpandBoundsToIncludePoint(&xmin, | |
| 455 &xmax, | |
| 456 &ymin, | |
| 457 &ymax, | |
| 458 ComputeClippedPointForEdge(h4, h1) | |
| 459 .CartesianPoint2d()); | |
| 460 | |
| 461 return gfx::RectF(gfx::PointF(xmin, ymin), | |
| 462 gfx::SizeF(xmax - xmin, ymax - ymin)); | |
| 463 } | |
| 464 | |
| 465 gfx::QuadF MathUtil::MapQuad(const gfx::Transform& transform, | |
| 466 const gfx::QuadF& q, | |
| 467 bool* clipped) { | |
| 468 if (transform.IsIdentityOrTranslation()) { | |
| 469 gfx::QuadF mapped_quad(q); | |
| 470 mapped_quad += gfx::Vector2dF(transform.matrix().getFloat(0, 3), | |
| 471 transform.matrix().getFloat(1, 3)); | |
| 472 *clipped = false; | |
| 473 return mapped_quad; | |
| 474 } | |
| 475 | |
| 476 HomogeneousCoordinate h1 = | |
| 477 MapHomogeneousPoint(transform, gfx::Point3F(q.p1())); | |
| 478 HomogeneousCoordinate h2 = | |
| 479 MapHomogeneousPoint(transform, gfx::Point3F(q.p2())); | |
| 480 HomogeneousCoordinate h3 = | |
| 481 MapHomogeneousPoint(transform, gfx::Point3F(q.p3())); | |
| 482 HomogeneousCoordinate h4 = | |
| 483 MapHomogeneousPoint(transform, gfx::Point3F(q.p4())); | |
| 484 | |
| 485 *clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() || | |
| 486 h3.ShouldBeClipped() || h4.ShouldBeClipped(); | |
| 487 | |
| 488 // Result will be invalid if clipped == true. But, compute it anyway just in | |
| 489 // case, to emulate existing behavior. | |
| 490 return gfx::QuadF(h1.CartesianPoint2d(), | |
| 491 h2.CartesianPoint2d(), | |
| 492 h3.CartesianPoint2d(), | |
| 493 h4.CartesianPoint2d()); | |
| 494 } | |
| 495 | |
| 496 gfx::QuadF MathUtil::MapQuad3d(const gfx::Transform& transform, | |
| 497 const gfx::QuadF& q, | |
| 498 gfx::Point3F* p, | |
| 499 bool* clipped) { | |
| 500 if (transform.IsIdentityOrTranslation()) { | |
| 501 gfx::QuadF mapped_quad(q); | |
| 502 mapped_quad += gfx::Vector2dF(transform.matrix().getFloat(0, 3), | |
| 503 transform.matrix().getFloat(1, 3)); | |
| 504 *clipped = false; | |
| 505 p[0] = gfx::Point3F(mapped_quad.p1().x(), mapped_quad.p1().y(), 0.0f); | |
| 506 p[1] = gfx::Point3F(mapped_quad.p2().x(), mapped_quad.p2().y(), 0.0f); | |
| 507 p[2] = gfx::Point3F(mapped_quad.p3().x(), mapped_quad.p3().y(), 0.0f); | |
| 508 p[3] = gfx::Point3F(mapped_quad.p4().x(), mapped_quad.p4().y(), 0.0f); | |
| 509 return mapped_quad; | |
| 510 } | |
| 511 | |
| 512 HomogeneousCoordinate h1 = | |
| 513 MapHomogeneousPoint(transform, gfx::Point3F(q.p1())); | |
| 514 HomogeneousCoordinate h2 = | |
| 515 MapHomogeneousPoint(transform, gfx::Point3F(q.p2())); | |
| 516 HomogeneousCoordinate h3 = | |
| 517 MapHomogeneousPoint(transform, gfx::Point3F(q.p3())); | |
| 518 HomogeneousCoordinate h4 = | |
| 519 MapHomogeneousPoint(transform, gfx::Point3F(q.p4())); | |
| 520 | |
| 521 *clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() || | |
| 522 h3.ShouldBeClipped() || h4.ShouldBeClipped(); | |
| 523 | |
| 524 // Result will be invalid if clipped == true. But, compute it anyway just in | |
| 525 // case, to emulate existing behavior. | |
| 526 p[0] = h1.CartesianPoint3d(); | |
| 527 p[1] = h2.CartesianPoint3d(); | |
| 528 p[2] = h3.CartesianPoint3d(); | |
| 529 p[3] = h4.CartesianPoint3d(); | |
| 530 | |
| 531 return gfx::QuadF(h1.CartesianPoint2d(), | |
| 532 h2.CartesianPoint2d(), | |
| 533 h3.CartesianPoint2d(), | |
| 534 h4.CartesianPoint2d()); | |
| 535 } | |
| 536 | |
| 537 gfx::PointF MathUtil::MapPoint(const gfx::Transform& transform, | |
| 538 const gfx::PointF& p, | |
| 539 bool* clipped) { | |
| 540 HomogeneousCoordinate h = MapHomogeneousPoint(transform, gfx::Point3F(p)); | |
| 541 | |
| 542 if (h.w() > 0) { | |
| 543 *clipped = false; | |
| 544 return h.CartesianPoint2d(); | |
| 545 } | |
| 546 | |
| 547 // The cartesian coordinates will be invalid after dividing by w. | |
| 548 *clipped = true; | |
| 549 | |
| 550 // Avoid dividing by w if w == 0. | |
| 551 if (!h.w()) | |
| 552 return gfx::PointF(); | |
| 553 | |
| 554 // This return value will be invalid because clipped == true, but (1) users of | |
| 555 // this code should be ignoring the return value when clipped == true anyway, | |
| 556 // and (2) this behavior is more consistent with existing behavior of WebKit | |
| 557 // transforms if the user really does not ignore the return value. | |
| 558 return h.CartesianPoint2d(); | |
| 559 } | |
| 560 | |
| 561 gfx::Point3F MathUtil::MapPoint(const gfx::Transform& transform, | |
| 562 const gfx::Point3F& p, | |
| 563 bool* clipped) { | |
| 564 HomogeneousCoordinate h = MapHomogeneousPoint(transform, p); | |
| 565 | |
| 566 if (h.w() > 0) { | |
| 567 *clipped = false; | |
| 568 return h.CartesianPoint3d(); | |
| 569 } | |
| 570 | |
| 571 // The cartesian coordinates will be invalid after dividing by w. | |
| 572 *clipped = true; | |
| 573 | |
| 574 // Avoid dividing by w if w == 0. | |
| 575 if (!h.w()) | |
| 576 return gfx::Point3F(); | |
| 577 | |
| 578 // This return value will be invalid because clipped == true, but (1) users of | |
| 579 // this code should be ignoring the return value when clipped == true anyway, | |
| 580 // and (2) this behavior is more consistent with existing behavior of WebKit | |
| 581 // transforms if the user really does not ignore the return value. | |
| 582 return h.CartesianPoint3d(); | |
| 583 } | |
| 584 | |
| 585 gfx::QuadF MathUtil::ProjectQuad(const gfx::Transform& transform, | |
| 586 const gfx::QuadF& q, | |
| 587 bool* clipped) { | |
| 588 gfx::QuadF projected_quad; | |
| 589 bool clipped_point; | |
| 590 projected_quad.set_p1(ProjectPoint(transform, q.p1(), &clipped_point)); | |
| 591 *clipped = clipped_point; | |
| 592 projected_quad.set_p2(ProjectPoint(transform, q.p2(), &clipped_point)); | |
| 593 *clipped |= clipped_point; | |
| 594 projected_quad.set_p3(ProjectPoint(transform, q.p3(), &clipped_point)); | |
| 595 *clipped |= clipped_point; | |
| 596 projected_quad.set_p4(ProjectPoint(transform, q.p4(), &clipped_point)); | |
| 597 *clipped |= clipped_point; | |
| 598 | |
| 599 return projected_quad; | |
| 600 } | |
| 601 | |
| 602 gfx::PointF MathUtil::ProjectPoint(const gfx::Transform& transform, | |
| 603 const gfx::PointF& p, | |
| 604 bool* clipped) { | |
| 605 HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p, clipped); | |
| 606 // Avoid dividing by w if w == 0. | |
| 607 if (!h.w()) | |
| 608 return gfx::PointF(); | |
| 609 | |
| 610 // This return value will be invalid if clipped == true, but (1) users of | |
| 611 // this code should be ignoring the return value when clipped == true anyway, | |
| 612 // and (2) this behavior is more consistent with existing behavior of WebKit | |
| 613 // transforms if the user really does not ignore the return value. | |
| 614 return h.CartesianPoint2d(); | |
| 615 } | |
| 616 | |
| 617 gfx::Point3F MathUtil::ProjectPoint3D(const gfx::Transform& transform, | |
| 618 const gfx::PointF& p, | |
| 619 bool* clipped) { | |
| 620 HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p, clipped); | |
| 621 if (!h.w()) | |
| 622 return gfx::Point3F(); | |
| 623 return h.CartesianPoint3d(); | |
| 624 } | |
| 625 | |
| 626 gfx::RectF MathUtil::ScaleRectProportional(const gfx::RectF& input_outer_rect, | |
| 627 const gfx::RectF& scale_outer_rect, | |
| 628 const gfx::RectF& scale_inner_rect) { | |
| 629 gfx::RectF output_inner_rect = input_outer_rect; | |
| 630 float scale_rect_to_input_scale_x = | |
| 631 scale_outer_rect.width() / input_outer_rect.width(); | |
| 632 float scale_rect_to_input_scale_y = | |
| 633 scale_outer_rect.height() / input_outer_rect.height(); | |
| 634 | |
| 635 gfx::Vector2dF top_left_diff = | |
| 636 scale_inner_rect.origin() - scale_outer_rect.origin(); | |
| 637 gfx::Vector2dF bottom_right_diff = | |
| 638 scale_inner_rect.bottom_right() - scale_outer_rect.bottom_right(); | |
| 639 output_inner_rect.Inset(top_left_diff.x() / scale_rect_to_input_scale_x, | |
| 640 top_left_diff.y() / scale_rect_to_input_scale_y, | |
| 641 -bottom_right_diff.x() / scale_rect_to_input_scale_x, | |
| 642 -bottom_right_diff.y() / scale_rect_to_input_scale_y); | |
| 643 return output_inner_rect; | |
| 644 } | |
| 645 | |
| 646 static inline bool NearlyZero(double value) { | |
| 647 return std::abs(value) < std::numeric_limits<double>::epsilon(); | |
| 648 } | |
| 649 | |
| 650 static inline float ScaleOnAxis(double a, double b, double c) { | |
| 651 if (NearlyZero(b) && NearlyZero(c)) | |
| 652 return std::abs(a); | |
| 653 if (NearlyZero(a) && NearlyZero(c)) | |
| 654 return std::abs(b); | |
| 655 if (NearlyZero(a) && NearlyZero(b)) | |
| 656 return std::abs(c); | |
| 657 | |
| 658 // Do the sqrt as a double to not lose precision. | |
| 659 return static_cast<float>(std::sqrt(a * a + b * b + c * c)); | |
| 660 } | |
| 661 | |
| 662 gfx::Vector2dF MathUtil::ComputeTransform2dScaleComponents( | |
| 663 const gfx::Transform& transform, | |
| 664 float fallback_value) { | |
| 665 if (transform.HasPerspective()) | |
| 666 return gfx::Vector2dF(fallback_value, fallback_value); | |
| 667 float x_scale = ScaleOnAxis(transform.matrix().getDouble(0, 0), | |
| 668 transform.matrix().getDouble(1, 0), | |
| 669 transform.matrix().getDouble(2, 0)); | |
| 670 float y_scale = ScaleOnAxis(transform.matrix().getDouble(0, 1), | |
| 671 transform.matrix().getDouble(1, 1), | |
| 672 transform.matrix().getDouble(2, 1)); | |
| 673 return gfx::Vector2dF(x_scale, y_scale); | |
| 674 } | |
| 675 | |
| 676 float MathUtil::SmallestAngleBetweenVectors(const gfx::Vector2dF& v1, | |
| 677 const gfx::Vector2dF& v2) { | |
| 678 double dot_product = gfx::DotProduct(v1, v2) / v1.Length() / v2.Length(); | |
| 679 // Clamp to compensate for rounding errors. | |
| 680 dot_product = std::max(-1.0, std::min(1.0, dot_product)); | |
| 681 return static_cast<float>(Rad2Deg(std::acos(dot_product))); | |
| 682 } | |
| 683 | |
| 684 gfx::Vector2dF MathUtil::ProjectVector(const gfx::Vector2dF& source, | |
| 685 const gfx::Vector2dF& destination) { | |
| 686 float projected_length = | |
| 687 gfx::DotProduct(source, destination) / destination.LengthSquared(); | |
| 688 return gfx::Vector2dF(projected_length * destination.x(), | |
| 689 projected_length * destination.y()); | |
| 690 } | |
| 691 | |
| 692 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Size& s) { | |
| 693 scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue()); | |
| 694 res->SetDouble("width", s.width()); | |
| 695 res->SetDouble("height", s.height()); | |
| 696 return res.Pass(); | |
| 697 } | |
| 698 | |
| 699 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Rect& r) { | |
| 700 scoped_ptr<base::ListValue> res(new base::ListValue()); | |
| 701 res->AppendInteger(r.x()); | |
| 702 res->AppendInteger(r.y()); | |
| 703 res->AppendInteger(r.width()); | |
| 704 res->AppendInteger(r.height()); | |
| 705 return res.Pass(); | |
| 706 } | |
| 707 | |
| 708 bool MathUtil::FromValue(const base::Value* raw_value, gfx::Rect* out_rect) { | |
| 709 const base::ListValue* value = nullptr; | |
| 710 if (!raw_value->GetAsList(&value)) | |
| 711 return false; | |
| 712 | |
| 713 if (value->GetSize() != 4) | |
| 714 return false; | |
| 715 | |
| 716 int x, y, w, h; | |
| 717 bool ok = true; | |
| 718 ok &= value->GetInteger(0, &x); | |
| 719 ok &= value->GetInteger(1, &y); | |
| 720 ok &= value->GetInteger(2, &w); | |
| 721 ok &= value->GetInteger(3, &h); | |
| 722 if (!ok) | |
| 723 return false; | |
| 724 | |
| 725 *out_rect = gfx::Rect(x, y, w, h); | |
| 726 return true; | |
| 727 } | |
| 728 | |
| 729 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::PointF& pt) { | |
| 730 scoped_ptr<base::ListValue> res(new base::ListValue()); | |
| 731 res->AppendDouble(pt.x()); | |
| 732 res->AppendDouble(pt.y()); | |
| 733 return res.Pass(); | |
| 734 } | |
| 735 | |
| 736 void MathUtil::AddToTracedValue(const char* name, | |
| 737 const gfx::Size& s, | |
| 738 base::trace_event::TracedValue* res) { | |
| 739 res->BeginDictionary(name); | |
| 740 res->SetDouble("width", s.width()); | |
| 741 res->SetDouble("height", s.height()); | |
| 742 res->EndDictionary(); | |
| 743 } | |
| 744 | |
| 745 void MathUtil::AddToTracedValue(const char* name, | |
| 746 const gfx::SizeF& s, | |
| 747 base::trace_event::TracedValue* res) { | |
| 748 res->BeginDictionary(name); | |
| 749 res->SetDouble("width", s.width()); | |
| 750 res->SetDouble("height", s.height()); | |
| 751 res->EndDictionary(); | |
| 752 } | |
| 753 | |
| 754 void MathUtil::AddToTracedValue(const char* name, | |
| 755 const gfx::Rect& r, | |
| 756 base::trace_event::TracedValue* res) { | |
| 757 res->BeginArray(name); | |
| 758 res->AppendInteger(r.x()); | |
| 759 res->AppendInteger(r.y()); | |
| 760 res->AppendInteger(r.width()); | |
| 761 res->AppendInteger(r.height()); | |
| 762 res->EndArray(); | |
| 763 } | |
| 764 | |
| 765 void MathUtil::AddToTracedValue(const char* name, | |
| 766 const gfx::PointF& pt, | |
| 767 base::trace_event::TracedValue* res) { | |
| 768 res->BeginArray(name); | |
| 769 res->AppendDouble(pt.x()); | |
| 770 res->AppendDouble(pt.y()); | |
| 771 res->EndArray(); | |
| 772 } | |
| 773 | |
| 774 void MathUtil::AddToTracedValue(const char* name, | |
| 775 const gfx::Point3F& pt, | |
| 776 base::trace_event::TracedValue* res) { | |
| 777 res->BeginArray(name); | |
| 778 res->AppendDouble(pt.x()); | |
| 779 res->AppendDouble(pt.y()); | |
| 780 res->AppendDouble(pt.z()); | |
| 781 res->EndArray(); | |
| 782 } | |
| 783 | |
| 784 void MathUtil::AddToTracedValue(const char* name, | |
| 785 const gfx::Vector2d& v, | |
| 786 base::trace_event::TracedValue* res) { | |
| 787 res->BeginArray(name); | |
| 788 res->AppendInteger(v.x()); | |
| 789 res->AppendInteger(v.y()); | |
| 790 res->EndArray(); | |
| 791 } | |
| 792 | |
| 793 void MathUtil::AddToTracedValue(const char* name, | |
| 794 const gfx::Vector2dF& v, | |
| 795 base::trace_event::TracedValue* res) { | |
| 796 res->BeginArray(name); | |
| 797 res->AppendDouble(v.x()); | |
| 798 res->AppendDouble(v.y()); | |
| 799 res->EndArray(); | |
| 800 } | |
| 801 | |
| 802 void MathUtil::AddToTracedValue(const char* name, | |
| 803 const gfx::ScrollOffset& v, | |
| 804 base::trace_event::TracedValue* res) { | |
| 805 res->BeginArray(name); | |
| 806 res->AppendDouble(v.x()); | |
| 807 res->AppendDouble(v.y()); | |
| 808 res->EndArray(); | |
| 809 } | |
| 810 | |
| 811 void MathUtil::AddToTracedValue(const char* name, | |
| 812 const gfx::QuadF& q, | |
| 813 base::trace_event::TracedValue* res) { | |
| 814 res->BeginArray(name); | |
| 815 res->AppendDouble(q.p1().x()); | |
| 816 res->AppendDouble(q.p1().y()); | |
| 817 res->AppendDouble(q.p2().x()); | |
| 818 res->AppendDouble(q.p2().y()); | |
| 819 res->AppendDouble(q.p3().x()); | |
| 820 res->AppendDouble(q.p3().y()); | |
| 821 res->AppendDouble(q.p4().x()); | |
| 822 res->AppendDouble(q.p4().y()); | |
| 823 res->EndArray(); | |
| 824 } | |
| 825 | |
| 826 void MathUtil::AddToTracedValue(const char* name, | |
| 827 const gfx::RectF& rect, | |
| 828 base::trace_event::TracedValue* res) { | |
| 829 res->BeginArray(name); | |
| 830 res->AppendDouble(rect.x()); | |
| 831 res->AppendDouble(rect.y()); | |
| 832 res->AppendDouble(rect.width()); | |
| 833 res->AppendDouble(rect.height()); | |
| 834 res->EndArray(); | |
| 835 } | |
| 836 | |
| 837 void MathUtil::AddToTracedValue(const char* name, | |
| 838 const gfx::Transform& transform, | |
| 839 base::trace_event::TracedValue* res) { | |
| 840 res->BeginArray(name); | |
| 841 const SkMatrix44& m = transform.matrix(); | |
| 842 for (int row = 0; row < 4; ++row) { | |
| 843 for (int col = 0; col < 4; ++col) | |
| 844 res->AppendDouble(m.getDouble(row, col)); | |
| 845 } | |
| 846 res->EndArray(); | |
| 847 } | |
| 848 | |
| 849 void MathUtil::AddToTracedValue(const char* name, | |
| 850 const gfx::BoxF& box, | |
| 851 base::trace_event::TracedValue* res) { | |
| 852 res->BeginArray(name); | |
| 853 res->AppendInteger(box.x()); | |
| 854 res->AppendInteger(box.y()); | |
| 855 res->AppendInteger(box.z()); | |
| 856 res->AppendInteger(box.width()); | |
| 857 res->AppendInteger(box.height()); | |
| 858 res->AppendInteger(box.depth()); | |
| 859 res->EndArray(); | |
| 860 } | |
| 861 | |
| 862 double MathUtil::AsDoubleSafely(double value) { | |
| 863 return std::min(value, std::numeric_limits<double>::max()); | |
| 864 } | |
| 865 | |
| 866 float MathUtil::AsFloatSafely(float value) { | |
| 867 return std::min(value, std::numeric_limits<float>::max()); | |
| 868 } | |
| 869 | |
| 870 } // namespace cc | |
| OLD | NEW |
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