src/cc/base/math_util.cc

   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/values.h"
  12 #include "ui/gfx/quad_f.h"
  13 #include "ui/gfx/rect.h"
  14 #include "ui/gfx/rect_conversions.h"
  15 #include "ui/gfx/rect_f.h"
  16 #include "ui/gfx/transform.h"
  17 #include "ui/gfx/vector2d_f.h"
  18
  19 namespace cc {
  20
  21 const double MathUtil::kPiDouble = 3.14159265358979323846;
  22 const float MathUtil::kPiFloat = 3.14159265358979323846f;
  23
  24 static HomogeneousCoordinate ProjectHomogeneousPoint(
  25     const gfx::Transform& transform,
  26     const gfx::PointF& p) {
  27   // In this case, the layer we are trying to project onto is perpendicular to
  28   // ray (point p and z-axis direction) that we are trying to project. This
  29   // happens when the layer is rotated so that it is infinitesimally thin, or
  30   // when it is co-planar with the camera origin -- i.e. when the layer is
  31   // invisible anyway.
  32   if (!transform.matrix().get(2, 2))
  33     return HomogeneousCoordinate(0.0, 0.0, 0.0, 1.0);
  34
  35   SkMScalar z = -(transform.matrix().get(2, 0) * p.x() +
  36              transform.matrix().get(2, 1) * p.y() +
  37              transform.matrix().get(2, 3)) /
  38              transform.matrix().get(2, 2);
  39   HomogeneousCoordinate result(p.x(), p.y(), z, 1.0);
  40   transform.matrix().mapMScalars(result.vec, result.vec);
  41   return result;
  42 }
  43
  44 static HomogeneousCoordinate MapHomogeneousPoint(
  45     const gfx::Transform& transform,
  46     const gfx::Point3F& p) {
  47   HomogeneousCoordinate result(p.x(), p.y(), p.z(), 1.0);
  48   transform.matrix().mapMScalars(result.vec, result.vec);
  49   return result;
  50 }
  51
  52 static HomogeneousCoordinate ComputeClippedPointForEdge(
  53     const HomogeneousCoordinate& h1,
  54     const HomogeneousCoordinate& h2) {
  55   // Points h1 and h2 form a line in 4d, and any point on that line can be
  56   // represented as an interpolation between h1 and h2:
  57   //    p = (1-t) h1 + (t) h2
  58   //
  59   // We want to compute point p such that p.w == epsilon, where epsilon is a
  60   // small non-zero number. (but the smaller the number is, the higher the risk
  61   // of overflow)
  62   // To do this, we solve for t in the following equation:
  63   //    p.w = epsilon = (1-t) * h1.w + (t) * h2.w
  64   //
  65   // Once paramter t is known, the rest of p can be computed via
  66   //    p = (1-t) h1 + (t) h2.
  67
  68   // Technically this is a special case of the following assertion, but its a
  69   // good idea to keep it an explicit sanity check here.
  70   DCHECK_NE(h2.w(), h1.w());
  71   // Exactly one of h1 or h2 (but not both) must be on the negative side of the
  72   // w plane when this is called.
  73   DCHECK(h1.ShouldBeClipped() ^ h2.ShouldBeClipped());
  74
  75   // ...or any positive non-zero small epsilon
  76   SkMScalar w = 0.00001f;
  77   SkMScalar t = (w - h1.w()) / (h2.w() - h1.w());
  78
  79   SkMScalar x = (SK_MScalar1 - t) * h1.x() + t * h2.x();
  80   SkMScalar y = (SK_MScalar1 - t) * h1.y() + t * h2.y();
  81   SkMScalar z = (SK_MScalar1 - t) * h1.z() + t * h2.z();
  82
  83   return HomogeneousCoordinate(x, y, z, w);
  84 }
  85
  86 static inline void ExpandBoundsToIncludePoint(float* xmin,
  87                                               float* xmax,
  88                                               float* ymin,
  89                                               float* ymax,
  90                                               const gfx::PointF& p) {
  91   *xmin = std::min(p.x(), *xmin);
  92   *xmax = std::max(p.x(), *xmax);
  93   *ymin = std::min(p.y(), *ymin);
  94   *ymax = std::max(p.y(), *ymax);
  95 }
  96
  97 static inline void AddVertexToClippedQuad(const gfx::PointF& new_vertex,
  98                                           gfx::PointF clipped_quad[8],
  99                                           int* num_vertices_in_clipped_quad) {
 100   clipped_quad[*num_vertices_in_clipped_quad] = new_vertex;
 101   (*num_vertices_in_clipped_quad)++;
 102 }
 103
 104 gfx::Rect MathUtil::MapEnclosingClippedRect(const gfx::Transform& transform,
 105                                             const gfx::Rect& src_rect) {
 106   if (transform.IsIdentityOrIntegerTranslation()) {
 107     return src_rect +
 108            gfx::Vector2d(
 109                static_cast<int>(SkMScalarToFloat(transform.matrix().get(0, 3))),
 110                static_cast<int>(
 111                    SkMScalarToFloat(transform.matrix().get(1, 3))));
 112   }
 113   return gfx::ToEnclosingRect(MapClippedRect(transform, gfx::RectF(src_rect)));
 114 }
 115
 116 gfx::RectF MathUtil::MapClippedRect(const gfx::Transform& transform,
 117                                     const gfx::RectF& src_rect) {
 118   if (transform.IsIdentityOrTranslation()) {
 119     return src_rect +
 120            gfx::Vector2dF(SkMScalarToFloat(transform.matrix().get(0, 3)),
 121                           SkMScalarToFloat(transform.matrix().get(1, 3)));
 122   }
 123
 124   // Apply the transform, but retain the result in homogeneous coordinates.
 125
 126   SkMScalar quad[4 * 2];  // input: 4 x 2D points
 127   quad[0] = src_rect.x();
 128   quad[1] = src_rect.y();
 129   quad[2] = src_rect.right();
 130   quad[3] = src_rect.y();
 131   quad[4] = src_rect.right();
 132   quad[5] = src_rect.bottom();
 133   quad[6] = src_rect.x();
 134   quad[7] = src_rect.bottom();
 135
 136   SkMScalar result[4 * 4];  // output: 4 x 4D homogeneous points
 137   transform.matrix().map2(quad, 4, result);
 138
 139   HomogeneousCoordinate hc0(result[0], result[1], result[2], result[3]);
 140   HomogeneousCoordinate hc1(result[4], result[5], result[6], result[7]);
 141   HomogeneousCoordinate hc2(result[8], result[9], result[10], result[11]);
 142   HomogeneousCoordinate hc3(result[12], result[13], result[14], result[15]);
 143   return ComputeEnclosingClippedRect(hc0, hc1, hc2, hc3);
 144 }
 145
 146 gfx::Rect MathUtil::ProjectEnclosingClippedRect(const gfx::Transform& transform,
 147                                                 const gfx::Rect& src_rect) {
 148   if (transform.IsIdentityOrIntegerTranslation()) {
 149     return src_rect +
 150            gfx::Vector2d(
 151                static_cast<int>(SkMScalarToFloat(transform.matrix().get(0, 3))),
 152                static_cast<int>(
 153                    SkMScalarToFloat(transform.matrix().get(1, 3))));
 154   }
 155   return gfx::ToEnclosingRect(
 156       ProjectClippedRect(transform, gfx::RectF(src_rect)));
 157 }
 158
 159 gfx::RectF MathUtil::ProjectClippedRect(const gfx::Transform& transform,
 160                                         const gfx::RectF& src_rect) {
 161   if (transform.IsIdentityOrTranslation()) {
 162     return src_rect +
 163            gfx::Vector2dF(SkMScalarToFloat(transform.matrix().get(0, 3)),
 164                           SkMScalarToFloat(transform.matrix().get(1, 3)));
 165   }
 166
 167   // Perform the projection, but retain the result in homogeneous coordinates.
 168   gfx::QuadF q = gfx::QuadF(src_rect);
 169   HomogeneousCoordinate h1 = ProjectHomogeneousPoint(transform, q.p1());
 170   HomogeneousCoordinate h2 = ProjectHomogeneousPoint(transform, q.p2());
 171   HomogeneousCoordinate h3 = ProjectHomogeneousPoint(transform, q.p3());
 172   HomogeneousCoordinate h4 = ProjectHomogeneousPoint(transform, q.p4());
 173
 174   return ComputeEnclosingClippedRect(h1, h2, h3, h4);
 175 }
 176
 177 void MathUtil::MapClippedQuad(const gfx::Transform& transform,
 178                               const gfx::QuadF& src_quad,
 179                               gfx::PointF clipped_quad[8],
 180                               int* num_vertices_in_clipped_quad) {
 181   HomogeneousCoordinate h1 =
 182       MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p1()));
 183   HomogeneousCoordinate h2 =
 184       MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p2()));
 185   HomogeneousCoordinate h3 =
 186       MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p3()));
 187   HomogeneousCoordinate h4 =
 188       MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p4()));
 189
 190   // The order of adding the vertices to the array is chosen so that
 191   // clockwise / counter-clockwise orientation is retained.
 192
 193   *num_vertices_in_clipped_quad = 0;
 194
 195   if (!h1.ShouldBeClipped()) {
 196     AddVertexToClippedQuad(
 197         h1.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad);
 198   }
 199
 200   if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) {
 201     AddVertexToClippedQuad(
 202         ComputeClippedPointForEdge(h1, h2).CartesianPoint2d(),
 203         clipped_quad,
 204         num_vertices_in_clipped_quad);
 205   }
 206
 207   if (!h2.ShouldBeClipped()) {
 208     AddVertexToClippedQuad(
 209         h2.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad);
 210   }
 211
 212   if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) {
 213     AddVertexToClippedQuad(
 214         ComputeClippedPointForEdge(h2, h3).CartesianPoint2d(),
 215         clipped_quad,
 216         num_vertices_in_clipped_quad);
 217   }
 218
 219   if (!h3.ShouldBeClipped()) {
 220     AddVertexToClippedQuad(
 221         h3.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad);
 222   }
 223
 224   if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) {
 225     AddVertexToClippedQuad(
 226         ComputeClippedPointForEdge(h3, h4).CartesianPoint2d(),
 227         clipped_quad,
 228         num_vertices_in_clipped_quad);
 229   }
 230
 231   if (!h4.ShouldBeClipped()) {
 232     AddVertexToClippedQuad(
 233         h4.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad);
 234   }
 235
 236   if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) {
 237     AddVertexToClippedQuad(
 238         ComputeClippedPointForEdge(h4, h1).CartesianPoint2d(),
 239         clipped_quad,
 240         num_vertices_in_clipped_quad);
 241   }
 242
 243   DCHECK_LE(*num_vertices_in_clipped_quad, 8);
 244 }
 245
 246 gfx::RectF MathUtil::ComputeEnclosingRectOfVertices(
 247     const gfx::PointF vertices[],
 248     int num_vertices) {
 249   if (num_vertices < 2)
 250     return gfx::RectF();
 251
 252   float xmin = std::numeric_limits<float>::max();
 253   float xmax = -std::numeric_limits<float>::max();
 254   float ymin = std::numeric_limits<float>::max();
 255   float ymax = -std::numeric_limits<float>::max();
 256
 257   for (int i = 0; i < num_vertices; ++i)
 258     ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, vertices[i]);
 259
 260   return gfx::RectF(gfx::PointF(xmin, ymin),
 261                     gfx::SizeF(xmax - xmin, ymax - ymin));
 262 }
 263
 264 gfx::RectF MathUtil::ComputeEnclosingClippedRect(
 265     const HomogeneousCoordinate& h1,
 266     const HomogeneousCoordinate& h2,
 267     const HomogeneousCoordinate& h3,
 268     const HomogeneousCoordinate& h4) {
 269   // This function performs clipping as necessary and computes the enclosing 2d
 270   // gfx::RectF of the vertices. Doing these two steps simultaneously allows us
 271   // to avoid the overhead of storing an unknown number of clipped vertices.
 272
 273   // If no vertices on the quad are clipped, then we can simply return the
 274   // enclosing rect directly.
 275   bool something_clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() ||
 276                            h3.ShouldBeClipped() || h4.ShouldBeClipped();
 277   if (!something_clipped) {
 278     gfx::QuadF mapped_quad = gfx::QuadF(h1.CartesianPoint2d(),
 279                                         h2.CartesianPoint2d(),
 280                                         h3.CartesianPoint2d(),
 281                                         h4.CartesianPoint2d());
 282     return mapped_quad.BoundingBox();
 283   }
 284
 285   bool everything_clipped = h1.ShouldBeClipped() && h2.ShouldBeClipped() &&
 286                             h3.ShouldBeClipped() && h4.ShouldBeClipped();
 287   if (everything_clipped)
 288     return gfx::RectF();
 289
 290   float xmin = std::numeric_limits<float>::max();
 291   float xmax = -std::numeric_limits<float>::max();
 292   float ymin = std::numeric_limits<float>::max();
 293   float ymax = -std::numeric_limits<float>::max();
 294
 295   if (!h1.ShouldBeClipped())
 296     ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax,
 297                                h1.CartesianPoint2d());
 298
 299   if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped())
 300     ExpandBoundsToIncludePoint(&xmin,
 301                                &xmax,
 302                                &ymin,
 303                                &ymax,
 304                                ComputeClippedPointForEdge(h1, h2)
 305                                    .CartesianPoint2d());
 306
 307   if (!h2.ShouldBeClipped())
 308     ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax,
 309                                h2.CartesianPoint2d());
 310
 311   if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped())
 312     ExpandBoundsToIncludePoint(&xmin,
 313                                &xmax,
 314                                &ymin,
 315                                &ymax,
 316                                ComputeClippedPointForEdge(h2, h3)
 317                                    .CartesianPoint2d());
 318
 319   if (!h3.ShouldBeClipped())
 320     ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax,
 321                                h3.CartesianPoint2d());
 322
 323   if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped())
 324     ExpandBoundsToIncludePoint(&xmin,
 325                                &xmax,
 326                                &ymin,
 327                                &ymax,
 328                                ComputeClippedPointForEdge(h3, h4)
 329                                    .CartesianPoint2d());
 330
 331   if (!h4.ShouldBeClipped())
 332     ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax,
 333                                h4.CartesianPoint2d());
 334
 335   if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped())
 336     ExpandBoundsToIncludePoint(&xmin,
 337                                &xmax,
 338                                &ymin,
 339                                &ymax,
 340                                ComputeClippedPointForEdge(h4, h1)
 341                                    .CartesianPoint2d());
 342
 343   return gfx::RectF(gfx::PointF(xmin, ymin),
 344                     gfx::SizeF(xmax - xmin, ymax - ymin));
 345 }
 346
 347 gfx::QuadF MathUtil::MapQuad(const gfx::Transform& transform,
 348                              const gfx::QuadF& q,
 349                              bool* clipped) {
 350   if (transform.IsIdentityOrTranslation()) {
 351     gfx::QuadF mapped_quad(q);
 352     mapped_quad +=
 353         gfx::Vector2dF(SkMScalarToFloat(transform.matrix().get(0, 3)),
 354                        SkMScalarToFloat(transform.matrix().get(1, 3)));
 355     *clipped = false;
 356     return mapped_quad;
 357   }
 358
 359   HomogeneousCoordinate h1 =
 360       MapHomogeneousPoint(transform, gfx::Point3F(q.p1()));
 361   HomogeneousCoordinate h2 =
 362       MapHomogeneousPoint(transform, gfx::Point3F(q.p2()));
 363   HomogeneousCoordinate h3 =
 364       MapHomogeneousPoint(transform, gfx::Point3F(q.p3()));
 365   HomogeneousCoordinate h4 =
 366       MapHomogeneousPoint(transform, gfx::Point3F(q.p4()));
 367
 368   *clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() ||
 369             h3.ShouldBeClipped() || h4.ShouldBeClipped();
 370
 371   // Result will be invalid if clipped == true. But, compute it anyway just in
 372   // case, to emulate existing behavior.
 373   return gfx::QuadF(h1.CartesianPoint2d(),
 374                     h2.CartesianPoint2d(),
 375                     h3.CartesianPoint2d(),
 376                     h4.CartesianPoint2d());
 377 }
 378
 379 gfx::PointF MathUtil::MapPoint(const gfx::Transform& transform,
 380                                const gfx::PointF& p,
 381                                bool* clipped) {
 382   HomogeneousCoordinate h = MapHomogeneousPoint(transform, gfx::Point3F(p));
 383
 384   if (h.w() > 0) {
 385     *clipped = false;
 386     return h.CartesianPoint2d();
 387   }
 388
 389   // The cartesian coordinates will be invalid after dividing by w.
 390   *clipped = true;
 391
 392   // Avoid dividing by w if w == 0.
 393   if (!h.w())
 394     return gfx::PointF();
 395
 396   // This return value will be invalid because clipped == true, but (1) users of
 397   // this code should be ignoring the return value when clipped == true anyway,
 398   // and (2) this behavior is more consistent with existing behavior of WebKit
 399   // transforms if the user really does not ignore the return value.
 400   return h.CartesianPoint2d();
 401 }
 402
 403 gfx::Point3F MathUtil::MapPoint(const gfx::Transform& transform,
 404                                 const gfx::Point3F& p,
 405                                 bool* clipped) {
 406   HomogeneousCoordinate h = MapHomogeneousPoint(transform, p);
 407
 408   if (h.w() > 0) {
 409     *clipped = false;
 410     return h.CartesianPoint3d();
 411   }
 412
 413   // The cartesian coordinates will be invalid after dividing by w.
 414   *clipped = true;
 415
 416   // Avoid dividing by w if w == 0.
 417   if (!h.w())
 418     return gfx::Point3F();
 419
 420   // This return value will be invalid because clipped == true, but (1) users of
 421   // this code should be ignoring the return value when clipped == true anyway,
 422   // and (2) this behavior is more consistent with existing behavior of WebKit
 423   // transforms if the user really does not ignore the return value.
 424   return h.CartesianPoint3d();
 425 }
 426
 427 gfx::QuadF MathUtil::ProjectQuad(const gfx::Transform& transform,
 428                                  const gfx::QuadF& q,
 429                                  bool* clipped) {
 430   gfx::QuadF projected_quad;
 431   bool clipped_point;
 432   projected_quad.set_p1(ProjectPoint(transform, q.p1(), &clipped_point));
 433   *clipped = clipped_point;
 434   projected_quad.set_p2(ProjectPoint(transform, q.p2(), &clipped_point));
 435   *clipped |= clipped_point;
 436   projected_quad.set_p3(ProjectPoint(transform, q.p3(), &clipped_point));
 437   *clipped |= clipped_point;
 438   projected_quad.set_p4(ProjectPoint(transform, q.p4(), &clipped_point));
 439   *clipped |= clipped_point;
 440
 441   return projected_quad;
 442 }
 443
 444 gfx::PointF MathUtil::ProjectPoint(const gfx::Transform& transform,
 445                                    const gfx::PointF& p,
 446                                    bool* clipped) {
 447   HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p);
 448
 449   if (h.w() > 0) {
 450     // The cartesian coordinates will be valid in this case.
 451     *clipped = false;
 452     return h.CartesianPoint2d();
 453   }
 454
 455   // The cartesian coordinates will be invalid after dividing by w.
 456   *clipped = true;
 457
 458   // Avoid dividing by w if w == 0.
 459   if (!h.w())
 460     return gfx::PointF();
 461
 462   // This return value will be invalid because clipped == true, but (1) users of
 463   // this code should be ignoring the return value when clipped == true anyway,
 464   // and (2) this behavior is more consistent with existing behavior of WebKit
 465   // transforms if the user really does not ignore the return value.
 466   return h.CartesianPoint2d();
 467 }
 468
 469 gfx::RectF MathUtil::ScaleRectProportional(const gfx::RectF& input_outer_rect,
 470                                            const gfx::RectF& scale_outer_rect,
 471                                            const gfx::RectF& scale_inner_rect) {
 472   gfx::RectF output_inner_rect = input_outer_rect;
 473   float scale_rect_to_input_scale_x =
 474       scale_outer_rect.width() / input_outer_rect.width();
 475   float scale_rect_to_input_scale_y =
 476       scale_outer_rect.height() / input_outer_rect.height();
 477
 478   gfx::Vector2dF top_left_diff =
 479       scale_inner_rect.origin() - scale_outer_rect.origin();
 480   gfx::Vector2dF bottom_right_diff =
 481       scale_inner_rect.bottom_right() - scale_outer_rect.bottom_right();
 482   output_inner_rect.Inset(top_left_diff.x() / scale_rect_to_input_scale_x,
 483                           top_left_diff.y() / scale_rect_to_input_scale_y,
 484                           -bottom_right_diff.x() / scale_rect_to_input_scale_x,
 485                           -bottom_right_diff.y() / scale_rect_to_input_scale_y);
 486   return output_inner_rect;
 487 }
 488
 489 static inline bool NearlyZero(double value) {
 490   return std::abs(value) < std::numeric_limits<double>::epsilon();
 491 }
 492
 493 static inline float ScaleOnAxis(double a, double b, double c) {
 494   if (NearlyZero(b) && NearlyZero(c))
 495     return std::abs(a);
 496   if (NearlyZero(a) && NearlyZero(c))
 497     return std::abs(b);
 498   if (NearlyZero(a) && NearlyZero(b))
 499     return std::abs(c);
 500
 501   // Do the sqrt as a double to not lose precision.
 502   return static_cast<float>(std::sqrt(a * a + b * b + c * c));
 503 }
 504
 505 gfx::Vector2dF MathUtil::ComputeTransform2dScaleComponents(
 506     const gfx::Transform& transform,
 507     float fallback_value) {
 508   if (transform.HasPerspective())
 509     return gfx::Vector2dF(fallback_value, fallback_value);
 510   float x_scale = ScaleOnAxis(transform.matrix().getDouble(0, 0),
 511                               transform.matrix().getDouble(1, 0),
 512                               transform.matrix().getDouble(2, 0));
 513   float y_scale = ScaleOnAxis(transform.matrix().getDouble(0, 1),
 514                               transform.matrix().getDouble(1, 1),
 515                               transform.matrix().getDouble(2, 1));
 516   return gfx::Vector2dF(x_scale, y_scale);
 517 }
 518
 519 float MathUtil::SmallestAngleBetweenVectors(const gfx::Vector2dF& v1,
 520                                             const gfx::Vector2dF& v2) {
 521   double dot_product = gfx::DotProduct(v1, v2) / v1.Length() / v2.Length();
 522   // Clamp to compensate for rounding errors.
 523   dot_product = std::max(-1.0, std::min(1.0, dot_product));
 524   return static_cast<float>(Rad2Deg(std::acos(dot_product)));
 525 }
 526
 527 gfx::Vector2dF MathUtil::ProjectVector(const gfx::Vector2dF& source,
 528                                        const gfx::Vector2dF& destination) {
 529   float projected_length =
 530       gfx::DotProduct(source, destination) / destination.LengthSquared();
 531   return gfx::Vector2dF(projected_length * destination.x(),
 532                         projected_length * destination.y());
 533 }
 534
 535 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Size& s) {
 536   scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue());
 537   res->SetDouble("width", s.width());
 538   res->SetDouble("height", s.height());
 539   return res.PassAs<base::Value>();
 540 }
 541
 542 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::SizeF& s) {
 543   scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue());
 544   res->SetDouble("width", s.width());
 545   res->SetDouble("height", s.height());
 546   return res.PassAs<base::Value>();
 547 }
 548
 549 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Rect& r) {
 550   scoped_ptr<base::ListValue> res(new base::ListValue());
 551   res->AppendInteger(r.x());
 552   res->AppendInteger(r.y());
 553   res->AppendInteger(r.width());
 554   res->AppendInteger(r.height());
 555   return res.PassAs<base::Value>();
 556 }
 557
 558 bool MathUtil::FromValue(const base::Value* raw_value, gfx::Rect* out_rect) {
 559   const base::ListValue* value = NULL;
 560   if (!raw_value->GetAsList(&value))
 561     return false;
 562
 563   if (value->GetSize() != 4)
 564     return false;
 565
 566   int x, y, w, h;
 567   bool ok = true;
 568   ok &= value->GetInteger(0, &x);
 569   ok &= value->GetInteger(1, &y);
 570   ok &= value->GetInteger(2, &w);
 571   ok &= value->GetInteger(3, &h);
 572   if (!ok)
 573     return false;
 574
 575   *out_rect = gfx::Rect(x, y, w, h);
 576   return true;
 577 }
 578
 579 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::PointF& pt) {
 580   scoped_ptr<base::ListValue> res(new base::ListValue());
 581   res->AppendDouble(pt.x());
 582   res->AppendDouble(pt.y());
 583   return res.PassAs<base::Value>();
 584 }
 585
 586 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Vector2d& v) {
 587   scoped_ptr<base::ListValue> res(new base::ListValue());
 588   res->AppendInteger(v.x());
 589   res->AppendInteger(v.y());
 590   return res.PassAs<base::Value>();
 591 }
 592
 593 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::QuadF& q) {
 594   scoped_ptr<base::ListValue> res(new base::ListValue());
 595   res->AppendDouble(q.p1().x());
 596   res->AppendDouble(q.p1().y());
 597   res->AppendDouble(q.p2().x());
 598   res->AppendDouble(q.p2().y());
 599   res->AppendDouble(q.p3().x());
 600   res->AppendDouble(q.p3().y());
 601   res->AppendDouble(q.p4().x());
 602   res->AppendDouble(q.p4().y());
 603   return res.PassAs<base::Value>();
 604 }
 605
 606 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::RectF& rect) {
 607   scoped_ptr<base::ListValue> res(new base::ListValue());
 608   res->AppendDouble(rect.x());
 609   res->AppendDouble(rect.y());
 610   res->AppendDouble(rect.width());
 611   res->AppendDouble(rect.height());
 612   return res.PassAs<base::Value>();
 613 }
 614
 615 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Transform& transform) {
 616   scoped_ptr<base::ListValue> res(new base::ListValue());
 617   const SkMatrix44& m = transform.matrix();
 618   for (int row = 0; row < 4; ++row) {
 619     for (int col = 0; col < 4; ++col)
 620       res->AppendDouble(m.getDouble(row, col));
 621   }
 622   return res.PassAs<base::Value>();
 623 }
 624
 625 scoped_ptr<base::Value> MathUtil::AsValue(const gfx::BoxF& box) {
 626   scoped_ptr<base::ListValue> res(new base::ListValue());
 627   res->AppendInteger(box.x());
 628   res->AppendInteger(box.y());
 629   res->AppendInteger(box.z());
 630   res->AppendInteger(box.width());
 631   res->AppendInteger(box.height());
 632   res->AppendInteger(box.depth());
 633   return res.PassAs<base::Value>();
 634 }
 635
 636 scoped_ptr<base::Value> MathUtil::AsValueSafely(double value) {
 637   return scoped_ptr<base::Value>(base::Value::CreateDoubleValue(
 638       std::min(value, std::numeric_limits<double>::max())));
 639 }
 640
 641 scoped_ptr<base::Value> MathUtil::AsValueSafely(float value) {
 642   return scoped_ptr<base::Value>(base::Value::CreateDoubleValue(
 643       std::min(value, std::numeric_limits<float>::max())));
 644 }
 645
 646 }  // namespace cc