cc/animation/transform_operation.cc

   1 // Copyright 2013 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 // Needed on Windows to get |M_PI| from <cmath>
   6 #ifdef _WIN32
   7 #define _USE_MATH_DEFINES
   8 #endif
   9
  10 #include <algorithm>
  11 #include <cmath>
  12 #include <limits>
  13
  14 #include "base/logging.h"
  15 #include "cc/animation/transform_operation.h"
  16 #include "cc/animation/transform_operations.h"
  17 #include "ui/gfx/geometry/box_f.h"
  18 #include "ui/gfx/geometry/vector3d_f.h"
  19 #include "ui/gfx/transform_util.h"
  20
  21 namespace {
  22 const SkMScalar kAngleEpsilon = 1e-4f;
  23 }
  24
  25 namespace cc {
  26
  27 bool TransformOperation::IsIdentity() const {
  28   return matrix.IsIdentity();
  29 }
  30
  31 static bool IsOperationIdentity(const TransformOperation* operation) {
  32   return !operation || operation->IsIdentity();
  33 }
  34
  35 static bool ShareSameAxis(const TransformOperation* from,
  36                           const TransformOperation* to,
  37                           SkMScalar* axis_x,
  38                           SkMScalar* axis_y,
  39                           SkMScalar* axis_z,
  40                           SkMScalar* angle_from) {
  41   if (IsOperationIdentity(from) && IsOperationIdentity(to))
  42     return false;
  43
  44   if (IsOperationIdentity(from) && !IsOperationIdentity(to)) {
  45     *axis_x = to->rotate.axis.x;
  46     *axis_y = to->rotate.axis.y;
  47     *axis_z = to->rotate.axis.z;
  48     *angle_from = 0;
  49     return true;
  50   }
  51
  52   if (!IsOperationIdentity(from) && IsOperationIdentity(to)) {
  53     *axis_x = from->rotate.axis.x;
  54     *axis_y = from->rotate.axis.y;
  55     *axis_z = from->rotate.axis.z;
  56     *angle_from = from->rotate.angle;
  57     return true;
  58   }
  59
  60   SkMScalar length_2 = from->rotate.axis.x * from->rotate.axis.x +
  61                        from->rotate.axis.y * from->rotate.axis.y +
  62                        from->rotate.axis.z * from->rotate.axis.z;
  63   SkMScalar other_length_2 = to->rotate.axis.x * to->rotate.axis.x +
  64                              to->rotate.axis.y * to->rotate.axis.y +
  65                              to->rotate.axis.z * to->rotate.axis.z;
  66
  67   if (length_2 <= kAngleEpsilon || other_length_2 <= kAngleEpsilon)
  68     return false;
  69
  70   SkMScalar dot = to->rotate.axis.x * from->rotate.axis.x +
  71                   to->rotate.axis.y * from->rotate.axis.y +
  72                   to->rotate.axis.z * from->rotate.axis.z;
  73   SkMScalar error =
  74       std::abs(SK_MScalar1 - (dot * dot) / (length_2 * other_length_2));
  75   bool result = error < kAngleEpsilon;
  76   if (result) {
  77     *axis_x = to->rotate.axis.x;
  78     *axis_y = to->rotate.axis.y;
  79     *axis_z = to->rotate.axis.z;
  80     // If the axes are pointing in opposite directions, we need to reverse
  81     // the angle.
  82     *angle_from = dot > 0 ? from->rotate.angle : -from->rotate.angle;
  83   }
  84   return result;
  85 }
  86
  87 static SkMScalar BlendSkMScalars(SkMScalar from,
  88                                  SkMScalar to,
  89                                  SkMScalar progress) {
  90   return from * (1 - progress) + to * progress;
  91 }
  92
  93 bool TransformOperation::BlendTransformOperations(
  94     const TransformOperation* from,
  95     const TransformOperation* to,
  96     SkMScalar progress,
  97     gfx::Transform* result) {
  98   if (IsOperationIdentity(from) && IsOperationIdentity(to))
  99     return true;
 100
 101   TransformOperation::Type interpolation_type =
 102       TransformOperation::TransformOperationIdentity;
 103   if (IsOperationIdentity(to))
 104     interpolation_type = from->type;
 105   else
 106     interpolation_type = to->type;
 107
 108   switch (interpolation_type) {
 109   case TransformOperation::TransformOperationTranslate: {
 110     SkMScalar from_x = IsOperationIdentity(from) ? 0 : from->translate.x;
 111     SkMScalar from_y = IsOperationIdentity(from) ? 0 : from->translate.y;
 112     SkMScalar from_z = IsOperationIdentity(from) ? 0 : from->translate.z;
 113     SkMScalar to_x = IsOperationIdentity(to) ? 0 : to->translate.x;
 114     SkMScalar to_y = IsOperationIdentity(to) ? 0 : to->translate.y;
 115     SkMScalar to_z = IsOperationIdentity(to) ? 0 : to->translate.z;
 116     result->Translate3d(BlendSkMScalars(from_x, to_x, progress),
 117                         BlendSkMScalars(from_y, to_y, progress),
 118                         BlendSkMScalars(from_z, to_z, progress));
 119     break;
 120   }
 121   case TransformOperation::TransformOperationRotate: {
 122     SkMScalar axis_x = 0;
 123     SkMScalar axis_y = 0;
 124     SkMScalar axis_z = 1;
 125     SkMScalar from_angle = 0;
 126     SkMScalar to_angle = IsOperationIdentity(to) ? 0 : to->rotate.angle;
 127     if (ShareSameAxis(from, to, &axis_x, &axis_y, &axis_z, &from_angle)) {
 128       result->RotateAbout(gfx::Vector3dF(axis_x, axis_y, axis_z),
 129                           BlendSkMScalars(from_angle, to_angle, progress));
 130     } else {
 131       gfx::Transform to_matrix;
 132       if (!IsOperationIdentity(to))
 133         to_matrix = to->matrix;
 134       gfx::Transform from_matrix;
 135       if (!IsOperationIdentity(from))
 136         from_matrix = from->matrix;
 137       *result = to_matrix;
 138       if (!result->Blend(from_matrix, progress))
 139         return false;
 140     }
 141     break;
 142   }
 143   case TransformOperation::TransformOperationScale: {
 144     SkMScalar from_x = IsOperationIdentity(from) ? 1 : from->scale.x;
 145     SkMScalar from_y = IsOperationIdentity(from) ? 1 : from->scale.y;
 146     SkMScalar from_z = IsOperationIdentity(from) ? 1 : from->scale.z;
 147     SkMScalar to_x = IsOperationIdentity(to) ? 1 : to->scale.x;
 148     SkMScalar to_y = IsOperationIdentity(to) ? 1 : to->scale.y;
 149     SkMScalar to_z = IsOperationIdentity(to) ? 1 : to->scale.z;
 150     result->Scale3d(BlendSkMScalars(from_x, to_x, progress),
 151                     BlendSkMScalars(from_y, to_y, progress),
 152                     BlendSkMScalars(from_z, to_z, progress));
 153     break;
 154   }
 155   case TransformOperation::TransformOperationSkew: {
 156     SkMScalar from_x = IsOperationIdentity(from) ? 0 : from->skew.x;
 157     SkMScalar from_y = IsOperationIdentity(from) ? 0 : from->skew.y;
 158     SkMScalar to_x = IsOperationIdentity(to) ? 0 : to->skew.x;
 159     SkMScalar to_y = IsOperationIdentity(to) ? 0 : to->skew.y;
 160     result->SkewX(BlendSkMScalars(from_x, to_x, progress));
 161     result->SkewY(BlendSkMScalars(from_y, to_y, progress));
 162     break;
 163   }
 164   case TransformOperation::TransformOperationPerspective: {
 165     SkMScalar from_perspective_depth =
 166         IsOperationIdentity(from) ? std::numeric_limits<SkMScalar>::max()
 167                                   : from->perspective_depth;
 168     SkMScalar to_perspective_depth =
 169         IsOperationIdentity(to) ? std::numeric_limits<SkMScalar>::max()
 170                                 : to->perspective_depth;
 171     if (from_perspective_depth == 0.f || to_perspective_depth == 0.f)
 172       return false;
 173
 174     SkMScalar blended_perspective_depth = BlendSkMScalars(
 175         1.f / from_perspective_depth, 1.f / to_perspective_depth, progress);
 176
 177     if (blended_perspective_depth == 0.f)
 178       return false;
 179
 180     result->ApplyPerspectiveDepth(1.f / blended_perspective_depth);
 181     break;
 182   }
 183   case TransformOperation::TransformOperationMatrix: {
 184     gfx::Transform to_matrix;
 185     if (!IsOperationIdentity(to))
 186       to_matrix = to->matrix;
 187     gfx::Transform from_matrix;
 188     if (!IsOperationIdentity(from))
 189       from_matrix = from->matrix;
 190     *result = to_matrix;
 191     if (!result->Blend(from_matrix, progress))
 192       return false;
 193     break;
 194   }
 195   case TransformOperation::TransformOperationIdentity:
 196     // Do nothing.
 197     break;
 198   }
 199
 200   return true;
 201 }
 202
 203 // If p = (px, py) is a point in the plane being rotated about (0, 0, nz), this
 204 // function computes the angles we would have to rotate from p to get to
 205 // (length(p), 0), (-length(p), 0), (0, length(p)), (0, -length(p)). If nz is
 206 // negative, these angles will need to be reversed.
 207 static void FindCandidatesInPlane(float px,
 208                                   float py,
 209                                   float nz,
 210                                   double* candidates,
 211                                   int* num_candidates) {
 212   double phi = atan2(px, py);
 213   *num_candidates = 4;
 214   candidates[0] = phi;
 215   for (int i = 1; i < *num_candidates; ++i)
 216     candidates[i] = candidates[i - 1] + M_PI_2;
 217   if (nz < 0.f) {
 218     for (int i = 0; i < *num_candidates; ++i)
 219       candidates[i] *= -1.f;
 220   }
 221 }
 222
 223 static float RadiansToDegrees(float radians) {
 224   return (180.f * radians) / M_PI;
 225 }
 226
 227 static float DegreesToRadians(float degrees) {
 228   return (M_PI * degrees) / 180.f;
 229 }
 230
 231 static void BoundingBoxForArc(const gfx::Point3F& point,
 232                               const TransformOperation* from,
 233                               const TransformOperation* to,
 234                               SkMScalar min_progress,
 235                               SkMScalar max_progress,
 236                               gfx::BoxF* box) {
 237   const TransformOperation* exemplar = from ? from : to;
 238   gfx::Vector3dF axis(exemplar->rotate.axis.x,
 239                       exemplar->rotate.axis.y,
 240                       exemplar->rotate.axis.z);
 241
 242   const bool x_is_zero = axis.x() == 0.f;
 243   const bool y_is_zero = axis.y() == 0.f;
 244   const bool z_is_zero = axis.z() == 0.f;
 245
 246   // We will have at most 6 angles to test (excluding from->angle and
 247   // to->angle).
 248   static const int kMaxNumCandidates = 6;
 249   double candidates[kMaxNumCandidates];
 250   int num_candidates = kMaxNumCandidates;
 251
 252   if (x_is_zero && y_is_zero && z_is_zero)
 253     return;
 254
 255   SkMScalar from_angle = from ? from->rotate.angle : 0.f;
 256   SkMScalar to_angle = to ? to->rotate.angle : 0.f;
 257
 258   // If the axes of rotation are pointing in opposite directions, we need to
 259   // flip one of the angles. Note, if both |from| and |to| exist, then axis will
 260   // correspond to |from|.
 261   if (from && to) {
 262     gfx::Vector3dF other_axis(
 263         to->rotate.axis.x, to->rotate.axis.y, to->rotate.axis.z);
 264     if (gfx::DotProduct(axis, other_axis) < 0.f)
 265       to_angle *= -1.f;
 266   }
 267
 268   float min_degrees =
 269       SkMScalarToFloat(BlendSkMScalars(from_angle, to_angle, min_progress));
 270   float max_degrees =
 271       SkMScalarToFloat(BlendSkMScalars(from_angle, to_angle, max_progress));
 272   if (max_degrees < min_degrees)
 273     std::swap(min_degrees, max_degrees);
 274
 275   gfx::Transform from_transform;
 276   from_transform.RotateAbout(axis, min_degrees);
 277   gfx::Transform to_transform;
 278   to_transform.RotateAbout(axis, max_degrees);
 279
 280   *box = gfx::BoxF();
 281
 282   gfx::Point3F point_rotated_from = point;
 283   from_transform.TransformPoint(&point_rotated_from);
 284   gfx::Point3F point_rotated_to = point;
 285   to_transform.TransformPoint(&point_rotated_to);
 286
 287   box->set_origin(point_rotated_from);
 288   box->ExpandTo(point_rotated_to);
 289
 290   if (x_is_zero && y_is_zero) {
 291     FindCandidatesInPlane(
 292         point.x(), point.y(), axis.z(), candidates, &num_candidates);
 293   } else if (x_is_zero && z_is_zero) {
 294     FindCandidatesInPlane(
 295         point.z(), point.x(), axis.y(), candidates, &num_candidates);
 296   } else if (y_is_zero && z_is_zero) {
 297     FindCandidatesInPlane(
 298         point.y(), point.z(), axis.x(), candidates, &num_candidates);
 299   } else {
 300     gfx::Vector3dF normal = axis;
 301     normal.Scale(1.f / normal.Length());
 302
 303     // First, find center of rotation.
 304     gfx::Point3F origin;
 305     gfx::Vector3dF to_point = point - origin;
 306     gfx::Point3F center =
 307         origin + gfx::ScaleVector3d(normal, gfx::DotProduct(to_point, normal));
 308
 309     // Now we need to find two vectors in the plane of rotation. One pointing
 310     // towards point and another, perpendicular vector in the plane.
 311     gfx::Vector3dF v1 = point - center;
 312     float v1_length = v1.Length();
 313     if (v1_length == 0.f)
 314       return;
 315
 316     v1.Scale(1.f / v1_length);
 317     gfx::Vector3dF v2 = gfx::CrossProduct(normal, v1);
 318     // v1 is the basis vector in the direction of the point.
 319     // i.e. with a rotation of 0, v1 is our +x vector.
 320     // v2 is a perpenticular basis vector of our plane (+y).
 321
 322     // Take the parametric equation of a circle.
 323     // x = r*cos(t); y = r*sin(t);
 324     // We can treat that as a circle on the plane v1xv2.
 325     // From that we get the parametric equations for a circle on the
 326     // plane in 3d space of:
 327     // x(t) = r*cos(t)*v1.x + r*sin(t)*v2.x + cx
 328     // y(t) = r*cos(t)*v1.y + r*sin(t)*v2.y + cy
 329     // z(t) = r*cos(t)*v1.z + r*sin(t)*v2.z + cz
 330     // Taking the derivative of (x, y, z) and solving for 0 gives us our
 331     // maximum/minimum x, y, z values.
 332     // x'(t) = r*cos(t)*v2.x - r*sin(t)*v1.x = 0
 333     // tan(t) = v2.x/v1.x
 334     // t = atan2(v2.x, v1.x) + n*M_PI;
 335     candidates[0] = atan2(v2.x(), v1.x());
 336     candidates[1] = candidates[0] + M_PI;
 337     candidates[2] = atan2(v2.y(), v1.y());
 338     candidates[3] = candidates[2] + M_PI;
 339     candidates[4] = atan2(v2.z(), v1.z());
 340     candidates[5] = candidates[4] + M_PI;
 341   }
 342
 343   double min_radians = DegreesToRadians(min_degrees);
 344   double max_radians = DegreesToRadians(max_degrees);
 345
 346   for (int i = 0; i < num_candidates; ++i) {
 347     double radians = candidates[i];
 348     while (radians < min_radians)
 349       radians += 2.0 * M_PI;
 350     while (radians > max_radians)
 351       radians -= 2.0 * M_PI;
 352     if (radians < min_radians)
 353       continue;
 354
 355     gfx::Transform rotation;
 356     rotation.RotateAbout(axis, RadiansToDegrees(radians));
 357     gfx::Point3F rotated = point;
 358     rotation.TransformPoint(&rotated);
 359
 360     box->ExpandTo(rotated);
 361   }
 362 }
 363
 364 bool TransformOperation::BlendedBoundsForBox(const gfx::BoxF& box,
 365                                              const TransformOperation* from,
 366                                              const TransformOperation* to,
 367                                              SkMScalar min_progress,
 368                                              SkMScalar max_progress,
 369                                              gfx::BoxF* bounds) {
 370   bool is_identity_from = IsOperationIdentity(from);
 371   bool is_identity_to = IsOperationIdentity(to);
 372   if (is_identity_from && is_identity_to) {
 373     *bounds = box;
 374     return true;
 375   }
 376
 377   TransformOperation::Type interpolation_type =
 378       TransformOperation::TransformOperationIdentity;
 379   if (is_identity_to)
 380     interpolation_type = from->type;
 381   else
 382     interpolation_type = to->type;
 383
 384   switch (interpolation_type) {
 385     case TransformOperation::TransformOperationIdentity:
 386       *bounds = box;
 387       return true;
 388     case TransformOperation::TransformOperationTranslate:
 389     case TransformOperation::TransformOperationSkew:
 390     case TransformOperation::TransformOperationPerspective:
 391     case TransformOperation::TransformOperationScale: {
 392       gfx::Transform from_transform;
 393       gfx::Transform to_transform;
 394       if (!BlendTransformOperations(from, to, min_progress, &from_transform) ||
 395           !BlendTransformOperations(from, to, max_progress, &to_transform))
 396         return false;
 397
 398       *bounds = box;
 399       from_transform.TransformBox(bounds);
 400
 401       gfx::BoxF to_box = box;
 402       to_transform.TransformBox(&to_box);
 403       bounds->ExpandTo(to_box);
 404
 405       return true;
 406     }
 407     case TransformOperation::TransformOperationRotate: {
 408       SkMScalar axis_x = 0;
 409       SkMScalar axis_y = 0;
 410       SkMScalar axis_z = 1;
 411       SkMScalar from_angle = 0;
 412       if (!ShareSameAxis(from, to, &axis_x, &axis_y, &axis_z, &from_angle))
 413         return false;
 414
 415       bool first_point = true;
 416       for (int i = 0; i < 8; ++i) {
 417         gfx::Point3F corner = box.origin();
 418         corner += gfx::Vector3dF(i & 1 ? box.width() : 0.f,
 419                                  i & 2 ? box.height() : 0.f,
 420                                  i & 4 ? box.depth() : 0.f);
 421         gfx::BoxF box_for_arc;
 422         BoundingBoxForArc(
 423             corner, from, to, min_progress, max_progress, &box_for_arc);
 424         if (first_point)
 425           *bounds = box_for_arc;
 426         else
 427           bounds->Union(box_for_arc);
 428         first_point = false;
 429       }
 430       return true;
 431     }
 432     case TransformOperation::TransformOperationMatrix:
 433       return false;
 434   }
 435   NOTREACHED();
 436   return false;
 437 }
 438
 439 }  // namespace cc