ui/gfx/transform_util.cc

   1 // Copyright (c) 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 "ui/gfx/transform_util.h"
   6
   7 #include <algorithm>
   8 #include <cmath>
   9 #include <string>
  10
  11 #include "base/logging.h"
  12 #include "base/strings/stringprintf.h"
  13 #include "ui/gfx/point.h"
  14 #include "ui/gfx/point3_f.h"
  15 #include "ui/gfx/rect.h"
  16
  17 namespace gfx {
  18
  19 namespace {
  20
  21 SkMScalar Length3(SkMScalar v[3]) {
  22   double vd[3] = {SkMScalarToDouble(v[0]), SkMScalarToDouble(v[1]),
  23                   SkMScalarToDouble(v[2])};
  24   return SkDoubleToMScalar(
  25       std::sqrt(vd[0] * vd[0] + vd[1] * vd[1] + vd[2] * vd[2]));
  26 }
  27
  28 template <int n>
  29 SkMScalar Dot(const SkMScalar* a, const SkMScalar* b) {
  30   double total = 0.0;
  31   for (int i = 0; i < n; ++i)
  32     total += a[i] * b[i];
  33   return SkDoubleToMScalar(total);
  34 }
  35
  36 template <int n>
  37 void Combine(SkMScalar* out,
  38              const SkMScalar* a,
  39              const SkMScalar* b,
  40              double scale_a,
  41              double scale_b) {
  42   for (int i = 0; i < n; ++i)
  43     out[i] = SkDoubleToMScalar(a[i] * scale_a + b[i] * scale_b);
  44 }
  45
  46 void Cross3(SkMScalar out[3], SkMScalar a[3], SkMScalar b[3]) {
  47   SkMScalar x = a[1] * b[2] - a[2] * b[1];
  48   SkMScalar y = a[2] * b[0] - a[0] * b[2];
  49   SkMScalar z = a[0] * b[1] - a[1] * b[0];
  50   out[0] = x;
  51   out[1] = y;
  52   out[2] = z;
  53 }
  54
  55 SkMScalar Round(SkMScalar n) {
  56   return SkDoubleToMScalar(std::floor(SkMScalarToDouble(n) + 0.5));
  57 }
  58
  59 // Taken from http://www.w3.org/TR/css3-transforms/.
  60 bool Slerp(SkMScalar out[4],
  61            const SkMScalar q1[4],
  62            const SkMScalar q2[4],
  63            double progress) {
  64   double product = Dot<4>(q1, q2);
  65
  66   // Clamp product to -1.0 <= product <= 1.0.
  67   product = std::min(std::max(product, -1.0), 1.0);
  68
  69   // Interpolate angles along the shortest path. For example, to interpolate
  70   // between a 175 degree angle and a 185 degree angle, interpolate along the
  71   // 10 degree path from 175 to 185, rather than along the 350 degree path in
  72   // the opposite direction. This matches WebKit's implementation but not
  73   // the current W3C spec. Fixing the spec to match this approach is discussed
  74   // at:
  75   // http://lists.w3.org/Archives/Public/www-style/2013May/0131.html
  76   double scale1 = 1.0;
  77   if (product < 0) {
  78     product = -product;
  79     scale1 = -1.0;
  80   }
  81
  82   const double epsilon = 1e-5;
  83   if (std::abs(product - 1.0) < epsilon) {
  84     for (int i = 0; i < 4; ++i)
  85       out[i] = q1[i];
  86     return true;
  87   }
  88
  89   double denom = std::sqrt(1.0 - product * product);
  90   double theta = std::acos(product);
  91   double w = std::sin(progress * theta) * (1.0 / denom);
  92
  93   scale1 *= std::cos(progress * theta) - product * w;
  94   double scale2 = w;
  95   Combine<4>(out, q1, q2, scale1, scale2);
  96
  97   return true;
  98 }
  99
 100 // Returns false if the matrix cannot be normalized.
 101 bool Normalize(SkMatrix44& m) {
 102   if (m.get(3, 3) == 0.0)
 103     // Cannot normalize.
 104     return false;
 105
 106   SkMScalar scale = SK_MScalar1 / m.get(3, 3);
 107   for (int i = 0; i < 4; i++)
 108     for (int j = 0; j < 4; j++)
 109       m.set(i, j, m.get(i, j) * scale);
 110
 111   return true;
 112 }
 113
 114 SkMatrix44 BuildPerspectiveMatrix(const DecomposedTransform& decomp) {
 115   SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
 116
 117   for (int i = 0; i < 4; i++)
 118     matrix.setDouble(3, i, decomp.perspective[i]);
 119   return matrix;
 120 }
 121
 122 SkMatrix44 BuildTranslationMatrix(const DecomposedTransform& decomp) {
 123   SkMatrix44 matrix(SkMatrix44::kUninitialized_Constructor);
 124   // Implicitly calls matrix.setIdentity()
 125   matrix.setTranslate(SkDoubleToMScalar(decomp.translate[0]),
 126                       SkDoubleToMScalar(decomp.translate[1]),
 127                       SkDoubleToMScalar(decomp.translate[2]));
 128   return matrix;
 129 }
 130
 131 SkMatrix44 BuildSnappedTranslationMatrix(DecomposedTransform decomp) {
 132   decomp.translate[0] = Round(decomp.translate[0]);
 133   decomp.translate[1] = Round(decomp.translate[1]);
 134   decomp.translate[2] = Round(decomp.translate[2]);
 135   return BuildTranslationMatrix(decomp);
 136 }
 137
 138 SkMatrix44 BuildRotationMatrix(const DecomposedTransform& decomp) {
 139   double x = decomp.quaternion[0];
 140   double y = decomp.quaternion[1];
 141   double z = decomp.quaternion[2];
 142   double w = decomp.quaternion[3];
 143
 144   SkMatrix44 matrix(SkMatrix44::kUninitialized_Constructor);
 145
 146   // Implicitly calls matrix.setIdentity()
 147   matrix.set3x3(SkDoubleToMScalar(1.0 - 2.0 * (y * y + z * z)),
 148                 SkDoubleToMScalar(2.0 * (x * y + z * w)),
 149                 SkDoubleToMScalar(2.0 * (x * z - y * w)),
 150                 SkDoubleToMScalar(2.0 * (x * y - z * w)),
 151                 SkDoubleToMScalar(1.0 - 2.0 * (x * x + z * z)),
 152                 SkDoubleToMScalar(2.0 * (y * z + x * w)),
 153                 SkDoubleToMScalar(2.0 * (x * z + y * w)),
 154                 SkDoubleToMScalar(2.0 * (y * z - x * w)),
 155                 SkDoubleToMScalar(1.0 - 2.0 * (x * x + y * y)));
 156   return matrix;
 157 }
 158
 159 SkMatrix44 BuildSnappedRotationMatrix(const DecomposedTransform& decomp) {
 160   // Create snapped rotation.
 161   SkMatrix44 rotation_matrix = BuildRotationMatrix(decomp);
 162   for (int i = 0; i < 3; ++i) {
 163     for (int j = 0; j < 3; ++j) {
 164       SkMScalar value = rotation_matrix.get(i, j);
 165       // Snap values to -1, 0 or 1.
 166       if (value < -0.5f) {
 167         value = -1.0f;
 168       } else if (value > 0.5f) {
 169         value = 1.0f;
 170       } else {
 171         value = 0.0f;
 172       }
 173       rotation_matrix.set(i, j, value);
 174     }
 175   }
 176   return rotation_matrix;
 177 }
 178
 179 SkMatrix44 BuildSkewMatrix(const DecomposedTransform& decomp) {
 180   SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
 181
 182   SkMatrix44 temp(SkMatrix44::kIdentity_Constructor);
 183   if (decomp.skew[2]) {
 184     temp.setDouble(1, 2, decomp.skew[2]);
 185     matrix.preConcat(temp);
 186   }
 187
 188   if (decomp.skew[1]) {
 189     temp.setDouble(1, 2, 0);
 190     temp.setDouble(0, 2, decomp.skew[1]);
 191     matrix.preConcat(temp);
 192   }
 193
 194   if (decomp.skew[0]) {
 195     temp.setDouble(0, 2, 0);
 196     temp.setDouble(0, 1, decomp.skew[0]);
 197     matrix.preConcat(temp);
 198   }
 199   return matrix;
 200 }
 201
 202 SkMatrix44 BuildScaleMatrix(const DecomposedTransform& decomp) {
 203   SkMatrix44 matrix(SkMatrix44::kUninitialized_Constructor);
 204   matrix.setScale(SkDoubleToMScalar(decomp.scale[0]),
 205                   SkDoubleToMScalar(decomp.scale[1]),
 206                   SkDoubleToMScalar(decomp.scale[2]));
 207   return matrix;
 208 }
 209
 210 SkMatrix44 BuildSnappedScaleMatrix(DecomposedTransform decomp) {
 211   decomp.scale[0] = Round(decomp.scale[0]);
 212   decomp.scale[1] = Round(decomp.scale[1]);
 213   decomp.scale[2] = Round(decomp.scale[2]);
 214   return BuildScaleMatrix(decomp);
 215 }
 216
 217 Transform ComposeTransform(const SkMatrix44& perspective,
 218                            const SkMatrix44& translation,
 219                            const SkMatrix44& rotation,
 220                            const SkMatrix44& skew,
 221                            const SkMatrix44& scale) {
 222   SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
 223
 224   matrix.preConcat(perspective);
 225   matrix.preConcat(translation);
 226   matrix.preConcat(rotation);
 227   matrix.preConcat(skew);
 228   matrix.preConcat(scale);
 229
 230   Transform to_return;
 231   to_return.matrix() = matrix;
 232   return to_return;
 233 }
 234
 235 bool CheckViewportPointMapsWithinOnePixel(const Point& point,
 236                                           const Transform& transform) {
 237   Point3F point_original(point);
 238   Point3F point_transformed(point);
 239
 240   // Can't use TransformRect here since it would give us the axis-aligned
 241   // bounding rect of the 4 points in the initial rectable which is not what we
 242   // want.
 243   transform.TransformPoint(&point_transformed);
 244
 245   if ((point_transformed - point_original).Length() > 1.f) {
 246     // The changed distance should not be more than 1 pixel.
 247     return false;
 248   }
 249   return true;
 250 }
 251
 252 bool CheckTransformsMapsIntViewportWithinOnePixel(const Rect& viewport,
 253                                                   const Transform& original,
 254                                                   const Transform& snapped) {
 255
 256   Transform original_inv(Transform::kSkipInitialization);
 257   bool invertible = true;
 258   invertible &= original.GetInverse(&original_inv);
 259   DCHECK(invertible) << "Non-invertible transform, cannot snap.";
 260
 261   Transform combined = snapped * original_inv;
 262
 263   return CheckViewportPointMapsWithinOnePixel(viewport.origin(), combined) &&
 264          CheckViewportPointMapsWithinOnePixel(viewport.top_right(), combined) &&
 265          CheckViewportPointMapsWithinOnePixel(viewport.bottom_left(),
 266                                               combined) &&
 267          CheckViewportPointMapsWithinOnePixel(viewport.bottom_right(),
 268                                               combined);
 269 }
 270
 271 }  // namespace
 272
 273 Transform GetScaleTransform(const Point& anchor, float scale) {
 274   Transform transform;
 275   transform.Translate(anchor.x() * (1 - scale),
 276                       anchor.y() * (1 - scale));
 277   transform.Scale(scale, scale);
 278   return transform;
 279 }
 280
 281 DecomposedTransform::DecomposedTransform() {
 282   translate[0] = translate[1] = translate[2] = 0.0;
 283   scale[0] = scale[1] = scale[2] = 1.0;
 284   skew[0] = skew[1] = skew[2] = 0.0;
 285   perspective[0] = perspective[1] = perspective[2] = 0.0;
 286   quaternion[0] = quaternion[1] = quaternion[2] = 0.0;
 287   perspective[3] = quaternion[3] = 1.0;
 288 }
 289
 290 bool BlendDecomposedTransforms(DecomposedTransform* out,
 291                                const DecomposedTransform& to,
 292                                const DecomposedTransform& from,
 293                                double progress) {
 294   double scalea = progress;
 295   double scaleb = 1.0 - progress;
 296   Combine<3>(out->translate, to.translate, from.translate, scalea, scaleb);
 297   Combine<3>(out->scale, to.scale, from.scale, scalea, scaleb);
 298   Combine<3>(out->skew, to.skew, from.skew, scalea, scaleb);
 299   Combine<4>(
 300       out->perspective, to.perspective, from.perspective, scalea, scaleb);
 301   return Slerp(out->quaternion, from.quaternion, to.quaternion, progress);
 302 }
 303
 304 // Taken from http://www.w3.org/TR/css3-transforms/.
 305 bool DecomposeTransform(DecomposedTransform* decomp,
 306                         const Transform& transform) {
 307   if (!decomp)
 308     return false;
 309
 310   // We'll operate on a copy of the matrix.
 311   SkMatrix44 matrix = transform.matrix();
 312
 313   // If we cannot normalize the matrix, then bail early as we cannot decompose.
 314   if (!Normalize(matrix))
 315     return false;
 316
 317   SkMatrix44 perspectiveMatrix = matrix;
 318
 319   for (int i = 0; i < 3; ++i)
 320     perspectiveMatrix.set(3, i, 0.0);
 321
 322   perspectiveMatrix.set(3, 3, 1.0);
 323
 324   // If the perspective matrix is not invertible, we are also unable to
 325   // decompose, so we'll bail early. Constant taken from SkMatrix44::invert.
 326   if (std::abs(perspectiveMatrix.determinant()) < 1e-8)
 327     return false;
 328
 329   if (matrix.get(3, 0) != 0.0 || matrix.get(3, 1) != 0.0 ||
 330       matrix.get(3, 2) != 0.0) {
 331     // rhs is the right hand side of the equation.
 332     SkMScalar rhs[4] = {
 333       matrix.get(3, 0),
 334       matrix.get(3, 1),
 335       matrix.get(3, 2),
 336       matrix.get(3, 3)
 337     };
 338
 339     // Solve the equation by inverting perspectiveMatrix and multiplying
 340     // rhs by the inverse.
 341     SkMatrix44 inversePerspectiveMatrix(SkMatrix44::kUninitialized_Constructor);
 342     if (!perspectiveMatrix.invert(&inversePerspectiveMatrix))
 343       return false;
 344
 345     SkMatrix44 transposedInversePerspectiveMatrix =
 346         inversePerspectiveMatrix;
 347
 348     transposedInversePerspectiveMatrix.transpose();
 349     transposedInversePerspectiveMatrix.mapMScalars(rhs);
 350
 351     for (int i = 0; i < 4; ++i)
 352       decomp->perspective[i] = rhs[i];
 353
 354   } else {
 355     // No perspective.
 356     for (int i = 0; i < 3; ++i)
 357       decomp->perspective[i] = 0.0;
 358     decomp->perspective[3] = 1.0;
 359   }
 360
 361   for (int i = 0; i < 3; i++)
 362     decomp->translate[i] = matrix.get(i, 3);
 363
 364   SkMScalar row[3][3];
 365   for (int i = 0; i < 3; i++)
 366     for (int j = 0; j < 3; ++j)
 367       row[i][j] = matrix.get(j, i);
 368
 369   // Compute X scale factor and normalize first row.
 370   decomp->scale[0] = Length3(row[0]);
 371   if (decomp->scale[0] != 0.0) {
 372     row[0][0] /= decomp->scale[0];
 373     row[0][1] /= decomp->scale[0];
 374     row[0][2] /= decomp->scale[0];
 375   }
 376
 377   // Compute XY shear factor and make 2nd row orthogonal to 1st.
 378   decomp->skew[0] = Dot<3>(row[0], row[1]);
 379   Combine<3>(row[1], row[1], row[0], 1.0, -decomp->skew[0]);
 380
 381   // Now, compute Y scale and normalize 2nd row.
 382   decomp->scale[1] = Length3(row[1]);
 383   if (decomp->scale[1] != 0.0) {
 384     row[1][0] /= decomp->scale[1];
 385     row[1][1] /= decomp->scale[1];
 386     row[1][2] /= decomp->scale[1];
 387   }
 388
 389   decomp->skew[0] /= decomp->scale[1];
 390
 391   // Compute XZ and YZ shears, orthogonalize 3rd row
 392   decomp->skew[1] = Dot<3>(row[0], row[2]);
 393   Combine<3>(row[2], row[2], row[0], 1.0, -decomp->skew[1]);
 394   decomp->skew[2] = Dot<3>(row[1], row[2]);
 395   Combine<3>(row[2], row[2], row[1], 1.0, -decomp->skew[2]);
 396
 397   // Next, get Z scale and normalize 3rd row.
 398   decomp->scale[2] = Length3(row[2]);
 399   if (decomp->scale[2] != 0.0) {
 400     row[2][0] /= decomp->scale[2];
 401     row[2][1] /= decomp->scale[2];
 402     row[2][2] /= decomp->scale[2];
 403   }
 404
 405   decomp->skew[1] /= decomp->scale[2];
 406   decomp->skew[2] /= decomp->scale[2];
 407
 408   // At this point, the matrix (in rows) is orthonormal.
 409   // Check for a coordinate system flip.  If the determinant
 410   // is -1, then negate the matrix and the scaling factors.
 411   SkMScalar pdum3[3];
 412   Cross3(pdum3, row[1], row[2]);
 413   if (Dot<3>(row[0], pdum3) < 0) {
 414     for (int i = 0; i < 3; i++) {
 415       decomp->scale[i] *= -1.0;
 416       for (int j = 0; j < 3; ++j)
 417         row[i][j] *= -1.0;
 418     }
 419   }
 420
 421   double row00 = SkMScalarToDouble(row[0][0]);
 422   double row11 = SkMScalarToDouble(row[1][1]);
 423   double row22 = SkMScalarToDouble(row[2][2]);
 424   decomp->quaternion[0] = SkDoubleToMScalar(
 425       0.5 * std::sqrt(std::max(1.0 + row00 - row11 - row22, 0.0)));
 426   decomp->quaternion[1] = SkDoubleToMScalar(
 427       0.5 * std::sqrt(std::max(1.0 - row00 + row11 - row22, 0.0)));
 428   decomp->quaternion[2] = SkDoubleToMScalar(
 429       0.5 * std::sqrt(std::max(1.0 - row00 - row11 + row22, 0.0)));
 430   decomp->quaternion[3] = SkDoubleToMScalar(
 431       0.5 * std::sqrt(std::max(1.0 + row00 + row11 + row22, 0.0)));
 432
 433   if (row[2][1] > row[1][2])
 434       decomp->quaternion[0] = -decomp->quaternion[0];
 435   if (row[0][2] > row[2][0])
 436       decomp->quaternion[1] = -decomp->quaternion[1];
 437   if (row[1][0] > row[0][1])
 438       decomp->quaternion[2] = -decomp->quaternion[2];
 439
 440   return true;
 441 }
 442
 443 // Taken from http://www.w3.org/TR/css3-transforms/.
 444 Transform ComposeTransform(const DecomposedTransform& decomp) {
 445   SkMatrix44 perspective = BuildPerspectiveMatrix(decomp);
 446   SkMatrix44 translation = BuildTranslationMatrix(decomp);
 447   SkMatrix44 rotation = BuildRotationMatrix(decomp);
 448   SkMatrix44 skew = BuildSkewMatrix(decomp);
 449   SkMatrix44 scale = BuildScaleMatrix(decomp);
 450
 451   return ComposeTransform(perspective, translation, rotation, skew, scale);
 452 }
 453
 454 bool SnapTransform(Transform* out,
 455                    const Transform& transform,
 456                    const Rect& viewport) {
 457   DecomposedTransform decomp;
 458   DecomposeTransform(&decomp, transform);
 459
 460   SkMatrix44 rotation_matrix = BuildSnappedRotationMatrix(decomp);
 461   SkMatrix44 translation = BuildSnappedTranslationMatrix(decomp);
 462   SkMatrix44 scale = BuildSnappedScaleMatrix(decomp);
 463
 464   // Rebuild matrices for other unchanged components.
 465   SkMatrix44 perspective = BuildPerspectiveMatrix(decomp);
 466
 467   // Completely ignore the skew.
 468   SkMatrix44 skew(SkMatrix44::kIdentity_Constructor);
 469
 470   // Get full tranform
 471   Transform snapped =
 472       ComposeTransform(perspective, translation, rotation_matrix, skew, scale);
 473
 474   // Verify that viewport is not moved unnaturally.
 475   bool snappable =
 476     CheckTransformsMapsIntViewportWithinOnePixel(viewport, transform, snapped);
 477   if (snappable) {
 478     *out = snapped;
 479   }
 480   return snappable;
 481 }
 482
 483 Transform TransformAboutPivot(const gfx::Point& pivot,
 484                               const gfx::Transform& transform) {
 485   gfx::Transform result;
 486   result.Translate(pivot.x(), pivot.y());
 487   result.PreconcatTransform(transform);
 488   result.Translate(-pivot.x(), -pivot.y());
 489   return result;
 490 }
 491
 492 std::string DecomposedTransform::ToString() const {
 493   return base::StringPrintf(
 494       "translate: %+0.4f %+0.4f %+0.4f\n"
 495       "scale: %+0.4f %+0.4f %+0.4f\n"
 496       "skew: %+0.4f %+0.4f %+0.4f\n"
 497       "perspective: %+0.4f %+0.4f %+0.4f %+0.4f\n"
 498       "quaternion: %+0.4f %+0.4f %+0.4f %+0.4f\n",
 499       translate[0],
 500       translate[1],
 501       translate[2],
 502       scale[0],
 503       scale[1],
 504       scale[2],
 505       skew[0],
 506       skew[1],
 507       skew[2],
 508       perspective[0],
 509       perspective[1],
 510       perspective[2],
 511       perspective[3],
 512       quaternion[0],
 513       quaternion[1],
 514       quaternion[2],
 515       quaternion[3]);
 516 }
 517
 518 }  // namespace gfx