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