Implement transform snapping for gfx::Transforms.

ui/gfx/transform_util.cc

 // Copyright (c) 2012 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include "ui/gfx/transform_util.h"
 
 #include <cmath>
 
+#include "base/logging.h"
 #include "ui/gfx/point.h"
+#include "ui/gfx/point3_f.h"
+#include "ui/gfx/rect_f.h"
 
 namespace gfx {
 
 namespace {
 
+// Taken from SkMatrix44
+const float kNearIntEpsilon = 1e-8;

[Ian Vollick, 2013/09/11 12:19:48]

Can we expose this from SkMatrix44? I think we'll want a function static
SkMScalar SkMatrix44::near_int_epsilon() since we'll want a different constant
depending on whether SkMScalar is a float or a double.

[avallee, 2013/09/14 01:32:25]

Done.

+
+bool NearInteger(float f) {
+  return (std::abs(f-std::round(f)) < kNearIntEpsilon);
+}
+
 double Length3(double v[3]) {
   return std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 }
 
 void Scale3(double v[3], double scale) {
   for (int i = 0; i < 3; ++i)
     v[i] *= scale;
 }
 
 template <int n>
@@ skipping 232 matching lines @@
   if (row[2][1] > row[1][2])
       decomp->quaternion[0] = -decomp->quaternion[0];
   if (row[0][2] > row[2][0])
       decomp->quaternion[1] = -decomp->quaternion[1];
   if (row[1][0] > row[0][1])
       decomp->quaternion[2] = -decomp->quaternion[2];
 
   return true;
 }
 
-// Taken from http://www.w3.org/TR/css3-transforms/.
-Transform ComposeTransform(const DecomposedTransform& decomp) {
-  SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
-  for (int i = 0; i < 4; i++)
-    matrix.setDouble(3, i, decomp.perspective[i]);
-
-  matrix.preTranslate(SkDoubleToMScalar(decomp.translate[0]),
-                      SkDoubleToMScalar(decomp.translate[1]),
-                      SkDoubleToMScalar(decomp.translate[2]));
-
-  double x = decomp.quaternion[0];
-  double y = decomp.quaternion[1];
-  double z = decomp.quaternion[2];
-  double w = decomp.quaternion[3];
+SkMatrix44 QuaternionToRotationMatrix(const double (& quaternion)[4]) {
+  double x = quaternion[0];
+  double y = quaternion[1];
+  double z = quaternion[2];
+  double w = quaternion[3];
 
   SkMatrix44 rotation_matrix(SkMatrix44::kUninitialized_Constructor);
   rotation_matrix.set3x3(1.0 - 2.0 * (y * y + z * z),
                          2.0 * (x * y + z * w),
                          2.0 * (x * z - y * w),
                          2.0 * (x * y - z * w),
                          1.0 - 2.0 * (x * x + z * z),
                          2.0 * (y * z + x * w),
                          2.0 * (x * z + y * w),
                          2.0 * (y * z - x * w),
                          1.0 - 2.0 * (x * x + y * y));
 
-  matrix.preConcat(rotation_matrix);
+  return rotation_matrix;
+}
 
+void ApplyPerspectiveTranslation(SkMatrix44* matrix,
+                                 const DecomposedTransform& decomp) {
+  for (int i = 0; i < 4; i++)
+    matrix->setDouble(3, i, decomp.perspective[i]);

[Ian Vollick, 2013/09/11 12:19:48]

If we're going to be breaking things up into separate Apply* functions, let's
separate perspective and translation, too.

[avallee, 2013/09/14 01:32:25]

Followed the comment from the bottom. Create all the matrices and the fat
compose just multiplies them all.

+
+  matrix->preTranslate(SkDoubleToMScalar(decomp.translate[0]),
+                       SkDoubleToMScalar(decomp.translate[1]),
+                       SkDoubleToMScalar(decomp.translate[2]));
+}
+
+void ApplySkewScale(SkMatrix44* matrix,
+                   const DecomposedTransform& decomp) {
   SkMatrix44 temp(SkMatrix44::kIdentity_Constructor);
   if (decomp.skew[2]) {
     temp.setDouble(1, 2, decomp.skew[2]);
-    matrix.preConcat(temp);
+    matrix->preConcat(temp);
   }
 
   if (decomp.skew[1]) {
     temp.setDouble(1, 2, 0);
     temp.setDouble(0, 2, decomp.skew[1]);
-    matrix.preConcat(temp);
+    matrix->preConcat(temp);
   }
 
   if (decomp.skew[0]) {
     temp.setDouble(0, 2, 0);
     temp.setDouble(0, 1, decomp.skew[0]);
-    matrix.preConcat(temp);
+    matrix->preConcat(temp);
   }

[Ian Vollick, 2013/09/11 12:19:48]

Same with skew and scale.

[avallee, 2013/09/14 01:32:25]

Done.

 
-  matrix.preScale(SkDoubleToMScalar(decomp.scale[0]),
-                  SkDoubleToMScalar(decomp.scale[1]),
-                  SkDoubleToMScalar(decomp.scale[2]));
+  matrix->preScale(SkDoubleToMScalar(decomp.scale[0]),
+                   SkDoubleToMScalar(decomp.scale[1]),
+                   SkDoubleToMScalar(decomp.scale[2]));
+}
+
+// Taken from http://www.w3.org/TR/css3-transforms/.
+Transform ComposeTransform(const DecomposedTransform& decomp) {
+  SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
+  ApplyPerspectiveTranslation(&matrix, decomp);
+
+  matrix.preConcat(QuaternionToRotationMatrix(decomp.quaternion));
+
+  ApplySkewScale(&matrix, decomp);
 
   Transform to_return;
   to_return.matrix() = matrix;
   return to_return;
 }
 
+Transform ComposeWithRotation(const DecomposedTransform& decomp,
+                              const SkMatrix44& rotation_matrix) {
+  SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
+  ApplyPerspectiveTranslation(&matrix, decomp);
+  matrix.preConcat(rotation_matrix);
+
+  ApplySkewScale(&matrix, decomp);
+
+  Transform to_return;
+  to_return.matrix() = matrix;
+  return to_return;
+}
+
+bool CheckTansformPoint(const PointF& point, const Transform& transform_a,
+    const Transform& transform_b) {
+  Point3F point_a, point_b;
+  point_a = point_b = Point3F(point.x(), point.y(), 0.f);
+
+  // Can't use TransformRect here since it would give us the axis-aligned
+  // bounding rect of the 4 points in the initial rectable which is not what we
+  // want.
+  bool invertible = true;
+  invertible &= transform_a.TransformPointReverse(&point_a);
+  invertible &= transform_b.TransformPointReverse(&point_b);
+  DCHECK(invertible) << "Non-invertible transform, cannot snap.";
+
+  if (!(NearInteger(point_b.x()) && NearInteger(point_b.y()))) {
+    // Integers should get mapped back into integer points.
+    return false;
+  }
+
+  if ((point_b - point_a).Length() > 1.0) {
+    // The changed distance should not be more than 1 pixel.
+    return false;
+  }
+  return true;
+}
+
+bool SnapRotation(DecomposedTransform* out, const DecomposedTransform& in,
+                  const RectF& viewport) {
+
+  // Create snapped rotation.
+  SkMatrix44 rotation_matrix = QuaternionToRotationMatrix(in.quaternion);
+  for (int i = 0; i < 3; ++i) {
+    for (int j = 0; j < 3; ++j) {
+      SkMScalar value = rotation_matrix.get(i, j);
+      // Snap values to -1, 0 or 1.
+      if (value < -0.5f) {
+        value = -1.0f;
+      } else if (value > 0.5f) {
+        value = 1.0f;
+      } else {
+        value = 0.0f;
+      }
+      rotation_matrix.set(i, j, value);
+    }
+  }
+
+  // Get full tranforms
+  Transform original = ComposeTransform(in);

[Ian Vollick, 2013/09/11 12:19:48]

This is wasteful. The caller will have the composed original on hand. Please
take it as a parameter rather than recomposing it here.

[avallee, 2013/09/14 01:32:25]

Done.

+  Transform snapped = ComposeWithRotation(in, rotation_matrix);

[Ian Vollick, 2013/09/11 12:19:48]

This isn't going generalize well when we want to snap more than rotation.
Compose works by concat'ing a bunch SkMatrix44's which are in turn built based
on the values in the DecomposedTransforms. I suggest you create the following:
static buildTranslationMatrix(SkMatrix44* out, const DecomposedTransform&
decomp);
static buildRotationMatrix(SkMatrix44* out, const DecomposedTransform& decomp);
...etc, and then add:

ComposeTransform(const SkMatrix44& perspective,
                 const SkMatrix44& translation, ...);

..and then you could do:
ComposeTransform(const DecomposedTransform& decomp) {
  SkMatrix44 perspective(k-don't-initialize-thanks);
  ...
  buildPerspectiveMatrix(&perspective, decomp);
  ...
  ComposeTransform(perspective,
                   translation, ...);
}

Once you've done this, it'll be easy to call the wide ComposeTransform with your
snapped components (you should make helper functions to generate the snapped
components, perhaps just with a bool snap parameter to the other build*Matrix
fn's) -- rotation for now, but probably scale and others shortly.

[avallee, 2013/09/14 01:32:25]

Done.

+
+  // Verify that viewport is not moved unnaturally.
+
+  bool snappable = CheckTansformPoint(viewport.origin(), original, snapped) &&
+      CheckTansformPoint(viewport.top_right(), original, snapped) &&
+      CheckTansformPoint(viewport.bottom_left(), original, snapped) &&
+      CheckTansformPoint(viewport.bottom_right(), original, snapped);
+  if (snappable) {
+    DecomposeTransform(out, snapped);
+  }
+  return snappable;
+}
+
 }  // namespace ui