Fixed the order of applying transform operations for animation bounds.

cc/animation/transform_operation.cc

 // Copyright 2013 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.
 
 // Needed on Windows to get |M_PI| from <cmath>
 #ifdef _WIN32
 #define _USE_MATH_DEFINES
 #endif
 
 #include <algorithm>
@@ skipping 296 matching lines @@
         origin + gfx::ScaleVector3d(normal, gfx::DotProduct(to_point, normal));
 
     // Now we need to find two vectors in the plane of rotation. One pointing
     // towards point and another, perpendicular vector in the plane.
     gfx::Vector3dF v1 = point - center;
     float v1_length = v1.Length();
     if (v1_length == 0.f)
       return;
 
     v1.Scale(1.f / v1_length);
+    gfx::Vector3dF v2 = gfx::CrossProduct(normal, v1);
+    // v1 is the basis vector in the direction of the point.
+    // i.e. with a rotation of 0, v1 is our +x vector.
+    // v2 is a perpenticular basis vector of our plane (+y).
 
-    gfx::Vector3dF v2 = gfx::CrossProduct(normal, v1);
-
-    // Now figure out where (1, 0, 0) and (0, 0, 1) project on the rotation
-    // plane.
-    gfx::Point3F px(1.f, 0.f, 0.f);
-    gfx::Vector3dF to_px = px - center;
-    gfx::Point3F px_projected =
-        px - gfx::ScaleVector3d(normal, gfx::DotProduct(to_px, normal));
-    gfx::Vector3dF vx = px_projected - origin;
-
-    gfx::Point3F pz(0.f, 0.f, 1.f);
-    gfx::Vector3dF to_pz = pz - center;
-    gfx::Point3F pz_projected =
-        pz - ScaleVector3d(normal, gfx::DotProduct(to_pz, normal));
-    gfx::Vector3dF vz = pz_projected - origin;
-
-    double phi_x = atan2(gfx::DotProduct(v2, vx), gfx::DotProduct(v1, vx));
-    double phi_z = atan2(gfx::DotProduct(v2, vz), gfx::DotProduct(v1, vz));
-
-    candidates[0] = atan2(normal.y(), normal.x() * normal.z()) + phi_x;
+    // Take the parametric equation of a circle.
+    // x = r*cos(t); y = r*sin(t);
+    // We can treat that as a circle on the plane v1xv2.
+    // From that we get the parametric equations for a circle on the
+    // plane in 3d space of:
+    // x(t) = r*cos(t)*v1.x + r*sin(t)*v2.x + cx
+    // y(t) = r*cos(t)*v1.y + r*sin(t)*v2.y + cy
+    // z(t) = r*cos(t)*v1.z + r*sin(t)*v2.z + cz
+    // Taking the derivative of (x, y, z) and solving for 0 gives us our
+    // maximum/minimum x, y, z values.
+    // x'(t) = r*cos(t)*v2.x - r*sin(t)*v1.x = 0
+    // tan(t) = v2.x/v1.x
+    // t = atan2(v2.x, v1.x) + n*M_PI;

[ajuma, 2014/05/27 16:00:54]

Very nice!

+    candidates[0] = atan2(v2.x(), v1.x());
     candidates[1] = candidates[0] + M_PI;
-    candidates[2] = atan2(-normal.z(), normal.x() * normal.y()) + phi_x;
+    candidates[2] = atan2(v2.y(), v1.y());
     candidates[3] = candidates[2] + M_PI;
-    candidates[4] = atan2(normal.y(), -normal.x() * normal.z()) + phi_z;
+    candidates[4] = atan2(v2.z(), v1.z());
     candidates[5] = candidates[4] + M_PI;
   }
 
   double min_radians = DegreesToRadians(min_degrees);
   double max_radians = DegreesToRadians(max_degrees);
 
   for (int i = 0; i < num_candidates; ++i) {
     double radians = candidates[i];
     while (radians < min_radians)
       radians += 2.0 * M_PI;
@@ skipping 80 matching lines @@
       return true;
     }
     case TransformOperation::TransformOperationMatrix:
       return false;
   }
   NOTREACHED();
   return false;
 }
 
 }  // namespace cc