| // 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> |
| #include <cmath> |
| #include <limits> |
| |
| #include "base/logging.h" |
| #include "cc/animation/transform_operation.h" |
| #include "cc/animation/transform_operations.h" |
| #include "ui/gfx/box_f.h" |
| #include "ui/gfx/transform_util.h" |
| #include "ui/gfx/vector3d_f.h" |
| |
| namespace { |
| const SkMScalar kAngleEpsilon = 1e-4f; |
| } |
| |
| namespace cc { |
| |
| bool TransformOperation::IsIdentity() const { |
| return matrix.IsIdentity(); |
| } |
| |
| static bool IsOperationIdentity(const TransformOperation* operation) { |
| return !operation || operation->IsIdentity(); |
| } |
| |
| static bool ShareSameAxis(const TransformOperation* from, |
| const TransformOperation* to, |
| SkMScalar* axis_x, |
| SkMScalar* axis_y, |
| SkMScalar* axis_z, |
| SkMScalar* angle_from) { |
| if (IsOperationIdentity(from) && IsOperationIdentity(to)) |
| return false; |
| |
| if (IsOperationIdentity(from) && !IsOperationIdentity(to)) { |
| *axis_x = to->rotate.axis.x; |
| *axis_y = to->rotate.axis.y; |
| *axis_z = to->rotate.axis.z; |
| *angle_from = 0; |
| return true; |
| } |
| |
| if (!IsOperationIdentity(from) && IsOperationIdentity(to)) { |
| *axis_x = from->rotate.axis.x; |
| *axis_y = from->rotate.axis.y; |
| *axis_z = from->rotate.axis.z; |
| *angle_from = from->rotate.angle; |
| return true; |
| } |
| |
| SkMScalar length_2 = from->rotate.axis.x * from->rotate.axis.x + |
| from->rotate.axis.y * from->rotate.axis.y + |
| from->rotate.axis.z * from->rotate.axis.z; |
| SkMScalar other_length_2 = to->rotate.axis.x * to->rotate.axis.x + |
| to->rotate.axis.y * to->rotate.axis.y + |
| to->rotate.axis.z * to->rotate.axis.z; |
| |
| if (length_2 <= kAngleEpsilon || other_length_2 <= kAngleEpsilon) |
| return false; |
| |
| SkMScalar dot = to->rotate.axis.x * from->rotate.axis.x + |
| to->rotate.axis.y * from->rotate.axis.y + |
| to->rotate.axis.z * from->rotate.axis.z; |
| SkMScalar error = |
| std::abs(SK_MScalar1 - (dot * dot) / (length_2 * other_length_2)); |
| bool result = error < kAngleEpsilon; |
| if (result) { |
| *axis_x = to->rotate.axis.x; |
| *axis_y = to->rotate.axis.y; |
| *axis_z = to->rotate.axis.z; |
| // If the axes are pointing in opposite directions, we need to reverse |
| // the angle. |
| *angle_from = dot > 0 ? from->rotate.angle : -from->rotate.angle; |
| } |
| return result; |
| } |
| |
| static SkMScalar BlendSkMScalars(SkMScalar from, |
| SkMScalar to, |
| SkMScalar progress) { |
| return from * (1 - progress) + to * progress; |
| } |
| |
| bool TransformOperation::BlendTransformOperations( |
| const TransformOperation* from, |
| const TransformOperation* to, |
| SkMScalar progress, |
| gfx::Transform* result) { |
| if (IsOperationIdentity(from) && IsOperationIdentity(to)) |
| return true; |
| |
| TransformOperation::Type interpolation_type = |
| TransformOperation::TransformOperationIdentity; |
| if (IsOperationIdentity(to)) |
| interpolation_type = from->type; |
| else |
| interpolation_type = to->type; |
| |
| switch (interpolation_type) { |
| case TransformOperation::TransformOperationTranslate: { |
| SkMScalar from_x = IsOperationIdentity(from) ? 0 : from->translate.x; |
| SkMScalar from_y = IsOperationIdentity(from) ? 0 : from->translate.y; |
| SkMScalar from_z = IsOperationIdentity(from) ? 0 : from->translate.z; |
| SkMScalar to_x = IsOperationIdentity(to) ? 0 : to->translate.x; |
| SkMScalar to_y = IsOperationIdentity(to) ? 0 : to->translate.y; |
| SkMScalar to_z = IsOperationIdentity(to) ? 0 : to->translate.z; |
| result->Translate3d(BlendSkMScalars(from_x, to_x, progress), |
| BlendSkMScalars(from_y, to_y, progress), |
| BlendSkMScalars(from_z, to_z, progress)); |
| break; |
| } |
| case TransformOperation::TransformOperationRotate: { |
| SkMScalar axis_x = 0; |
| SkMScalar axis_y = 0; |
| SkMScalar axis_z = 1; |
| SkMScalar from_angle = 0; |
| SkMScalar to_angle = IsOperationIdentity(to) ? 0 : to->rotate.angle; |
| if (ShareSameAxis(from, to, &axis_x, &axis_y, &axis_z, &from_angle)) { |
| result->RotateAbout(gfx::Vector3dF(axis_x, axis_y, axis_z), |
| BlendSkMScalars(from_angle, to_angle, progress)); |
| } else { |
| gfx::Transform to_matrix; |
| if (!IsOperationIdentity(to)) |
| to_matrix = to->matrix; |
| gfx::Transform from_matrix; |
| if (!IsOperationIdentity(from)) |
| from_matrix = from->matrix; |
| *result = to_matrix; |
| if (!result->Blend(from_matrix, progress)) |
| return false; |
| } |
| break; |
| } |
| case TransformOperation::TransformOperationScale: { |
| SkMScalar from_x = IsOperationIdentity(from) ? 1 : from->scale.x; |
| SkMScalar from_y = IsOperationIdentity(from) ? 1 : from->scale.y; |
| SkMScalar from_z = IsOperationIdentity(from) ? 1 : from->scale.z; |
| SkMScalar to_x = IsOperationIdentity(to) ? 1 : to->scale.x; |
| SkMScalar to_y = IsOperationIdentity(to) ? 1 : to->scale.y; |
| SkMScalar to_z = IsOperationIdentity(to) ? 1 : to->scale.z; |
| result->Scale3d(BlendSkMScalars(from_x, to_x, progress), |
| BlendSkMScalars(from_y, to_y, progress), |
| BlendSkMScalars(from_z, to_z, progress)); |
| break; |
| } |
| case TransformOperation::TransformOperationSkew: { |
| SkMScalar from_x = IsOperationIdentity(from) ? 0 : from->skew.x; |
| SkMScalar from_y = IsOperationIdentity(from) ? 0 : from->skew.y; |
| SkMScalar to_x = IsOperationIdentity(to) ? 0 : to->skew.x; |
| SkMScalar to_y = IsOperationIdentity(to) ? 0 : to->skew.y; |
| result->SkewX(BlendSkMScalars(from_x, to_x, progress)); |
| result->SkewY(BlendSkMScalars(from_y, to_y, progress)); |
| break; |
| } |
| case TransformOperation::TransformOperationPerspective: { |
| SkMScalar from_perspective_depth = |
| IsOperationIdentity(from) ? std::numeric_limits<SkMScalar>::max() |
| : from->perspective_depth; |
| SkMScalar to_perspective_depth = |
| IsOperationIdentity(to) ? std::numeric_limits<SkMScalar>::max() |
| : to->perspective_depth; |
| if (from_perspective_depth == 0.f || to_perspective_depth == 0.f) |
| return false; |
| |
| SkMScalar blended_perspective_depth = BlendSkMScalars( |
| 1.f / from_perspective_depth, 1.f / to_perspective_depth, progress); |
| |
| if (blended_perspective_depth == 0.f) |
| return false; |
| |
| result->ApplyPerspectiveDepth(1.f / blended_perspective_depth); |
| break; |
| } |
| case TransformOperation::TransformOperationMatrix: { |
| gfx::Transform to_matrix; |
| if (!IsOperationIdentity(to)) |
| to_matrix = to->matrix; |
| gfx::Transform from_matrix; |
| if (!IsOperationIdentity(from)) |
| from_matrix = from->matrix; |
| *result = to_matrix; |
| if (!result->Blend(from_matrix, progress)) |
| return false; |
| break; |
| } |
| case TransformOperation::TransformOperationIdentity: |
| // Do nothing. |
| break; |
| } |
| |
| return true; |
| } |
| |
| // If p = (px, py) is a point in the plane being rotated about (0, 0, nz), this |
| // function computes the angles we would have to rotate from p to get to |
| // (length(p), 0), (-length(p), 0), (0, length(p)), (0, -length(p)). If nz is |
| // negative, these angles will need to be reversed. |
| static void FindCandidatesInPlane(float px, |
| float py, |
| float nz, |
| double* candidates, |
| int* num_candidates) { |
| double phi = atan2(px, py); |
| *num_candidates = 4; |
| candidates[0] = phi; |
| for (int i = 1; i < *num_candidates; ++i) |
| candidates[i] = candidates[i - 1] + M_PI_2; |
| if (nz < 0.f) { |
| for (int i = 0; i < *num_candidates; ++i) |
| candidates[i] *= -1.f; |
| } |
| } |
| |
| static float RadiansToDegrees(float radians) { |
| return (180.f * radians) / M_PI; |
| } |
| |
| static float DegreesToRadians(float degrees) { |
| return (M_PI * degrees) / 180.f; |
| } |
| |
| static void BoundingBoxForArc(const gfx::Point3F& point, |
| const TransformOperation* from, |
| const TransformOperation* to, |
| SkMScalar min_progress, |
| SkMScalar max_progress, |
| gfx::BoxF* box) { |
| const TransformOperation* exemplar = from ? from : to; |
| gfx::Vector3dF axis(exemplar->rotate.axis.x, |
| exemplar->rotate.axis.y, |
| exemplar->rotate.axis.z); |
| |
| const bool x_is_zero = axis.x() == 0.f; |
| const bool y_is_zero = axis.y() == 0.f; |
| const bool z_is_zero = axis.z() == 0.f; |
| |
| // We will have at most 6 angles to test (excluding from->angle and |
| // to->angle). |
| static const int kMaxNumCandidates = 6; |
| double candidates[kMaxNumCandidates]; |
| int num_candidates = kMaxNumCandidates; |
| |
| if (x_is_zero && y_is_zero && z_is_zero) |
| return; |
| |
| SkMScalar from_angle = from ? from->rotate.angle : 0.f; |
| SkMScalar to_angle = to ? to->rotate.angle : 0.f; |
| |
| // If the axes of rotation are pointing in opposite directions, we need to |
| // flip one of the angles. Note, if both |from| and |to| exist, then axis will |
| // correspond to |from|. |
| if (from && to) { |
| gfx::Vector3dF other_axis( |
| to->rotate.axis.x, to->rotate.axis.y, to->rotate.axis.z); |
| if (gfx::DotProduct(axis, other_axis) < 0.f) |
| to_angle *= -1.f; |
| } |
| |
| float min_degrees = |
| SkMScalarToFloat(BlendSkMScalars(from_angle, to_angle, min_progress)); |
| float max_degrees = |
| SkMScalarToFloat(BlendSkMScalars(from_angle, to_angle, max_progress)); |
| if (max_degrees < min_degrees) |
| std::swap(min_degrees, max_degrees); |
| |
| gfx::Transform from_transform; |
| from_transform.RotateAbout(axis, min_degrees); |
| gfx::Transform to_transform; |
| to_transform.RotateAbout(axis, max_degrees); |
| |
| *box = gfx::BoxF(); |
| |
| gfx::Point3F point_rotated_from = point; |
| from_transform.TransformPoint(&point_rotated_from); |
| gfx::Point3F point_rotated_to = point; |
| to_transform.TransformPoint(&point_rotated_to); |
| |
| box->set_origin(point_rotated_from); |
| box->ExpandTo(point_rotated_to); |
| |
| if (x_is_zero && y_is_zero) { |
| FindCandidatesInPlane( |
| point.x(), point.y(), axis.z(), candidates, &num_candidates); |
| } else if (x_is_zero && z_is_zero) { |
| FindCandidatesInPlane( |
| point.z(), point.x(), axis.y(), candidates, &num_candidates); |
| } else if (y_is_zero && z_is_zero) { |
| FindCandidatesInPlane( |
| point.y(), point.z(), axis.x(), candidates, &num_candidates); |
| } else { |
| gfx::Vector3dF normal = axis; |
| normal.Scale(1.f / normal.Length()); |
| |
| // First, find center of rotation. |
| gfx::Point3F origin; |
| gfx::Vector3dF to_point = point - origin; |
| gfx::Point3F center = |
| 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). |
| |
| // 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; |
| candidates[0] = atan2(v2.x(), v1.x()); |
| candidates[1] = candidates[0] + M_PI; |
| candidates[2] = atan2(v2.y(), v1.y()); |
| candidates[3] = candidates[2] + M_PI; |
| 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; |
| while (radians > max_radians) |
| radians -= 2.0 * M_PI; |
| if (radians < min_radians) |
| continue; |
| |
| gfx::Transform rotation; |
| rotation.RotateAbout(axis, RadiansToDegrees(radians)); |
| gfx::Point3F rotated = point; |
| rotation.TransformPoint(&rotated); |
| |
| box->ExpandTo(rotated); |
| } |
| } |
| |
| bool TransformOperation::BlendedBoundsForBox(const gfx::BoxF& box, |
| const TransformOperation* from, |
| const TransformOperation* to, |
| SkMScalar min_progress, |
| SkMScalar max_progress, |
| gfx::BoxF* bounds) { |
| bool is_identity_from = IsOperationIdentity(from); |
| bool is_identity_to = IsOperationIdentity(to); |
| if (is_identity_from && is_identity_to) { |
| *bounds = box; |
| return true; |
| } |
| |
| TransformOperation::Type interpolation_type = |
| TransformOperation::TransformOperationIdentity; |
| if (is_identity_to) |
| interpolation_type = from->type; |
| else |
| interpolation_type = to->type; |
| |
| switch (interpolation_type) { |
| case TransformOperation::TransformOperationIdentity: |
| *bounds = box; |
| return true; |
| case TransformOperation::TransformOperationTranslate: |
| case TransformOperation::TransformOperationSkew: |
| case TransformOperation::TransformOperationPerspective: |
| case TransformOperation::TransformOperationScale: { |
| gfx::Transform from_transform; |
| gfx::Transform to_transform; |
| if (!BlendTransformOperations(from, to, min_progress, &from_transform) || |
| !BlendTransformOperations(from, to, max_progress, &to_transform)) |
| return false; |
| |
| *bounds = box; |
| from_transform.TransformBox(bounds); |
| |
| gfx::BoxF to_box = box; |
| to_transform.TransformBox(&to_box); |
| bounds->ExpandTo(to_box); |
| |
| return true; |
| } |
| case TransformOperation::TransformOperationRotate: { |
| SkMScalar axis_x = 0; |
| SkMScalar axis_y = 0; |
| SkMScalar axis_z = 1; |
| SkMScalar from_angle = 0; |
| if (!ShareSameAxis(from, to, &axis_x, &axis_y, &axis_z, &from_angle)) |
| return false; |
| |
| bool first_point = true; |
| for (int i = 0; i < 8; ++i) { |
| gfx::Point3F corner = box.origin(); |
| corner += gfx::Vector3dF(i & 1 ? box.width() : 0.f, |
| i & 2 ? box.height() : 0.f, |
| i & 4 ? box.depth() : 0.f); |
| gfx::BoxF box_for_arc; |
| BoundingBoxForArc( |
| corner, from, to, min_progress, max_progress, &box_for_arc); |
| if (first_point) |
| *bounds = box_for_arc; |
| else |
| bounds->Union(box_for_arc); |
| first_point = false; |
| } |
| return true; |
| } |
| case TransformOperation::TransformOperationMatrix: |
| return false; |
| } |
| NOTREACHED(); |
| return false; |
| } |
| |
| } // namespace cc |
