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>
#include <cmath>
#include <limits>

#include "base/logging.h"
#include "cc/animation/transform_operation.h"
#include "cc/animation/transform_operations.h"
#include "ui/gfx/geometry/box_f.h"
#include "ui/gfx/geometry/vector3d_f.h"
#include "ui/gfx/transform_util.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::TRANSFORM_OPERATION_IDENTITY;
  if (IsOperationIdentity(to))
    interpolation_type = from->type;
  else
    interpolation_type = to->type;

  switch (interpolation_type) {
    case TransformOperation::TRANSFORM_OPERATION_TRANSLATE: {
    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::TRANSFORM_OPERATION_ROTATE: {
    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::TRANSFORM_OPERATION_SCALE: {
    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::TRANSFORM_OPERATION_SKEW: {
    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->Skew(BlendSkMScalars(from_x, to_x, progress),
                 BlendSkMScalars(from_y, to_y, progress));
    break;
  }
  case TransformOperation::TRANSFORM_OPERATION_PERSPECTIVE: {
    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::TRANSFORM_OPERATION_MATRIX: {
    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::TRANSFORM_OPERATION_IDENTITY:
    // 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::TRANSFORM_OPERATION_IDENTITY;
  if (is_identity_to)
    interpolation_type = from->type;
  else
    interpolation_type = to->type;

  switch (interpolation_type) {
    case TransformOperation::TRANSFORM_OPERATION_IDENTITY:
      *bounds = box;
      return true;
    case TransformOperation::TRANSFORM_OPERATION_TRANSLATE:
    case TransformOperation::TRANSFORM_OPERATION_SKEW:
    case TransformOperation::TRANSFORM_OPERATION_PERSPECTIVE:
    case TransformOperation::TRANSFORM_OPERATION_SCALE: {
      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::TRANSFORM_OPERATION_ROTATE: {
      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::TRANSFORM_OPERATION_MATRIX:
      return false;
  }
  NOTREACHED();
  return false;
}

}  // namespace cc