text: // 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 <algorithm>
  #include <cmath>
  #include <string>
  
  #include "base/logging.h"
  #include "base/strings/stringprintf.h"
  #include "ui/gfx/geometry/point.h"
  #include "ui/gfx/geometry/point3_f.h"
  #include "ui/gfx/geometry/rect.h"
  
  namespace gfx {
  
  namespace {
  
  SkMScalar Length3(SkMScalar v[3]) {
    double vd[3] = {SkMScalarToDouble(v[0]), SkMScalarToDouble(v[1]),
                    SkMScalarToDouble(v[2])};
    return SkDoubleToMScalar(
        std::sqrt(vd[0] * vd[0] + vd[1] * vd[1] + vd[2] * vd[2]));
  }
  
  template <int n>
  SkMScalar Dot(const SkMScalar* a, const SkMScalar* b) {
    double total = 0.0;
    for (int i = 0; i < n; ++i)
      total += a[i] * b[i];
    return SkDoubleToMScalar(total);
  }
  
  template <int n>
  void Combine(SkMScalar* out,
               const SkMScalar* a,
               const SkMScalar* b,
               double scale_a,
               double scale_b) {
    for (int i = 0; i < n; ++i)
      out[i] = SkDoubleToMScalar(a[i] * scale_a + b[i] * scale_b);
  }
  
  void Cross3(SkMScalar out[3], SkMScalar a[3], SkMScalar b[3]) {
    SkMScalar x = a[1] * b[2] - a[2] * b[1];
    SkMScalar y = a[2] * b[0] - a[0] * b[2];
    SkMScalar z = a[0] * b[1] - a[1] * b[0];
    out[0] = x;
    out[1] = y;
    out[2] = z;
  }
  
  SkMScalar Round(SkMScalar n) {
    return SkDoubleToMScalar(std::floor(SkMScalarToDouble(n) + 0.5));
  }
  
  // Returns false if the matrix cannot be normalized.
  bool Normalize(SkMatrix44& m) {
    if (m.get(3, 3) == 0.0)
      // Cannot normalize.
      return false;
  
    SkMScalar scale = SK_MScalar1 / m.get(3, 3);
    for (int i = 0; i < 4; i++)
      for (int j = 0; j < 4; j++)
        m.set(i, j, m.get(i, j) * scale);
  
    return true;
  }
  
  SkMatrix44 BuildPerspectiveMatrix(const DecomposedTransform& decomp) {
    SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
  
    for (int i = 0; i < 4; i++)
      matrix.setDouble(3, i, decomp.perspective[i]);
    return matrix;
  }
  
  SkMatrix44 BuildTranslationMatrix(const DecomposedTransform& decomp) {
    SkMatrix44 matrix(SkMatrix44::kUninitialized_Constructor);
    // Implicitly calls matrix.setIdentity()
    matrix.setTranslate(SkDoubleToMScalar(decomp.translate[0]),
                        SkDoubleToMScalar(decomp.translate[1]),
                        SkDoubleToMScalar(decomp.translate[2]));
    return matrix;
  }
  
  SkMatrix44 BuildSnappedTranslationMatrix(DecomposedTransform decomp) {
    decomp.translate[0] = Round(decomp.translate[0]);
    decomp.translate[1] = Round(decomp.translate[1]);
    decomp.translate[2] = Round(decomp.translate[2]);
    return BuildTranslationMatrix(decomp);
  }
  
  SkMatrix44 BuildRotationMatrix(const DecomposedTransform& decomp) {
    return Transform(decomp.quaternion).matrix();
  }
  
  SkMatrix44 BuildSnappedRotationMatrix(const DecomposedTransform& decomp) {
    // Create snapped rotation.
    SkMatrix44 rotation_matrix = BuildRotationMatrix(decomp);
    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);
      }
    }
    return rotation_matrix;
  }
  
  SkMatrix44 BuildSkewMatrix(const DecomposedTransform& decomp) {
    SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
  
    SkMatrix44 temp(SkMatrix44::kIdentity_Constructor);
    if (decomp.skew[2]) {
      temp.setDouble(1, 2, decomp.skew[2]);
      matrix.preConcat(temp);
    }
  
    if (decomp.skew[1]) {
      temp.setDouble(1, 2, 0);
      temp.setDouble(0, 2, decomp.skew[1]);
      matrix.preConcat(temp);
    }
  
    if (decomp.skew[0]) {
      temp.setDouble(0, 2, 0);
      temp.setDouble(0, 1, decomp.skew[0]);
      matrix.preConcat(temp);
    }
    return matrix;
  }
  
  SkMatrix44 BuildScaleMatrix(const DecomposedTransform& decomp) {
    SkMatrix44 matrix(SkMatrix44::kUninitialized_Constructor);
    matrix.setScale(SkDoubleToMScalar(decomp.scale[0]),
                    SkDoubleToMScalar(decomp.scale[1]),
                    SkDoubleToMScalar(decomp.scale[2]));
    return matrix;
  }
  
  SkMatrix44 BuildSnappedScaleMatrix(DecomposedTransform decomp) {
    decomp.scale[0] = Round(decomp.scale[0]);
    decomp.scale[1] = Round(decomp.scale[1]);
    decomp.scale[2] = Round(decomp.scale[2]);
    return BuildScaleMatrix(decomp);
  }
  
  Transform ComposeTransform(const SkMatrix44& perspective,
                             const SkMatrix44& translation,
                             const SkMatrix44& rotation,
                             const SkMatrix44& skew,
                             const SkMatrix44& scale) {
    SkMatrix44 matrix(SkMatrix44::kIdentity_Constructor);
  
    matrix.preConcat(perspective);
    matrix.preConcat(translation);
    matrix.preConcat(rotation);
    matrix.preConcat(skew);
    matrix.preConcat(scale);
  
    Transform to_return;
    to_return.matrix() = matrix;
    return to_return;
  }
  
  bool CheckViewportPointMapsWithinOnePixel(const Point& point,
                                            const Transform& transform) {
    auto point_original = Point3F(PointF(point));
    auto point_transformed = Point3F(PointF(point));
  
    // 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.
    transform.TransformPoint(&point_transformed);
  
    if ((point_transformed - point_original).Length() > 1.f) {
      // The changed distance should not be more than 1 pixel.
      return false;
    }
    return true;
  }
  
  bool CheckTransformsMapsIntViewportWithinOnePixel(const Rect& viewport,
                                                    const Transform& original,
                                                    const Transform& snapped) {
  
    Transform original_inv(Transform::kSkipInitialization);
    bool invertible = true;
    invertible &= original.GetInverse(&original_inv);
    DCHECK(invertible) << "Non-invertible transform, cannot snap.";
  
    Transform combined = snapped * original_inv;
  
    return CheckViewportPointMapsWithinOnePixel(viewport.origin(), combined) &&
           CheckViewportPointMapsWithinOnePixel(viewport.top_right(), combined) &&
           CheckViewportPointMapsWithinOnePixel(viewport.bottom_left(),
                                                combined) &&
           CheckViewportPointMapsWithinOnePixel(viewport.bottom_right(),
                                                combined);
  }
  
  }  // namespace
  
  Transform GetScaleTransform(const Point& anchor, float scale) {
    Transform transform;
    transform.Translate(anchor.x() * (1 - scale),
                        anchor.y() * (1 - scale));
    transform.Scale(scale, scale);
    return transform;
  }
  
  DecomposedTransform::DecomposedTransform() {
    translate[0] = translate[1] = translate[2] = 0.0;
    scale[0] = scale[1] = scale[2] = 1.0;
    skew[0] = skew[1] = skew[2] = 0.0;
    perspective[0] = perspective[1] = perspective[2] = 0.0;
    perspective[3] = 1.0;
  }
  
  DecomposedTransform BlendDecomposedTransforms(const DecomposedTransform& to,
                                                const DecomposedTransform& from,
                                                double progress) {
    DecomposedTransform out;
    double scalea = progress;
    double scaleb = 1.0 - progress;
    Combine<3>(out.translate, to.translate, from.translate, scalea, scaleb);
    Combine<3>(out.scale, to.scale, from.scale, scalea, scaleb);
    Combine<3>(out.skew, to.skew, from.skew, scalea, scaleb);
    Combine<4>(out.perspective, to.perspective, from.perspective, scalea, scaleb);
    out.quaternion = from.quaternion.Slerp(to.quaternion, progress);
    return out;
  }
  
  // Taken from http://www.w3.org/TR/css3-transforms/.
  bool DecomposeTransform(DecomposedTransform* decomp,
                          const Transform& transform) {
    if (!decomp)
      return false;
  
    // We'll operate on a copy of the matrix.
    SkMatrix44 matrix = transform.matrix();
  
    // If we cannot normalize the matrix, then bail early as we cannot decompose.
    if (!Normalize(matrix))
      return false;
  
    SkMatrix44 perspectiveMatrix = matrix;
  
    for (int i = 0; i < 3; ++i)
      perspectiveMatrix.set(3, i, 0.0);
  
    perspectiveMatrix.set(3, 3, 1.0);
  
    // If the perspective matrix is not invertible, we are also unable to
    // decompose, so we'll bail early. Constant taken from SkMatrix44::invert.
    if (std::abs(perspectiveMatrix.determinant()) < 1e-8)
      return false;
  
    if (matrix.get(3, 0) != 0.0 || matrix.get(3, 1) != 0.0 ||
        matrix.get(3, 2) != 0.0) {
      // rhs is the right hand side of the equation.
      SkMScalar rhs[4] = {
        matrix.get(3, 0),
        matrix.get(3, 1),
        matrix.get(3, 2),
        matrix.get(3, 3)
      };
  
      // Solve the equation by inverting perspectiveMatrix and multiplying
      // rhs by the inverse.
      SkMatrix44 inversePerspectiveMatrix(SkMatrix44::kUninitialized_Constructor);
      if (!perspectiveMatrix.invert(&inversePerspectiveMatrix))
        return false;
  
      SkMatrix44 transposedInversePerspectiveMatrix =
          inversePerspectiveMatrix;
  
      transposedInversePerspectiveMatrix.transpose();
      transposedInversePerspectiveMatrix.mapMScalars(rhs);
  
      for (int i = 0; i < 4; ++i)
        decomp->perspective[i] = rhs[i];
  
    } else {
      // No perspective.
      for (int i = 0; i < 3; ++i)
        decomp->perspective[i] = 0.0;
      decomp->perspective[3] = 1.0;
    }
  
    for (int i = 0; i < 3; i++)
      decomp->translate[i] = matrix.get(i, 3);
  
    SkMScalar row[3][3];
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; ++j)
        row[i][j] = matrix.get(j, i);
  
    // Compute X scale factor and normalize first row.
    decomp->scale[0] = Length3(row[0]);
    if (decomp->scale[0] != 0.0) {
      row[0][0] /= decomp->scale[0];
      row[0][1] /= decomp->scale[0];
      row[0][2] /= decomp->scale[0];
    }
  
    // Compute XY shear factor and make 2nd row orthogonal to 1st.
    decomp->skew[0] = Dot<3>(row[0], row[1]);
    Combine<3>(row[1], row[1], row[0], 1.0, -decomp->skew[0]);
  
    // Now, compute Y scale and normalize 2nd row.
    decomp->scale[1] = Length3(row[1]);
    if (decomp->scale[1] != 0.0) {
      row[1][0] /= decomp->scale[1];
      row[1][1] /= decomp->scale[1];
      row[1][2] /= decomp->scale[1];
    }
  
    decomp->skew[0] /= decomp->scale[1];
  
    // Compute XZ and YZ shears, orthogonalize 3rd row
    decomp->skew[1] = Dot<3>(row[0], row[2]);
    Combine<3>(row[2], row[2], row[0], 1.0, -decomp->skew[1]);
    decomp->skew[2] = Dot<3>(row[1], row[2]);
    Combine<3>(row[2], row[2], row[1], 1.0, -decomp->skew[2]);
  
    // Next, get Z scale and normalize 3rd row.
    decomp->scale[2] = Length3(row[2]);
    if (decomp->scale[2] != 0.0) {
      row[2][0] /= decomp->scale[2];
      row[2][1] /= decomp->scale[2];
      row[2][2] /= decomp->scale[2];
    }
  
    decomp->skew[1] /= decomp->scale[2];
    decomp->skew[2] /= decomp->scale[2];
  
    // At this point, the matrix (in rows) is orthonormal.
    // Check for a coordinate system flip.  If the determinant
    // is -1, then negate the matrix and the scaling factors.
    SkMScalar pdum3[3];
    Cross3(pdum3, row[1], row[2]);
    if (Dot<3>(row[0], pdum3) < 0) {
      for (int i = 0; i < 3; i++) {
        decomp->scale[i] *= -1.0;
        for (int j = 0; j < 3; ++j)
          row[i][j] *= -1.0;
      }
    }
  
    double row00 = SkMScalarToDouble(row[0][0]);
    double row11 = SkMScalarToDouble(row[1][1]);
    double row22 = SkMScalarToDouble(row[2][2]);
  
    decomp->quaternion.set_x(SkDoubleToMScalar(
        0.5 * std::sqrt(std::max(1.0 + row00 - row11 - row22, 0.0))));
    decomp->quaternion.set_y(SkDoubleToMScalar(
        0.5 * std::sqrt(std::max(1.0 - row00 + row11 - row22, 0.0))));
    decomp->quaternion.set_z(SkDoubleToMScalar(
        0.5 * std::sqrt(std::max(1.0 - row00 - row11 + row22, 0.0))));
    decomp->quaternion.set_w(SkDoubleToMScalar(
        0.5 * std::sqrt(std::max(1.0 + row00 + row11 + row22, 0.0))));
  
    if (row[2][1] > row[1][2])
      decomp->quaternion.set_x(-decomp->quaternion.x());
    if (row[0][2] > row[2][0])
      decomp->quaternion.set_y(-decomp->quaternion.y());
    if (row[1][0] > row[0][1])
      decomp->quaternion.set_z(-decomp->quaternion.z());
  
    return true;
  }
  
  // Taken from http://www.w3.org/TR/css3-transforms/.
  Transform ComposeTransform(const DecomposedTransform& decomp) {
    SkMatrix44 perspective = BuildPerspectiveMatrix(decomp);
    SkMatrix44 translation = BuildTranslationMatrix(decomp);
    SkMatrix44 rotation = BuildRotationMatrix(decomp);
    SkMatrix44 skew = BuildSkewMatrix(decomp);
    SkMatrix44 scale = BuildScaleMatrix(decomp);
  
    return ComposeTransform(perspective, translation, rotation, skew, scale);
  }
  
  bool SnapTransform(Transform* out,
                     const Transform& transform,
                     const Rect& viewport) {
    DecomposedTransform decomp;
    DecomposeTransform(&decomp, transform);
  
    SkMatrix44 rotation_matrix = BuildSnappedRotationMatrix(decomp);
    SkMatrix44 translation = BuildSnappedTranslationMatrix(decomp);
    SkMatrix44 scale = BuildSnappedScaleMatrix(decomp);
  
    // Rebuild matrices for other unchanged components.
    SkMatrix44 perspective = BuildPerspectiveMatrix(decomp);
  
    // Completely ignore the skew.
    SkMatrix44 skew(SkMatrix44::kIdentity_Constructor);
  
    // Get full tranform
    Transform snapped =
        ComposeTransform(perspective, translation, rotation_matrix, skew, scale);
  
    // Verify that viewport is not moved unnaturally.
    bool snappable =
      CheckTransformsMapsIntViewportWithinOnePixel(viewport, transform, snapped);
    if (snappable) {
      *out = snapped;
    }
    return snappable;
  }
  
  Transform TransformAboutPivot(const gfx::Point& pivot,
                                const gfx::Transform& transform) {
    gfx::Transform result;
    result.Translate(pivot.x(), pivot.y());
    result.PreconcatTransform(transform);
    result.Translate(-pivot.x(), -pivot.y());
    return result;
  }
  
  std::string DecomposedTransform::ToString() const {
    return base::StringPrintf(
        "translate: %+0.4f %+0.4f %+0.4f\n"
        "scale: %+0.4f %+0.4f %+0.4f\n"
        "skew: %+0.4f %+0.4f %+0.4f\n"
        "perspective: %+0.4f %+0.4f %+0.4f %+0.4f\n"
        "quaternion: %+0.4f %+0.4f %+0.4f %+0.4f\n",
        translate[0], translate[1], translate[2], scale[0], scale[1], scale[2],
        skew[0], skew[1], skew[2], perspective[0], perspective[1], perspective[2],
        perspective[3], quaternion.x(), quaternion.y(), quaternion.z(),
        quaternion.w());
  }
  
  }  // namespace gfx
  