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// 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