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+// Copyright (c) 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.
+
+#include "ui/gfx/matrix3_f.h"
+
+#include <algorithm>
+#include <cmath>
+#include <limits>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+namespace {
+
+// This is only to make accessing indices self-explanatory.
+enum MatrixCoordinates {
+ M00,
+ M01,
+ M02,
+ M10,
+ M11,
+ M12,
+ M20,
+ M21,
+ M22,
+ M_END
+};
+
+template<typename T>
+double Determinant3x3(T data[M_END]) {
+ // This routine is separated from the Matrix3F::Determinant because in
+ // computing inverse we do want higher precision afforded by the explicit
+ // use of 'double'.
+ return
+ static_cast<double>(data[M00]) * (
+ static_cast<double>(data[M11]) * data[M22] -
+ static_cast<double>(data[M12]) * data[M21]) +
+ static_cast<double>(data[M01]) * (
+ static_cast<double>(data[M12]) * data[M20] -
+ static_cast<double>(data[M10]) * data[M22]) +
+ static_cast<double>(data[M02]) * (
+ static_cast<double>(data[M10]) * data[M21] -
+ static_cast<double>(data[M11]) * data[M20]);
+}
+
+} // namespace
+
+namespace gfx {
+
+Matrix3F::Matrix3F() {
+}
+
+Matrix3F::~Matrix3F() {
+}
+
+// static
+Matrix3F Matrix3F::Zeros() {
+ Matrix3F matrix;
+ matrix.set(0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f);
+ return matrix;
+}
+
+// static
+Matrix3F Matrix3F::Ones() {
+ Matrix3F matrix;
+ matrix.set(1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f);
+ return matrix;
+}
+
+// static
+Matrix3F Matrix3F::Identity() {
+ Matrix3F matrix;
+ matrix.set(1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f);
+ return matrix;
+}
+
+// static
+Matrix3F Matrix3F::FromOuterProduct(const Vector3dF& a, const Vector3dF& bt) {
+ Matrix3F matrix;
+ matrix.set(a.x() * bt.x(), a.x() * bt.y(), a.x() * bt.z(),
+ a.y() * bt.x(), a.y() * bt.y(), a.y() * bt.z(),
+ a.z() * bt.x(), a.z() * bt.y(), a.z() * bt.z());
+ return matrix;
+}
+
+bool Matrix3F::IsEqual(const Matrix3F& rhs) const {
+ return 0 == memcmp(data_, rhs.data_, sizeof(data_));
+}
+
+bool Matrix3F::IsNear(const Matrix3F& rhs, float precision) const {
+ DCHECK(precision >= 0);
+ for (int i = 0; i < M_END; ++i) {
+ if (std::abs(data_[i] - rhs.data_[i]) > precision)
+ return false;
+ }
+ return true;
+}
+
+Matrix3F Matrix3F::Inverse() const {
+ Matrix3F inverse = Matrix3F::Zeros();
+ double determinant = Determinant3x3(data_);
+ if (std::numeric_limits<float>::epsilon() > std::abs(determinant))
+ return inverse; // Singular matrix. Return Zeros().
+
+ inverse.set(
+ (data_[M11] * data_[M22] - data_[M12] * data_[M21]) / determinant,
+ (data_[M02] * data_[M21] - data_[M01] * data_[M22]) / determinant,
+ (data_[M01] * data_[M12] - data_[M02] * data_[M11]) / determinant,
+ (data_[M12] * data_[M20] - data_[M10] * data_[M22]) / determinant,
+ (data_[M00] * data_[M22] - data_[M02] * data_[M20]) / determinant,
+ (data_[M02] * data_[M10] - data_[M00] * data_[M12]) / determinant,
+ (data_[M10] * data_[M21] - data_[M11] * data_[M20]) / determinant,
+ (data_[M01] * data_[M20] - data_[M00] * data_[M21]) / determinant,
+ (data_[M00] * data_[M11] - data_[M01] * data_[M10]) / determinant);
+ return inverse;
+}
+
+float Matrix3F::Determinant() const {
+ return static_cast<float>(Determinant3x3(data_));
+}
+
+Vector3dF Matrix3F::SolveEigenproblem(Matrix3F* eigenvectors) const {
+ // The matrix must be symmetric.
+ const float epsilon = std::numeric_limits<float>::epsilon();
+ if (std::abs(data_[M01] - data_[M10]) > epsilon ||
+ std::abs(data_[M02] - data_[M20]) > epsilon ||
+ std::abs(data_[M12] - data_[M21]) > epsilon) {
+ NOTREACHED();
+ return Vector3dF();
+ }
+
+ float eigenvalues[3];
+ float p =
+ data_[M01] * data_[M01] +
+ data_[M02] * data_[M02] +
+ data_[M12] * data_[M12];
+
+ bool diagonal = std::abs(p) < epsilon;
+ if (diagonal) {
+ eigenvalues[0] = data_[M00];
+ eigenvalues[1] = data_[M11];
+ eigenvalues[2] = data_[M22];
+ } else {
+ float q = Trace() / 3.0f;
+ p = (data_[M00] - q) * (data_[M00] - q) +
+ (data_[M11] - q) * (data_[M11] - q) +
+ (data_[M22] - q) * (data_[M22] - q) +
+ 2 * p;
+ p = std::sqrt(p / 6);
+
+ // The computation below puts B as (A - qI) / p, where A is *this.
+ Matrix3F matrix_b(*this);
+ matrix_b.data_[M00] -= q;
+ matrix_b.data_[M11] -= q;
+ matrix_b.data_[M22] -= q;
+ for (int i = 0; i < M_END; ++i)
+ matrix_b.data_[i] /= p;
+
+ double half_det_b = Determinant3x3(matrix_b.data_) / 2.0;
+ // half_det_b should be in <-1, 1>, but beware of rounding error.
+ double phi = 0.0f;
+ if (half_det_b <= -1.0)
+ phi = M_PI / 3;
+ else if (half_det_b < 1.0)
+ phi = acos(half_det_b) / 3;
+
+ eigenvalues[0] = q + 2 * p * static_cast<float>(cos(phi));
+ eigenvalues[2] = q + 2 * p *
+ static_cast<float>(cos(phi + 2.0 * M_PI / 3.0));
+ eigenvalues[1] = 3 * q - eigenvalues[0] - eigenvalues[2];
+ }
+
+ // Put eigenvalues in the descending order.
+ int indices[3] = {0, 1, 2};
+ if (eigenvalues[2] > eigenvalues[1]) {
+ std::swap(eigenvalues[2], eigenvalues[1]);
+ std::swap(indices[2], indices[1]);
+ }
+
+ if (eigenvalues[1] > eigenvalues[0]) {
+ std::swap(eigenvalues[1], eigenvalues[0]);
+ std::swap(indices[1], indices[0]);
+ }
+
+ if (eigenvalues[2] > eigenvalues[1]) {
+ std::swap(eigenvalues[2], eigenvalues[1]);
+ std::swap(indices[2], indices[1]);
+ }
+
+ if (eigenvectors != NULL && diagonal) {
+ // Eigenvectors are e-vectors, just need to be sorted accordingly.
+ *eigenvectors = Zeros();
+ for (int i = 0; i < 3; ++i)
+ eigenvectors->set(indices[i], i, 1.0f);
+ } else if (eigenvectors != NULL) {
+ // Consult the following for a detailed discussion:
+ // Joachim Kopp
+ // Numerical diagonalization of hermitian 3x3 matrices
+ // arXiv.org preprint: physics/0610206
+ // Int. J. Mod. Phys. C19 (2008) 523-548
+
+ // TODO(motek): expand to handle correctly negative and multiple
+ // eigenvalues.
+ for (int i = 0; i < 3; ++i) {
+ float l = eigenvalues[i];
+ // B = A - l * I
+ Matrix3F matrix_b(*this);
+ matrix_b.data_[M00] -= l;
+ matrix_b.data_[M11] -= l;
+ matrix_b.data_[M22] -= l;
+ Vector3dF e1 = CrossProduct(matrix_b.get_column(0),
+ matrix_b.get_column(1));
+ Vector3dF e2 = CrossProduct(matrix_b.get_column(1),
+ matrix_b.get_column(2));
+ Vector3dF e3 = CrossProduct(matrix_b.get_column(2),
+ matrix_b.get_column(0));
+
+ // e1, e2 and e3 should point in the same direction.
+ if (DotProduct(e1, e2) < 0)
+ e2 = -e2;
+
+ if (DotProduct(e1, e3) < 0)
+ e3 = -e3;
+
+ Vector3dF eigvec = e1 + e2 + e3;
+ // Normalize.
+ eigvec.Scale(1.0f / eigvec.Length());
+ eigenvectors->set_column(i, eigvec);
+ }
+ }
+
+ return Vector3dF(eigenvalues[0], eigenvalues[1], eigenvalues[2]);
+}
+
+} // namespace gfx