New Matrix3F class added in gfx.

ui/gfx/matrix3_f.cc

+// 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 3.14159265358979323846f
+#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(const Matrix3F& rhs) {
+  memcpy(data_, rhs.data_, sizeof(data_));
+}
+
+Matrix3F::~Matrix3F() {
+}
+
+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;
+}
+
+void Matrix3F::set(float m00, float m01, float m02,
+                   float m10, float m11, float m12,
+                   float m20, float m21, float m22) {

[danakj, 2013/02/01 00:02:34]

oh, missed this. i think this belongs in the header as well as it's just
assignments.

[motek., 2013/02/01 00:14:02]

Done.

+  data_[0] = m00;
+  data_[1] = m01;
+  data_[2] = m02;
+  data_[3] = m10;
+  data_[4] = m11;
+  data_[5] = m12;
+  data_[6] = m20;
+  data_[7] = m21;
+  data_[8] = m22;
+}
+
+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_[M02]) > 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 = sqrt(p / 6);

[danakj, 2013/02/01 00:02:34]

nit: std::sqrt

[motek., 2013/02/01 00:14:02]

Done.

+
+    // The computation below puts B as (A - qI) / p, where A is *this.
+    Matrix3F matrix_B(*this);

[danakj, 2013/02/01 00:02:34]

nit: matrix_b

[motek., 2013/02/01 00:14:02]

Done.

+    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;
+
+    float half_det_b = matrix_B.Determinant() / 2.0f;
+    // half_det_b should be in <-1, 1>, but beware of rounding error.
+    float phi = 0.0f;
+    if (half_det_b <= -1.0f)
+      phi = M_PI / 3;
+    else if (half_det_b < 1.0f)
+      phi = acos(half_det_b) / 3;
+
+    eigenvalues[0] = q + 2 * p * cos(phi);
+    eigenvalues[2] = q + 2 * p * cos(phi + 2.0f * M_PI / 3.0f);
+    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.set_x(-e2.x());

[danakj, 2013/02/01 00:02:34]

can use e2 = -e2; ?

[motek., 2013/02/01 00:14:02]

Ah, didn't notice the op. Cool. Done.

+        e2.set_y(-e2.y());
+        e2.set_z(-e2.z());
+      }
+
+      if (DotProduct(e1, e3) < 0) {
+        e3.set_x(-e3.x());

[danakj, 2013/02/01 00:02:34]

e3 = -e3; ?

[motek., 2013/02/01 00:14:02]

Done.

+        e3.set_y(-e3.y());
+        e3.set_z(-e3.z());
+      }
+
+      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]);
+}
+
+// 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;
+}
+
+}  // namespace gfx