| // 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 "cobalt/math/matrix3_f.h" |
| |
| #include <algorithm> |
| #include <cmath> |
| #include <limits> |
| |
| namespace cobalt { |
| namespace math { |
| |
| 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 |
| |
| Matrix3F::Matrix3F() {} |
| |
| Matrix3F::~Matrix3F() {} |
| |
| // static |
| Matrix3F Matrix3F::Zeros() { |
| Matrix3F matrix; |
| matrix.SetMatrix(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.SetMatrix(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.SetMatrix(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.SetMatrix(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; |
| } |
| |
| // static |
| Matrix3F Matrix3F::FromArray(const float data[9]) { |
| Matrix3F matrix; |
| memcpy(matrix.data_, data, sizeof(float) * 9); |
| return matrix; |
| } |
| |
| // static |
| Matrix3F Matrix3F::FromValues(float m00, float m01, float m02, float m10, |
| float m11, float m12, float m20, float m21, |
| float m22) { |
| Matrix3F matrix; |
| matrix.SetMatrix(m00, m01, m02, m10, m11, m12, m20, m21, m22); |
| return matrix; |
| } |
| |
| bool Matrix3F::IsZeros() const { |
| return data_[M00] == 0.0f && data_[M01] == 0.0f && data_[M02] == 0.0f && |
| data_[M10] == 0.0f && data_[M11] == 0.0f && data_[M12] == 0.0f && |
| data_[M20] == 0.0f && data_[M21] == 0.0f && data_[M22] == 0.0f; |
| } |
| |
| bool Matrix3F::IsIdentity() const { |
| return data_[M00] == 1.0f && data_[M01] == 0.0f && data_[M02] == 0.0f && |
| data_[M10] == 0.0f && data_[M11] == 1.0f && data_[M12] == 0.0f && |
| data_[M20] == 0.0f && data_[M21] == 0.0f && data_[M22] == 1.0f; |
| } |
| |
| 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_GE(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.SetMatrix( |
| (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.column(0), matrix_b.column(1)); |
| Vector3dF e2 = CrossProduct(matrix_b.column(1), matrix_b.column(2)); |
| Vector3dF e3 = CrossProduct(matrix_b.column(2), matrix_b.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]); |
| } |
| |
| Matrix3F Matrix3F::operator*(const Matrix3F& other) const { |
| Matrix3F ret; |
| ret.data_[M00] = data_[M00] * other.data_[M00] + |
| data_[M01] * other.data_[M10] + |
| data_[M02] * other.data_[M20]; |
| ret.data_[M01] = data_[M00] * other.data_[M01] + |
| data_[M01] * other.data_[M11] + |
| data_[M02] * other.data_[M21]; |
| ret.data_[M02] = data_[M00] * other.data_[M02] + |
| data_[M01] * other.data_[M12] + |
| data_[M02] * other.data_[M22]; |
| |
| ret.data_[M10] = data_[M10] * other.data_[M00] + |
| data_[M11] * other.data_[M10] + |
| data_[M12] * other.data_[M20]; |
| ret.data_[M11] = data_[M10] * other.data_[M01] + |
| data_[M11] * other.data_[M11] + |
| data_[M12] * other.data_[M21]; |
| ret.data_[M12] = data_[M10] * other.data_[M02] + |
| data_[M11] * other.data_[M12] + |
| data_[M12] * other.data_[M22]; |
| |
| ret.data_[M20] = data_[M20] * other.data_[M00] + |
| data_[M21] * other.data_[M10] + |
| data_[M22] * other.data_[M20]; |
| ret.data_[M21] = data_[M20] * other.data_[M01] + |
| data_[M21] * other.data_[M11] + |
| data_[M22] * other.data_[M21]; |
| ret.data_[M22] = data_[M20] * other.data_[M02] + |
| data_[M21] * other.data_[M12] + |
| data_[M22] * other.data_[M22]; |
| |
| return ret; |
| } |
| |
| PointF Matrix3F::operator*(const PointF& rhs) const { |
| float x = rhs.x() * data_[M00] + rhs.y() * data_[M01] + data_[M02]; |
| float y = rhs.x() * data_[M10] + rhs.y() * data_[M11] + data_[M12]; |
| float z = rhs.x() * data_[M20] + rhs.y() * data_[M21] + data_[M22]; |
| DCHECK_NE(z, 0.f); |
| |
| return PointF(x / z, y / z); |
| } |
| |
| RectF Matrix3F::MapRect(const RectF& rect) { |
| PointF points[4]; |
| points[0] = *this * rect.origin(); |
| points[1] = *this * rect.top_right(); |
| points[2] = *this * rect.bottom_left(); |
| points[3] = *this * rect.bottom_right(); |
| |
| float min_x = std::numeric_limits<float>::max(); |
| float max_x = -std::numeric_limits<float>::max(); |
| float min_y = std::numeric_limits<float>::max(); |
| float max_y = -std::numeric_limits<float>::max(); |
| for (int i = 0; i < 4; ++i) { |
| min_x = std::min(min_x, points[i].x()); |
| max_x = std::max(max_x, points[i].x()); |
| min_y = std::min(min_y, points[i].y()); |
| max_y = std::max(max_y, points[i].y()); |
| } |
| |
| return RectF(min_x, min_y, max_x - min_x, max_y - min_y); |
| } |
| |
| } // namespace math |
| } // namespace cobalt |