| // |
| // Copyright 2015 The ANGLE Project Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| // |
| // Matrix: |
| // Utility class implementing various matrix operations. |
| // Supports matrices with minimum 2 and maximum 4 number of rows/columns. |
| // |
| // TODO: Check if we can merge Matrix.h in sample_util with this and replace it with this |
| // implementation. |
| // TODO: Rename this file to Matrix.h once we remove Matrix.h in sample_util. |
| |
| #ifndef COMMON_MATRIX_UTILS_H_ |
| #define COMMON_MATRIX_UTILS_H_ |
| |
| #include <vector> |
| |
| #include "common/debug.h" |
| #include "common/mathutil.h" |
| #include "common/vector_utils.h" |
| |
| namespace angle |
| { |
| |
| template <typename T> |
| class Matrix |
| { |
| public: |
| Matrix(const std::vector<T> &elements, const unsigned int numRows, const unsigned int numCols) |
| : mElements(elements), mRows(numRows), mCols(numCols) |
| { |
| ASSERT(rows() >= 1 && rows() <= 4); |
| ASSERT(columns() >= 1 && columns() <= 4); |
| } |
| |
| Matrix(const std::vector<T> &elements, const unsigned int size) |
| : mElements(elements), mRows(size), mCols(size) |
| { |
| ASSERT(rows() >= 1 && rows() <= 4); |
| ASSERT(columns() >= 1 && columns() <= 4); |
| } |
| |
| Matrix(const T *elements, const unsigned int size) : mRows(size), mCols(size) |
| { |
| ASSERT(rows() >= 1 && rows() <= 4); |
| ASSERT(columns() >= 1 && columns() <= 4); |
| for (size_t i = 0; i < size * size; i++) |
| mElements.push_back(elements[i]); |
| } |
| |
| const T &operator()(const unsigned int rowIndex, const unsigned int columnIndex) const |
| { |
| ASSERT(rowIndex < mRows); |
| ASSERT(columnIndex < mCols); |
| return mElements[rowIndex * columns() + columnIndex]; |
| } |
| |
| T &operator()(const unsigned int rowIndex, const unsigned int columnIndex) |
| { |
| ASSERT(rowIndex < mRows); |
| ASSERT(columnIndex < mCols); |
| return mElements[rowIndex * columns() + columnIndex]; |
| } |
| |
| const T &at(const unsigned int rowIndex, const unsigned int columnIndex) const |
| { |
| ASSERT(rowIndex < mRows); |
| ASSERT(columnIndex < mCols); |
| return operator()(rowIndex, columnIndex); |
| } |
| |
| Matrix<T> operator*(const Matrix<T> &m) |
| { |
| ASSERT(columns() == m.rows()); |
| |
| unsigned int resultRows = rows(); |
| unsigned int resultCols = m.columns(); |
| Matrix<T> result(std::vector<T>(resultRows * resultCols), resultRows, resultCols); |
| for (unsigned int i = 0; i < resultRows; i++) |
| { |
| for (unsigned int j = 0; j < resultCols; j++) |
| { |
| T tmp = 0.0f; |
| for (unsigned int k = 0; k < columns(); k++) |
| tmp += at(i, k) * m(k, j); |
| result(i, j) = tmp; |
| } |
| } |
| |
| return result; |
| } |
| |
| void operator*=(const Matrix<T> &m) |
| { |
| ASSERT(columns() == m.rows()); |
| Matrix<T> res = (*this) * m; |
| size_t numElts = res.elements().size(); |
| mElements.resize(numElts); |
| memcpy(mElements.data(), res.data(), numElts * sizeof(float)); |
| } |
| |
| bool operator==(const Matrix<T> &m) const |
| { |
| ASSERT(columns() == m.columns()); |
| ASSERT(rows() == m.rows()); |
| return mElements == m.elements(); |
| } |
| |
| bool operator!=(const Matrix<T> &m) const { return !(mElements == m.elements()); } |
| |
| bool nearlyEqual(T epsilon, const Matrix<T> &m) const |
| { |
| ASSERT(columns() == m.columns()); |
| ASSERT(rows() == m.rows()); |
| const auto &otherElts = m.elements(); |
| for (size_t i = 0; i < otherElts.size(); i++) |
| { |
| if ((mElements[i] - otherElts[i] > epsilon) && (otherElts[i] - mElements[i] > epsilon)) |
| return false; |
| } |
| return true; |
| } |
| |
| unsigned int size() const |
| { |
| ASSERT(rows() == columns()); |
| return rows(); |
| } |
| |
| unsigned int rows() const { return mRows; } |
| |
| unsigned int columns() const { return mCols; } |
| |
| std::vector<T> elements() const { return mElements; } |
| T *data() { return mElements.data(); } |
| |
| Matrix<T> compMult(const Matrix<T> &mat1) const |
| { |
| Matrix result(std::vector<T>(mElements.size()), rows(), columns()); |
| for (unsigned int i = 0; i < rows(); i++) |
| { |
| for (unsigned int j = 0; j < columns(); j++) |
| { |
| T lhs = at(i, j); |
| T rhs = mat1(i, j); |
| result(i, j) = rhs * lhs; |
| } |
| } |
| |
| return result; |
| } |
| |
| Matrix<T> outerProduct(const Matrix<T> &mat1) const |
| { |
| unsigned int cols = mat1.columns(); |
| Matrix result(std::vector<T>(rows() * cols), rows(), cols); |
| for (unsigned int i = 0; i < rows(); i++) |
| for (unsigned int j = 0; j < cols; j++) |
| result(i, j) = at(i, 0) * mat1(0, j); |
| |
| return result; |
| } |
| |
| Matrix<T> transpose() const |
| { |
| Matrix result(std::vector<T>(mElements.size()), columns(), rows()); |
| for (unsigned int i = 0; i < columns(); i++) |
| for (unsigned int j = 0; j < rows(); j++) |
| result(i, j) = at(j, i); |
| |
| return result; |
| } |
| |
| T determinant() const |
| { |
| ASSERT(rows() == columns()); |
| |
| switch (size()) |
| { |
| case 2: |
| return at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0); |
| |
| case 3: |
| return at(0, 0) * at(1, 1) * at(2, 2) + at(0, 1) * at(1, 2) * at(2, 0) + |
| at(0, 2) * at(1, 0) * at(2, 1) - at(0, 2) * at(1, 1) * at(2, 0) - |
| at(0, 1) * at(1, 0) * at(2, 2) - at(0, 0) * at(1, 2) * at(2, 1); |
| |
| case 4: |
| { |
| const float minorMatrices[4][3 * 3] = {{ |
| at(1, 1), |
| at(2, 1), |
| at(3, 1), |
| at(1, 2), |
| at(2, 2), |
| at(3, 2), |
| at(1, 3), |
| at(2, 3), |
| at(3, 3), |
| }, |
| { |
| at(1, 0), |
| at(2, 0), |
| at(3, 0), |
| at(1, 2), |
| at(2, 2), |
| at(3, 2), |
| at(1, 3), |
| at(2, 3), |
| at(3, 3), |
| }, |
| { |
| at(1, 0), |
| at(2, 0), |
| at(3, 0), |
| at(1, 1), |
| at(2, 1), |
| at(3, 1), |
| at(1, 3), |
| at(2, 3), |
| at(3, 3), |
| }, |
| { |
| at(1, 0), |
| at(2, 0), |
| at(3, 0), |
| at(1, 1), |
| at(2, 1), |
| at(3, 1), |
| at(1, 2), |
| at(2, 2), |
| at(3, 2), |
| }}; |
| return at(0, 0) * Matrix<T>(minorMatrices[0], 3).determinant() - |
| at(0, 1) * Matrix<T>(minorMatrices[1], 3).determinant() + |
| at(0, 2) * Matrix<T>(minorMatrices[2], 3).determinant() - |
| at(0, 3) * Matrix<T>(minorMatrices[3], 3).determinant(); |
| } |
| |
| default: |
| UNREACHABLE(); |
| break; |
| } |
| |
| return T(); |
| } |
| |
| Matrix<T> inverse() const |
| { |
| ASSERT(rows() == columns()); |
| |
| Matrix<T> cof(std::vector<T>(mElements.size()), rows(), columns()); |
| switch (size()) |
| { |
| case 2: |
| cof(0, 0) = at(1, 1); |
| cof(0, 1) = -at(1, 0); |
| cof(1, 0) = -at(0, 1); |
| cof(1, 1) = at(0, 0); |
| break; |
| |
| case 3: |
| cof(0, 0) = at(1, 1) * at(2, 2) - at(2, 1) * at(1, 2); |
| cof(0, 1) = -(at(1, 0) * at(2, 2) - at(2, 0) * at(1, 2)); |
| cof(0, 2) = at(1, 0) * at(2, 1) - at(2, 0) * at(1, 1); |
| cof(1, 0) = -(at(0, 1) * at(2, 2) - at(2, 1) * at(0, 2)); |
| cof(1, 1) = at(0, 0) * at(2, 2) - at(2, 0) * at(0, 2); |
| cof(1, 2) = -(at(0, 0) * at(2, 1) - at(2, 0) * at(0, 1)); |
| cof(2, 0) = at(0, 1) * at(1, 2) - at(1, 1) * at(0, 2); |
| cof(2, 1) = -(at(0, 0) * at(1, 2) - at(1, 0) * at(0, 2)); |
| cof(2, 2) = at(0, 0) * at(1, 1) - at(1, 0) * at(0, 1); |
| break; |
| |
| case 4: |
| cof(0, 0) = at(1, 1) * at(2, 2) * at(3, 3) + at(2, 1) * at(3, 2) * at(1, 3) + |
| at(3, 1) * at(1, 2) * at(2, 3) - at(1, 1) * at(3, 2) * at(2, 3) - |
| at(2, 1) * at(1, 2) * at(3, 3) - at(3, 1) * at(2, 2) * at(1, 3); |
| cof(0, 1) = -(at(1, 0) * at(2, 2) * at(3, 3) + at(2, 0) * at(3, 2) * at(1, 3) + |
| at(3, 0) * at(1, 2) * at(2, 3) - at(1, 0) * at(3, 2) * at(2, 3) - |
| at(2, 0) * at(1, 2) * at(3, 3) - at(3, 0) * at(2, 2) * at(1, 3)); |
| cof(0, 2) = at(1, 0) * at(2, 1) * at(3, 3) + at(2, 0) * at(3, 1) * at(1, 3) + |
| at(3, 0) * at(1, 1) * at(2, 3) - at(1, 0) * at(3, 1) * at(2, 3) - |
| at(2, 0) * at(1, 1) * at(3, 3) - at(3, 0) * at(2, 1) * at(1, 3); |
| cof(0, 3) = -(at(1, 0) * at(2, 1) * at(3, 2) + at(2, 0) * at(3, 1) * at(1, 2) + |
| at(3, 0) * at(1, 1) * at(2, 2) - at(1, 0) * at(3, 1) * at(2, 2) - |
| at(2, 0) * at(1, 1) * at(3, 2) - at(3, 0) * at(2, 1) * at(1, 2)); |
| cof(1, 0) = -(at(0, 1) * at(2, 2) * at(3, 3) + at(2, 1) * at(3, 2) * at(0, 3) + |
| at(3, 1) * at(0, 2) * at(2, 3) - at(0, 1) * at(3, 2) * at(2, 3) - |
| at(2, 1) * at(0, 2) * at(3, 3) - at(3, 1) * at(2, 2) * at(0, 3)); |
| cof(1, 1) = at(0, 0) * at(2, 2) * at(3, 3) + at(2, 0) * at(3, 2) * at(0, 3) + |
| at(3, 0) * at(0, 2) * at(2, 3) - at(0, 0) * at(3, 2) * at(2, 3) - |
| at(2, 0) * at(0, 2) * at(3, 3) - at(3, 0) * at(2, 2) * at(0, 3); |
| cof(1, 2) = -(at(0, 0) * at(2, 1) * at(3, 3) + at(2, 0) * at(3, 1) * at(0, 3) + |
| at(3, 0) * at(0, 1) * at(2, 3) - at(0, 0) * at(3, 1) * at(2, 3) - |
| at(2, 0) * at(0, 1) * at(3, 3) - at(3, 0) * at(2, 1) * at(0, 3)); |
| cof(1, 3) = at(0, 0) * at(2, 1) * at(3, 2) + at(2, 0) * at(3, 1) * at(0, 2) + |
| at(3, 0) * at(0, 1) * at(2, 2) - at(0, 0) * at(3, 1) * at(2, 2) - |
| at(2, 0) * at(0, 1) * at(3, 2) - at(3, 0) * at(2, 1) * at(0, 2); |
| cof(2, 0) = at(0, 1) * at(1, 2) * at(3, 3) + at(1, 1) * at(3, 2) * at(0, 3) + |
| at(3, 1) * at(0, 2) * at(1, 3) - at(0, 1) * at(3, 2) * at(1, 3) - |
| at(1, 1) * at(0, 2) * at(3, 3) - at(3, 1) * at(1, 2) * at(0, 3); |
| cof(2, 1) = -(at(0, 0) * at(1, 2) * at(3, 3) + at(1, 0) * at(3, 2) * at(0, 3) + |
| at(3, 0) * at(0, 2) * at(1, 3) - at(0, 0) * at(3, 2) * at(1, 3) - |
| at(1, 0) * at(0, 2) * at(3, 3) - at(3, 0) * at(1, 2) * at(0, 3)); |
| cof(2, 2) = at(0, 0) * at(1, 1) * at(3, 3) + at(1, 0) * at(3, 1) * at(0, 3) + |
| at(3, 0) * at(0, 1) * at(1, 3) - at(0, 0) * at(3, 1) * at(1, 3) - |
| at(1, 0) * at(0, 1) * at(3, 3) - at(3, 0) * at(1, 1) * at(0, 3); |
| cof(2, 3) = -(at(0, 0) * at(1, 1) * at(3, 2) + at(1, 0) * at(3, 1) * at(0, 2) + |
| at(3, 0) * at(0, 1) * at(1, 2) - at(0, 0) * at(3, 1) * at(1, 2) - |
| at(1, 0) * at(0, 1) * at(3, 2) - at(3, 0) * at(1, 1) * at(0, 2)); |
| cof(3, 0) = -(at(0, 1) * at(1, 2) * at(2, 3) + at(1, 1) * at(2, 2) * at(0, 3) + |
| at(2, 1) * at(0, 2) * at(1, 3) - at(0, 1) * at(2, 2) * at(1, 3) - |
| at(1, 1) * at(0, 2) * at(2, 3) - at(2, 1) * at(1, 2) * at(0, 3)); |
| cof(3, 1) = at(0, 0) * at(1, 2) * at(2, 3) + at(1, 0) * at(2, 2) * at(0, 3) + |
| at(2, 0) * at(0, 2) * at(1, 3) - at(0, 0) * at(2, 2) * at(1, 3) - |
| at(1, 0) * at(0, 2) * at(2, 3) - at(2, 0) * at(1, 2) * at(0, 3); |
| cof(3, 2) = -(at(0, 0) * at(1, 1) * at(2, 3) + at(1, 0) * at(2, 1) * at(0, 3) + |
| at(2, 0) * at(0, 1) * at(1, 3) - at(0, 0) * at(2, 1) * at(1, 3) - |
| at(1, 0) * at(0, 1) * at(2, 3) - at(2, 0) * at(1, 1) * at(0, 3)); |
| cof(3, 3) = at(0, 0) * at(1, 1) * at(2, 2) + at(1, 0) * at(2, 1) * at(0, 2) + |
| at(2, 0) * at(0, 1) * at(1, 2) - at(0, 0) * at(2, 1) * at(1, 2) - |
| at(1, 0) * at(0, 1) * at(2, 2) - at(2, 0) * at(1, 1) * at(0, 2); |
| break; |
| |
| default: |
| UNREACHABLE(); |
| break; |
| } |
| |
| // The inverse of A is the transpose of the cofactor matrix times the reciprocal of the |
| // determinant of A. |
| Matrix<T> adjugateMatrix(cof.transpose()); |
| T det = determinant(); |
| Matrix<T> result(std::vector<T>(mElements.size()), rows(), columns()); |
| for (unsigned int i = 0; i < rows(); i++) |
| for (unsigned int j = 0; j < columns(); j++) |
| result(i, j) = (det != static_cast<T>(0)) ? adjugateMatrix(i, j) / det : T(); |
| |
| return result; |
| } |
| |
| void setToIdentity() |
| { |
| ASSERT(rows() == columns()); |
| |
| const auto one = T(1); |
| const auto zero = T(0); |
| |
| for (auto &e : mElements) |
| e = zero; |
| |
| for (unsigned int i = 0; i < rows(); ++i) |
| { |
| const auto pos = i * columns() + (i % columns()); |
| mElements[pos] = one; |
| } |
| } |
| |
| template <unsigned int Size> |
| static void setToIdentity(T (&matrix)[Size]) |
| { |
| static_assert(gl::iSquareRoot<Size>() != 0, "Matrix is not square."); |
| |
| const auto cols = gl::iSquareRoot<Size>(); |
| const auto one = T(1); |
| const auto zero = T(0); |
| |
| for (auto &e : matrix) |
| e = zero; |
| |
| for (unsigned int i = 0; i < cols; ++i) |
| { |
| const auto pos = i * cols + (i % cols); |
| matrix[pos] = one; |
| } |
| } |
| |
| protected: |
| std::vector<T> mElements; |
| unsigned int mRows; |
| unsigned int mCols; |
| }; |
| |
| class Mat4 : public Matrix<float> |
| { |
| public: |
| Mat4(); |
| Mat4(const Matrix<float> generalMatrix); |
| Mat4(const std::vector<float> &elements); |
| Mat4(const float *elements); |
| Mat4(float m00, |
| float m01, |
| float m02, |
| float m03, |
| float m10, |
| float m11, |
| float m12, |
| float m13, |
| float m20, |
| float m21, |
| float m22, |
| float m23, |
| float m30, |
| float m31, |
| float m32, |
| float m33); |
| |
| static Mat4 Rotate(float angle, const Vector3 &axis); |
| static Mat4 Translate(const Vector3 &t); |
| static Mat4 Scale(const Vector3 &s); |
| static Mat4 Frustum(float l, float r, float b, float t, float n, float f); |
| static Mat4 Perspective(float fov, float aspectRatio, float n, float f); |
| static Mat4 Ortho(float l, float r, float b, float t, float n, float f); |
| |
| Mat4 product(const Mat4 &m); |
| Vector4 product(const Vector4 &b); |
| void dump(); |
| }; |
| |
| } // namespace angle |
| |
| #endif // COMMON_MATRIX_UTILS_H_ |
