| // |
| // Copyright (c) 2010 Linaro Limited |
| // |
| // All rights reserved. This program and the accompanying materials |
| // are made available under the terms of the MIT License which accompanies |
| // this distribution, and is available at |
| // http://www.opensource.org/licenses/mit-license.php |
| // |
| // Contributors: |
| // Jesse Barker - original implementation. |
| // |
| #ifndef MAT_H_ |
| #define MAT_H_ |
| #include <stdexcept> |
| #include <iostream> |
| #include <iomanip> |
| #include "vec.h" |
| #ifndef USE_EXCEPTIONS |
| // If we're not throwing exceptions, we'll need the logger to make sure the |
| // caller is informed of errors. |
| #include "log.h" |
| #endif // USE_EXCEPTIONS |
| |
| namespace LibMatrix |
| { |
| // Proxy class for providing the functionality of a doubly-dimensioned array |
| // representation of matrices. Each matrix class defines its operator[] |
| // to return an ArrayProxy. The ArrayProxy then returns the appropriate item |
| // from its operator[]. |
| template<typename T, unsigned int dimension> |
| class ArrayProxy |
| { |
| public: |
| ArrayProxy(T* data) { data_ = data; } |
| ~ArrayProxy() { data_ = 0; } |
| T& operator[](int index) |
| { |
| return data_[index * dimension]; |
| } |
| const T& operator[](int index) const |
| { |
| return data_[index * dimension]; |
| } |
| private: |
| T* data_; |
| }; |
| |
| |
| // Programming interfaces to all matrix objects are represented row-centric |
| // (i.e. C/C++ style references to the data appear as matrix[row][column]). |
| // However, the internal data representation is column-major, so when using |
| // the raw data access member to treat the data as a singly-dimensioned array, |
| // it does not have to be transposed. |
| // |
| // A template class for creating, managing and operating on a 2x2 matrix |
| // of any type you like (intended for built-in types, but as long as it |
| // supports the basic arithmetic and assignment operators, any type should |
| // work). |
| template<typename T> |
| class tmat2 |
| { |
| public: |
| tmat2() |
| { |
| setIdentity(); |
| } |
| tmat2(const tmat2& m) |
| { |
| m_[0] = m.m_[0]; |
| m_[1] = m.m_[1]; |
| m_[2] = m.m_[2]; |
| m_[3] = m.m_[3]; |
| } |
| tmat2(const T& c0r0, const T& c0r1, const T& c1r0, const T& c1r1) |
| { |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c1r0; |
| m_[3] = c1r1; |
| } |
| ~tmat2() {} |
| |
| // Reset this to the identity matrix. |
| void setIdentity() |
| { |
| m_[0] = 1; |
| m_[1] = 0; |
| m_[2] = 0; |
| m_[3] = 1; |
| } |
| |
| // Transpose this. Return a reference to this. |
| tmat2& transpose() |
| { |
| T tmp_val = m_[1]; |
| m_[1] = m_[2]; |
| m_[2] = tmp_val; |
| return *this; |
| } |
| |
| // Compute the determinant of this and return it. |
| T determinant() |
| { |
| return (m_[0] * m_[3]) - (m_[2] * m_[1]); |
| } |
| |
| // Invert this. Return a reference to this. |
| // |
| // NOTE: If this is non-invertible, we will |
| // throw to avoid undefined behavior. |
| tmat2& inverse() |
| #ifdef USE_EXCEPTIONS |
| throw(std::runtime_error) |
| #endif // USE_EXCEPTIONS |
| { |
| T d(determinant()); |
| if (d == static_cast<T>(0)) |
| { |
| #ifdef USE_EXCEPTIONS |
| throw std::runtime_error("Matrix is noninvertible!!!!"); |
| #else // !USE_EXCEPTIONS |
| Log::error("Matrix is noninvertible!!!!\n"); |
| return *this; |
| #endif // USE_EXCEPTIONS |
| } |
| T c0r0(m_[3] / d); |
| T c0r1(-m_[1] / d); |
| T c1r0(-m_[2] / d); |
| T c1r1(m_[0] / d); |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c1r0; |
| m_[3] = c1r1; |
| return *this; |
| } |
| |
| // Print the elements of the matrix to standard out. |
| // Really only useful for debug and test. |
| void print() const |
| { |
| static const int precision(6); |
| // row 0 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[0]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[2]; |
| std::cout << " |" << std::endl; |
| // row 1 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[1]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[3]; |
| std::cout << " |" << std::endl; |
| } |
| |
| // Allow raw data access for API calls and the like. |
| // For example, it is valid to pass a tmat2<float> into a call to |
| // the OpenGL command "glUniformMatrix2fv()". |
| operator const T*() const { return &m_[0];} |
| |
| // Test if 'rhs' is equal to this. |
| bool operator==(const tmat2& rhs) const |
| { |
| return m_[0] == rhs.m_[0] && |
| m_[1] == rhs.m_[1] && |
| m_[2] == rhs.m_[2] && |
| m_[3] == rhs.m_[3]; |
| } |
| |
| // Test if 'rhs' is not equal to this. |
| bool operator!=(const tmat2& rhs) const |
| { |
| return !(*this == rhs); |
| } |
| |
| // A direct assignment of 'rhs' to this. Return a reference to this. |
| tmat2& operator=(const tmat2& rhs) |
| { |
| if (this != &rhs) |
| { |
| m_[0] = rhs.m_[0]; |
| m_[1] = rhs.m_[1]; |
| m_[2] = rhs.m_[2]; |
| m_[3] = rhs.m_[3]; |
| } |
| return *this; |
| } |
| |
| // Add another matrix to this. Return a reference to this. |
| tmat2& operator+=(const tmat2& rhs) |
| { |
| m_[0] += rhs.m_[0]; |
| m_[1] += rhs.m_[1]; |
| m_[2] += rhs.m_[2]; |
| m_[3] += rhs.m_[3]; |
| return *this; |
| } |
| |
| // Add another matrix to a copy of this. Return the copy. |
| const tmat2 operator+(const tmat2& rhs) |
| { |
| return tmat2(*this) += rhs; |
| } |
| |
| // Subtract another matrix from this. Return a reference to this. |
| tmat2& operator-=(const tmat2& rhs) |
| { |
| m_[0] -= rhs.m_[0]; |
| m_[1] -= rhs.m_[1]; |
| m_[2] -= rhs.m_[2]; |
| m_[3] -= rhs.m_[3]; |
| return *this; |
| } |
| |
| // Subtract another matrix from a copy of this. Return the copy. |
| const tmat2 operator-(const tmat2& rhs) |
| { |
| return tmat2(*this) += rhs; |
| } |
| |
| // Multiply this by another matrix. Return a reference to this. |
| tmat2& operator*=(const tmat2& rhs) |
| { |
| T c0r0((m_[0] * rhs.m_[0]) + (m_[2] * rhs.m_[1])); |
| T c0r1((m_[1] * rhs.m_[0]) + (m_[3] * rhs.m_[1])); |
| T c1r0((m_[0] * rhs.m_[2]) + (m_[2] * rhs.m_[3])); |
| T c1r1((m_[1] * rhs.m_[2]) + (m_[3] * rhs.m_[3])); |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c1r0; |
| m_[3] = c1r1; |
| return *this; |
| } |
| |
| // Multiply a copy of this by another matrix. Return the copy. |
| const tmat2 operator*(const tmat2& rhs) |
| { |
| return tmat2(*this) *= rhs; |
| } |
| |
| // Multiply this by a scalar. Return a reference to this. |
| tmat2& operator*=(const T& rhs) |
| { |
| m_[0] *= rhs; |
| m_[1] *= rhs; |
| m_[2] *= rhs; |
| m_[3] *= rhs; |
| return *this; |
| } |
| |
| // Multiply a copy of this by a scalar. Return the copy. |
| const tmat2 operator*(const T& rhs) |
| { |
| return tmat2(*this) *= rhs; |
| } |
| |
| // Divide this by a scalar. Return a reference to this. |
| tmat2& operator/=(const T& rhs) |
| { |
| m_[0] /= rhs; |
| m_[1] /= rhs; |
| m_[2] /= rhs; |
| m_[3] /= rhs; |
| return *this; |
| } |
| |
| // Divide a copy of this by a scalar. Return the copy. |
| const tmat2 operator/(const T& rhs) |
| { |
| return tmat2(*this) /= rhs; |
| } |
| |
| // Use an instance of the ArrayProxy class to support double-indexed |
| // references to a matrix (i.e., m[1][1]). See comments above the |
| // ArrayProxy definition for more details. |
| ArrayProxy<T, 2> operator[](int index) |
| { |
| return ArrayProxy<T, 2>(&m_[index]); |
| } |
| const ArrayProxy<T, 2> operator[](int index) const |
| { |
| return ArrayProxy<T, 2>(const_cast<T*>(&m_[index])); |
| } |
| |
| private: |
| T m_[4]; |
| }; |
| |
| // Multiply a scalar and a matrix just like the member operator, but allow |
| // the scalar to be the left-hand operand. |
| template<typename T> |
| const tmat2<T> operator*(const T& lhs, const tmat2<T>& rhs) |
| { |
| return tmat2<T>(rhs) * lhs; |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is right-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec2<T> operator*(const tvec2<T>& lhs, const tmat2<T>& rhs) |
| { |
| T x((lhs.x() * rhs[0][0]) + (lhs.y() * rhs[1][0])); |
| T y((lhs.x() * rhs[0][1]) + (lhs.y() * rhs[1][1])); |
| return tvec2<T>(x,y); |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is left-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec2<T> operator*(const tmat2<T>& lhs, const tvec2<T>& rhs) |
| { |
| T x((lhs[0][0] * rhs.x()) + (lhs[0][1] * rhs.y())); |
| T y((lhs[1][0] * rhs.x()) + (lhs[1][1] * rhs.y())); |
| return tvec2<T>(x, y); |
| } |
| |
| // Compute the outer product of two vectors. Return the resultant matrix. |
| template<typename T> |
| const tmat2<T> outer(const tvec2<T>& a, const tvec2<T>& b) |
| { |
| tmat2<T> product; |
| product[0][0] = a.x() * b.x(); |
| product[0][1] = a.x() * b.y(); |
| product[1][0] = a.y() * b.x(); |
| product[1][1] = a.y() * b.y(); |
| return product; |
| } |
| |
| // A template class for creating, managing and operating on a 3x3 matrix |
| // of any type you like (intended for built-in types, but as long as it |
| // supports the basic arithmetic and assignment operators, any type should |
| // work). |
| template<typename T> |
| class tmat3 |
| { |
| public: |
| tmat3() |
| { |
| setIdentity(); |
| } |
| tmat3(const tmat3& m) |
| { |
| m_[0] = m.m_[0]; |
| m_[1] = m.m_[1]; |
| m_[2] = m.m_[2]; |
| m_[3] = m.m_[3]; |
| m_[4] = m.m_[4]; |
| m_[5] = m.m_[5]; |
| m_[6] = m.m_[6]; |
| m_[7] = m.m_[7]; |
| m_[8] = m.m_[8]; |
| } |
| tmat3(const T& c0r0, const T& c0r1, const T& c0r2, |
| const T& c1r0, const T& c1r1, const T& c1r2, |
| const T& c2r0, const T& c2r1, const T& c2r2) |
| { |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c0r2; |
| m_[3] = c1r0; |
| m_[4] = c1r1; |
| m_[5] = c1r2; |
| m_[6] = c2r0; |
| m_[7] = c2r1; |
| m_[8] = c2r2; |
| } |
| ~tmat3() {} |
| |
| // Reset this to the identity matrix. |
| void setIdentity() |
| { |
| m_[0] = 1; |
| m_[1] = 0; |
| m_[2] = 0; |
| m_[3] = 0; |
| m_[4] = 1; |
| m_[5] = 0; |
| m_[6] = 0; |
| m_[7] = 0; |
| m_[8] = 1; |
| } |
| |
| // Transpose this. Return a reference to this. |
| tmat3& transpose() |
| { |
| T tmp_val = m_[1]; |
| m_[1] = m_[3]; |
| m_[3] = tmp_val; |
| tmp_val = m_[2]; |
| m_[2] = m_[6]; |
| m_[6] = tmp_val; |
| tmp_val = m_[5]; |
| m_[5] = m_[7]; |
| m_[7] = tmp_val; |
| return *this; |
| } |
| |
| // Compute the determinant of this and return it. |
| T determinant() |
| { |
| tmat2<T> minor0(m_[4], m_[5], m_[7], m_[8]); |
| tmat2<T> minor3(m_[1], m_[2], m_[7], m_[8]); |
| tmat2<T> minor6(m_[1], m_[2], m_[4], m_[5]); |
| return (m_[0] * minor0.determinant()) - |
| (m_[3] * minor3.determinant()) + |
| (m_[6] * minor6.determinant()); |
| } |
| |
| // Invert this. Return a reference to this. |
| // |
| // NOTE: If this is non-invertible, we will |
| // throw to avoid undefined behavior. |
| tmat3& inverse() |
| #ifdef USE_EXCEPTIONS |
| throw(std::runtime_error) |
| #endif // USE_EXCEPTIONS |
| { |
| T d(determinant()); |
| if (d == static_cast<T>(0)) |
| { |
| #ifdef USE_EXCEPTIONS |
| throw std::runtime_error("Matrix is noninvertible!!!!"); |
| #else // !USE_EXCEPTIONS |
| Log::error("Matrix is noninvertible!!!!\n"); |
| return *this; |
| #endif // USE_EXCEPTIONS |
| } |
| tmat2<T> minor0(m_[4], m_[5], m_[7], m_[8]); |
| tmat2<T> minor1(m_[7], m_[8], m_[1], m_[2]); |
| tmat2<T> minor2(m_[1], m_[2], m_[4], m_[5]); |
| tmat2<T> minor3(m_[6], m_[8], m_[3], m_[5]); |
| tmat2<T> minor4(m_[0], m_[2], m_[6], m_[8]); |
| tmat2<T> minor5(m_[3], m_[5], m_[0], m_[2]); |
| tmat2<T> minor6(m_[3], m_[4], m_[6], m_[7]); |
| tmat2<T> minor7(m_[6], m_[7], m_[0], m_[1]); |
| tmat2<T> minor8(m_[0], m_[1], m_[3], m_[4]); |
| m_[0] = minor0.determinant() / d; |
| m_[1] = minor1.determinant() / d; |
| m_[2] = minor2.determinant() / d; |
| m_[3] = minor3.determinant() / d; |
| m_[4] = minor4.determinant() / d; |
| m_[5] = minor5.determinant() / d; |
| m_[6] = minor6.determinant() / d; |
| m_[7] = minor7.determinant() / d; |
| m_[8] = minor8.determinant() / d; |
| return *this; |
| } |
| |
| // Print the elements of the matrix to standard out. |
| // Really only useful for debug and test. |
| void print() const |
| { |
| static const int precision(6); |
| // row 0 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[0]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[3]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[6]; |
| std::cout << " |" << std::endl; |
| // row 1 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[1]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[4]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[7]; |
| std::cout << " |" << std::endl; |
| // row 2 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[2]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[5]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[8]; |
| std::cout << " |" << std::endl; |
| } |
| |
| // Allow raw data access for API calls and the like. |
| // For example, it is valid to pass a tmat3<float> into a call to |
| // the OpenGL command "glUniformMatrix3fv()". |
| operator const T*() const { return &m_[0];} |
| |
| // Test if 'rhs' is equal to this. |
| bool operator==(const tmat3& rhs) const |
| { |
| return m_[0] == rhs.m_[0] && |
| m_[1] == rhs.m_[1] && |
| m_[2] == rhs.m_[2] && |
| m_[3] == rhs.m_[3] && |
| m_[4] == rhs.m_[4] && |
| m_[5] == rhs.m_[5] && |
| m_[6] == rhs.m_[6] && |
| m_[7] == rhs.m_[7] && |
| m_[8] == rhs.m_[8]; |
| } |
| |
| // Test if 'rhs' is not equal to this. |
| bool operator!=(const tmat3& rhs) const |
| { |
| return !(*this == rhs); |
| } |
| |
| // A direct assignment of 'rhs' to this. Return a reference to this. |
| tmat3& operator=(const tmat3& rhs) |
| { |
| if (this != &rhs) |
| { |
| m_[0] = rhs.m_[0]; |
| m_[1] = rhs.m_[1]; |
| m_[2] = rhs.m_[2]; |
| m_[3] = rhs.m_[3]; |
| m_[4] = rhs.m_[4]; |
| m_[5] = rhs.m_[5]; |
| m_[6] = rhs.m_[6]; |
| m_[7] = rhs.m_[7]; |
| m_[8] = rhs.m_[8]; |
| } |
| return *this; |
| } |
| |
| // Add another matrix to this. Return a reference to this. |
| tmat3& operator+=(const tmat3& rhs) |
| { |
| m_[0] += rhs.m_[0]; |
| m_[1] += rhs.m_[1]; |
| m_[2] += rhs.m_[2]; |
| m_[3] += rhs.m_[3]; |
| m_[4] += rhs.m_[4]; |
| m_[5] += rhs.m_[5]; |
| m_[6] += rhs.m_[6]; |
| m_[7] += rhs.m_[7]; |
| m_[8] += rhs.m_[8]; |
| return *this; |
| } |
| |
| // Add another matrix to a copy of this. Return the copy. |
| const tmat3 operator+(const tmat3& rhs) |
| { |
| return tmat3(*this) += rhs; |
| } |
| |
| // Subtract another matrix from this. Return a reference to this. |
| tmat3& operator-=(const tmat3& rhs) |
| { |
| m_[0] -= rhs.m_[0]; |
| m_[1] -= rhs.m_[1]; |
| m_[2] -= rhs.m_[2]; |
| m_[3] -= rhs.m_[3]; |
| m_[4] -= rhs.m_[4]; |
| m_[5] -= rhs.m_[5]; |
| m_[6] -= rhs.m_[6]; |
| m_[7] -= rhs.m_[7]; |
| m_[8] -= rhs.m_[8]; |
| return *this; |
| } |
| |
| // Subtract another matrix from a copy of this. Return the copy. |
| const tmat3 operator-(const tmat3& rhs) |
| { |
| return tmat3(*this) -= rhs; |
| } |
| |
| // Multiply this by another matrix. Return a reference to this. |
| tmat3& operator*=(const tmat3& rhs) |
| { |
| T c0r0((m_[0] * rhs.m_[0]) + (m_[3] * rhs.m_[1]) + (m_[6] * rhs.m_[2])); |
| T c0r1((m_[1] * rhs.m_[0]) + (m_[4] * rhs.m_[1]) + (m_[7] * rhs.m_[2])); |
| T c0r2((m_[2] * rhs.m_[0]) + (m_[5] * rhs.m_[1]) + (m_[8] * rhs.m_[2])); |
| T c1r0((m_[0] * rhs.m_[3]) + (m_[3] * rhs.m_[4]) + (m_[6] * rhs.m_[5])); |
| T c1r1((m_[1] * rhs.m_[3]) + (m_[4] * rhs.m_[4]) + (m_[7] * rhs.m_[5])); |
| T c1r2((m_[2] * rhs.m_[3]) + (m_[5] * rhs.m_[4]) + (m_[8] * rhs.m_[5])); |
| T c2r0((m_[0] * rhs.m_[6]) + (m_[3] * rhs.m_[7]) + (m_[6] * rhs.m_[8])); |
| T c2r1((m_[1] * rhs.m_[6]) + (m_[4] * rhs.m_[7]) + (m_[7] * rhs.m_[8])); |
| T c2r2((m_[2] * rhs.m_[6]) + (m_[5] * rhs.m_[7]) + (m_[8] * rhs.m_[8])); |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c0r2; |
| m_[3] = c1r0; |
| m_[4] = c1r1; |
| m_[5] = c1r2; |
| m_[6] = c2r0; |
| m_[7] = c2r1; |
| m_[8] = c2r2; |
| return *this; |
| } |
| |
| // Multiply a copy of this by another matrix. Return the copy. |
| const tmat3 operator*(const tmat3& rhs) |
| { |
| return tmat3(*this) *= rhs; |
| } |
| |
| // Multiply this by a scalar. Return a reference to this. |
| tmat3& operator*=(const T& rhs) |
| { |
| m_[0] *= rhs; |
| m_[1] *= rhs; |
| m_[2] *= rhs; |
| m_[3] *= rhs; |
| m_[4] *= rhs; |
| m_[5] *= rhs; |
| m_[6] *= rhs; |
| m_[7] *= rhs; |
| m_[8] *= rhs; |
| return *this; |
| } |
| |
| // Multiply a copy of this by a scalar. Return the copy. |
| const tmat3 operator*(const T& rhs) |
| { |
| return tmat3(*this) *= rhs; |
| } |
| |
| // Divide this by a scalar. Return a reference to this. |
| tmat3& operator/=(const T& rhs) |
| { |
| m_[0] /= rhs; |
| m_[1] /= rhs; |
| m_[2] /= rhs; |
| m_[3] /= rhs; |
| m_[4] /= rhs; |
| m_[5] /= rhs; |
| m_[6] /= rhs; |
| m_[7] /= rhs; |
| m_[8] /= rhs; |
| return *this; |
| } |
| |
| // Divide a copy of this by a scalar. Return the copy. |
| const tmat3 operator/(const T& rhs) |
| { |
| return tmat3(*this) /= rhs; |
| } |
| |
| // Use an instance of the ArrayProxy class to support double-indexed |
| // references to a matrix (i.e., m[1][1]). See comments above the |
| // ArrayProxy definition for more details. |
| ArrayProxy<T, 3> operator[](int index) |
| { |
| return ArrayProxy<T, 3>(&m_[index]); |
| } |
| const ArrayProxy<T, 3> operator[](int index) const |
| { |
| return ArrayProxy<T, 3>(const_cast<T*>(&m_[index])); |
| } |
| |
| private: |
| T m_[9]; |
| }; |
| |
| // Multiply a scalar and a matrix just like the member operator, but allow |
| // the scalar to be the left-hand operand. |
| template<typename T> |
| const tmat3<T> operator*(const T& lhs, const tmat3<T>& rhs) |
| { |
| return tmat3<T>(rhs) * lhs; |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is right-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec3<T> operator*(const tvec3<T>& lhs, const tmat3<T>& rhs) |
| { |
| T x((lhs.x() * rhs[0][0]) + (lhs.y() * rhs[1][0]) + (lhs.z() * rhs[2][0])); |
| T y((lhs.x() * rhs[0][1]) + (lhs.y() * rhs[1][1]) + (lhs.z() * rhs[2][1])); |
| T z((lhs.x() * rhs[0][2]) + (lhs.y() * rhs[1][2]) + (lhs.z() * rhs[2][2])); |
| return tvec3<T>(x, y, z); |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is left-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec3<T> operator*(const tmat3<T>& lhs, const tvec3<T>& rhs) |
| { |
| T x((lhs[0][0] * rhs.x()) + (lhs[0][1] * rhs.y()) + (lhs[0][2] * rhs.z())); |
| T y((lhs[1][0] * rhs.x()) + (lhs[1][1] * rhs.y()) + (lhs[1][2] * rhs.z())); |
| T z((lhs[2][0] * rhs.x()) + (lhs[2][1] * rhs.y()) + (lhs[2][2] * rhs.z())); |
| return tvec3<T>(x, y, z); |
| } |
| |
| // Compute the outer product of two vectors. Return the resultant matrix. |
| template<typename T> |
| const tmat3<T> outer(const tvec3<T>& a, const tvec3<T>& b) |
| { |
| tmat3<T> product; |
| product[0][0] = a.x() * b.x(); |
| product[0][1] = a.x() * b.y(); |
| product[0][2] = a.x() * b.z(); |
| product[1][0] = a.y() * b.x(); |
| product[1][1] = a.y() * b.y(); |
| product[1][2] = a.y() * b.z(); |
| product[2][0] = a.z() * b.x(); |
| product[2][1] = a.z() * b.y(); |
| product[2][2] = a.z() * b.z(); |
| return product; |
| } |
| |
| // A template class for creating, managing and operating on a 4x4 matrix |
| // of any type you like (intended for built-in types, but as long as it |
| // supports the basic arithmetic and assignment operators, any type should |
| // work). |
| template<typename T> |
| class tmat4 |
| { |
| public: |
| tmat4() |
| { |
| setIdentity(); |
| } |
| tmat4(const tmat4& m) |
| { |
| m_[0] = m.m_[0]; |
| m_[1] = m.m_[1]; |
| m_[2] = m.m_[2]; |
| m_[3] = m.m_[3]; |
| m_[4] = m.m_[4]; |
| m_[5] = m.m_[5]; |
| m_[6] = m.m_[6]; |
| m_[7] = m.m_[7]; |
| m_[8] = m.m_[8]; |
| m_[9] = m.m_[9]; |
| m_[10] = m.m_[10]; |
| m_[11] = m.m_[11]; |
| m_[12] = m.m_[12]; |
| m_[13] = m.m_[13]; |
| m_[14] = m.m_[14]; |
| m_[15] = m.m_[15]; |
| } |
| ~tmat4() {} |
| |
| // Reset this to the identity matrix. |
| void setIdentity() |
| { |
| m_[0] = 1; |
| m_[1] = 0; |
| m_[2] = 0; |
| m_[3] = 0; |
| m_[4] = 0; |
| m_[5] = 1; |
| m_[6] = 0; |
| m_[7] = 0; |
| m_[8] = 0; |
| m_[9] = 0; |
| m_[10] = 1; |
| m_[11] = 0; |
| m_[12] = 0; |
| m_[13] = 0; |
| m_[14] = 0; |
| m_[15] = 1; |
| } |
| |
| // Transpose this. Return a reference to this. |
| tmat4& transpose() |
| { |
| T tmp_val = m_[1]; |
| m_[1] = m_[4]; |
| m_[4] = tmp_val; |
| tmp_val = m_[2]; |
| m_[2] = m_[8]; |
| m_[8] = tmp_val; |
| tmp_val = m_[3]; |
| m_[3] = m_[12]; |
| m_[12] = tmp_val; |
| tmp_val = m_[6]; |
| m_[6] = m_[9]; |
| m_[9] = tmp_val; |
| tmp_val = m_[7]; |
| m_[7] = m_[13]; |
| m_[13] = tmp_val; |
| tmp_val = m_[11]; |
| m_[11] = m_[14]; |
| m_[14] = tmp_val; |
| return *this; |
| } |
| |
| // Compute the determinant of this and return it. |
| T determinant() |
| { |
| tmat3<T> minor0(m_[5], m_[6], m_[7], m_[9], m_[10], m_[11], m_[13], m_[14], m_[15]); |
| tmat3<T> minor4(m_[1], m_[2], m_[3], m_[9], m_[10], m_[11], m_[13], m_[14], m_[15]); |
| tmat3<T> minor8(m_[1], m_[2], m_[3], m_[5], m_[6], m_[7], m_[13], m_[14], m_[15]); |
| tmat3<T> minor12(m_[1], m_[2], m_[3], m_[5], m_[6], m_[7], m_[9], m_[10], m_[11]); |
| return (m_[0] * minor0.determinant()) - |
| (m_[4] * minor4.determinant()) + |
| (m_[8] * minor8.determinant()) - |
| (m_[12] * minor12.determinant()); |
| } |
| |
| // Invert this. Return a reference to this. |
| // |
| // NOTE: If this is non-invertible, we will |
| // throw to avoid undefined behavior. |
| tmat4& inverse() |
| #ifdef USE_EXCEPTIONS |
| throw(std::runtime_error) |
| #endif // USE_EXCEPTIONS |
| { |
| T d(determinant()); |
| if (d == static_cast<T>(0)) |
| { |
| #ifdef USE_EXCEPTIONS |
| throw std::runtime_error("Matrix is noninvertible!!!!"); |
| #else // !USE_EXCEPTIONS |
| Log::error("Matrix is noninvertible!!!!\n"); |
| return *this; |
| #endif // USE_EXCEPTIONS |
| } |
| tmat3<T> minor0(m_[5], m_[6], m_[7], m_[9], m_[10], m_[11], m_[13], m_[14], m_[15]); |
| tmat3<T> minor1(m_[1], m_[2], m_[3], m_[13], m_[14], m_[15], m_[9], m_[10], m_[11]); |
| tmat3<T> minor2(m_[1], m_[2], m_[3], m_[5], m_[6], m_[7], m_[13], m_[14], m_[15]); |
| tmat3<T> minor3(m_[1], m_[2], m_[3], m_[9], m_[10], m_[11], m_[5], m_[6], m_[7]); |
| |
| tmat3<T> minor4(m_[4], m_[6], m_[7], m_[12], m_[14], m_[15], m_[8], m_[10], m_[11]); |
| tmat3<T> minor5(m_[0], m_[2], m_[3], m_[8], m_[10], m_[11], m_[12], m_[14], m_[15]); |
| tmat3<T> minor6(m_[0], m_[2], m_[3], m_[12], m_[14], m_[15], m_[4], m_[6], m_[7]); |
| tmat3<T> minor7(m_[0], m_[2], m_[3], m_[4], m_[6], m_[7], m_[8], m_[10], m_[11]); |
| |
| tmat3<T> minor8(m_[4], m_[5], m_[7], m_[8], m_[9], m_[11], m_[12], m_[13], m_[15]); |
| tmat3<T> minor9(m_[0], m_[1], m_[3], m_[12], m_[13], m_[15], m_[8], m_[9], m_[11]); |
| tmat3<T> minor10(m_[0], m_[1], m_[3], m_[4], m_[5], m_[7], m_[12], m_[13], m_[15]); |
| tmat3<T> minor11(m_[0], m_[1], m_[3], m_[8], m_[9], m_[11], m_[4], m_[5], m_[7]); |
| |
| tmat3<T> minor12(m_[4], m_[5], m_[6], m_[12], m_[13], m_[14], m_[8], m_[9], m_[10]); |
| tmat3<T> minor13(m_[0], m_[1], m_[2], m_[8], m_[9], m_[10], m_[12], m_[13], m_[14]); |
| tmat3<T> minor14(m_[0], m_[1], m_[2], m_[12], m_[13], m_[14], m_[4], m_[5], m_[6]); |
| tmat3<T> minor15(m_[0], m_[1], m_[2], m_[4], m_[5], m_[6], m_[8], m_[9], m_[10]); |
| m_[0] = minor0.determinant() / d; |
| m_[1] = minor1.determinant() / d; |
| m_[2] = minor2.determinant() / d; |
| m_[3] = minor3.determinant() / d; |
| m_[4] = minor4.determinant() / d; |
| m_[5] = minor5.determinant() / d; |
| m_[6] = minor6.determinant() / d; |
| m_[7] = minor7.determinant() / d; |
| m_[8] = minor8.determinant() / d; |
| m_[9] = minor9.determinant() / d; |
| m_[10] = minor10.determinant() / d; |
| m_[11] = minor11.determinant() / d; |
| m_[12] = minor12.determinant() / d; |
| m_[13] = minor13.determinant() / d; |
| m_[14] = minor14.determinant() / d; |
| m_[15] = minor15.determinant() / d; |
| return *this; |
| } |
| |
| // Print the elements of the matrix to standard out. |
| // Really only useful for debug and test. |
| void print() const |
| { |
| static const int precision(6); |
| // row 0 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[0]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[4]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[8]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[12]; |
| std::cout << " |" << std::endl; |
| // row 1 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[1]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[5]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[9]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[13]; |
| std::cout << " |" << std::endl; |
| // row 2 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[2]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[6]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[10]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[14]; |
| std::cout << " |" << std::endl; |
| // row 3 |
| std::cout << "| "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[3]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[7]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[11]; |
| std::cout << " "; |
| std::cout << std::fixed << std::showpoint << std::setprecision(precision) << m_[15]; |
| std::cout << " |" << std::endl; |
| } |
| |
| // Allow raw data access for API calls and the like. |
| // For example, it is valid to pass a tmat4<float> into a call to |
| // the OpenGL command "glUniformMatrix4fv()". |
| operator const T*() const { return &m_[0];} |
| |
| // Test if 'rhs' is equal to this. |
| bool operator==(const tmat4& rhs) const |
| { |
| return m_[0] == rhs.m_[0] && |
| m_[1] == rhs.m_[1] && |
| m_[2] == rhs.m_[2] && |
| m_[3] == rhs.m_[3] && |
| m_[4] == rhs.m_[4] && |
| m_[5] == rhs.m_[5] && |
| m_[6] == rhs.m_[6] && |
| m_[7] == rhs.m_[7] && |
| m_[8] == rhs.m_[8] && |
| m_[9] == rhs.m_[9] && |
| m_[10] == rhs.m_[10] && |
| m_[11] == rhs.m_[11] && |
| m_[12] == rhs.m_[12] && |
| m_[13] == rhs.m_[13] && |
| m_[14] == rhs.m_[14] && |
| m_[15] == rhs.m_[15]; |
| } |
| |
| // Test if 'rhs' is not equal to this. |
| bool operator!=(const tmat4& rhs) const |
| { |
| return !(*this == rhs); |
| } |
| |
| // A direct assignment of 'rhs' to this. Return a reference to this. |
| tmat4& operator=(const tmat4& rhs) |
| { |
| if (this != &rhs) |
| { |
| m_[0] = rhs.m_[0]; |
| m_[1] = rhs.m_[1]; |
| m_[2] = rhs.m_[2]; |
| m_[3] = rhs.m_[3]; |
| m_[4] = rhs.m_[4]; |
| m_[5] = rhs.m_[5]; |
| m_[6] = rhs.m_[6]; |
| m_[7] = rhs.m_[7]; |
| m_[8] = rhs.m_[8]; |
| m_[9] = rhs.m_[9]; |
| m_[10] = rhs.m_[10]; |
| m_[11] = rhs.m_[11]; |
| m_[12] = rhs.m_[12]; |
| m_[13] = rhs.m_[13]; |
| m_[14] = rhs.m_[14]; |
| m_[15] = rhs.m_[15]; |
| } |
| return *this; |
| } |
| |
| // Add another matrix to this. Return a reference to this. |
| tmat4& operator+=(const tmat4& rhs) |
| { |
| m_[0] += rhs.m_[0]; |
| m_[1] += rhs.m_[1]; |
| m_[2] += rhs.m_[2]; |
| m_[3] += rhs.m_[3]; |
| m_[4] += rhs.m_[4]; |
| m_[5] += rhs.m_[5]; |
| m_[6] += rhs.m_[6]; |
| m_[7] += rhs.m_[7]; |
| m_[8] += rhs.m_[8]; |
| m_[9] += rhs.m_[9]; |
| m_[10] += rhs.m_[10]; |
| m_[11] += rhs.m_[11]; |
| m_[12] += rhs.m_[12]; |
| m_[13] += rhs.m_[13]; |
| m_[14] += rhs.m_[14]; |
| m_[15] += rhs.m_[15]; |
| return *this; |
| } |
| |
| // Add another matrix to a copy of this. Return the copy. |
| const tmat4 operator+(const tmat4& rhs) |
| { |
| return tmat4(*this) += rhs; |
| } |
| |
| // Subtract another matrix from this. Return a reference to this. |
| tmat4& operator-=(const tmat4& rhs) |
| { |
| m_[0] -= rhs.m_[0]; |
| m_[1] -= rhs.m_[1]; |
| m_[2] -= rhs.m_[2]; |
| m_[3] -= rhs.m_[3]; |
| m_[4] -= rhs.m_[4]; |
| m_[5] -= rhs.m_[5]; |
| m_[6] -= rhs.m_[6]; |
| m_[7] -= rhs.m_[7]; |
| m_[8] -= rhs.m_[8]; |
| m_[9] -= rhs.m_[9]; |
| m_[10] -= rhs.m_[10]; |
| m_[11] -= rhs.m_[11]; |
| m_[12] -= rhs.m_[12]; |
| m_[13] -= rhs.m_[13]; |
| m_[14] -= rhs.m_[14]; |
| m_[15] -= rhs.m_[15]; |
| return *this; |
| } |
| |
| // Subtract another matrix from a copy of this. Return the copy. |
| const tmat4 operator-(const tmat4& rhs) |
| { |
| return tmat4(*this) -= rhs; |
| } |
| |
| // Multiply this by another matrix. Return a reference to this. |
| tmat4& operator*=(const tmat4& rhs) |
| { |
| T c0r0((m_[0] * rhs.m_[0]) + (m_[4] * rhs.m_[1]) + (m_[8] * rhs.m_[2]) + (m_[12] * rhs.m_[3])); |
| T c0r1((m_[1] * rhs.m_[0]) + (m_[5] * rhs.m_[1]) + (m_[9] * rhs.m_[2]) + (m_[13] * rhs.m_[3])); |
| T c0r2((m_[2] * rhs.m_[0]) + (m_[6] * rhs.m_[1]) + (m_[10] * rhs.m_[2]) + (m_[14] * rhs.m_[3])); |
| T c0r3((m_[3] * rhs.m_[0]) + (m_[7] * rhs.m_[1]) + (m_[11] * rhs.m_[2]) + (m_[15] * rhs.m_[3])); |
| T c1r0((m_[0] * rhs.m_[4]) + (m_[4] * rhs.m_[5]) + (m_[8] * rhs.m_[6]) + (m_[12] * rhs.m_[7])); |
| T c1r1((m_[1] * rhs.m_[4]) + (m_[5] * rhs.m_[5]) + (m_[9] * rhs.m_[6]) + (m_[13] * rhs.m_[7])); |
| T c1r2((m_[2] * rhs.m_[4]) + (m_[6] * rhs.m_[5]) + (m_[10] * rhs.m_[6]) + (m_[14] * rhs.m_[7])); |
| T c1r3((m_[3] * rhs.m_[4]) + (m_[7] * rhs.m_[5]) + (m_[11] * rhs.m_[6]) + (m_[15] * rhs.m_[7])); |
| T c2r0((m_[0] * rhs.m_[8]) + (m_[4] * rhs.m_[9]) + (m_[8] * rhs.m_[10]) + (m_[12] * rhs.m_[11])); |
| T c2r1((m_[1] * rhs.m_[8]) + (m_[5] * rhs.m_[9]) + (m_[9] * rhs.m_[10]) + (m_[13] * rhs.m_[11])); |
| T c2r2((m_[2] * rhs.m_[8]) + (m_[6] * rhs.m_[9]) + (m_[10] * rhs.m_[10]) + (m_[14] * rhs.m_[11])); |
| T c2r3((m_[3] * rhs.m_[8]) + (m_[7] * rhs.m_[9]) + (m_[11] * rhs.m_[10]) + (m_[15] * rhs.m_[11])); |
| T c3r0((m_[0] * rhs.m_[12]) + (m_[4] * rhs.m_[13]) + (m_[8] * rhs.m_[14]) + (m_[12] * rhs.m_[15])); |
| T c3r1((m_[1] * rhs.m_[12]) + (m_[5] * rhs.m_[13]) + (m_[9] * rhs.m_[14]) + (m_[13] * rhs.m_[15])); |
| T c3r2((m_[2] * rhs.m_[12]) + (m_[6] * rhs.m_[13]) + (m_[10] * rhs.m_[14]) + (m_[14] * rhs.m_[15])); |
| T c3r3((m_[3] * rhs.m_[12]) + (m_[7] * rhs.m_[13]) + (m_[11] * rhs.m_[14]) + (m_[15] * rhs.m_[15])); |
| m_[0] = c0r0; |
| m_[1] = c0r1; |
| m_[2] = c0r2; |
| m_[3] = c0r3; |
| m_[4] = c1r0; |
| m_[5] = c1r1; |
| m_[6] = c1r2; |
| m_[7] = c1r3; |
| m_[8] = c2r0; |
| m_[9] = c2r1; |
| m_[10] = c2r2; |
| m_[11] = c2r3; |
| m_[12] = c3r0; |
| m_[13] = c3r1; |
| m_[14] = c3r2; |
| m_[15] = c3r3; |
| return *this; |
| } |
| |
| // Multiply a copy of this by another matrix. Return the copy. |
| const tmat4 operator*(const tmat4& rhs) |
| { |
| return tmat4(*this) *= rhs; |
| } |
| |
| // Multiply this by a scalar. Return a reference to this. |
| tmat4& operator*=(const T& rhs) |
| { |
| m_[0] *= rhs; |
| m_[1] *= rhs; |
| m_[2] *= rhs; |
| m_[3] *= rhs; |
| m_[4] *= rhs; |
| m_[5] *= rhs; |
| m_[6] *= rhs; |
| m_[7] *= rhs; |
| m_[8] *= rhs; |
| m_[9] *= rhs; |
| m_[10] *= rhs; |
| m_[11] *= rhs; |
| m_[12] *= rhs; |
| m_[13] *= rhs; |
| m_[14] *= rhs; |
| m_[15] *= rhs; |
| return *this; |
| } |
| |
| // Multiply a copy of this by a scalar. Return the copy. |
| const tmat4 operator*(const T& rhs) |
| { |
| return tmat4(*this) *= rhs; |
| } |
| |
| // Divide this by a scalar. Return a reference to this. |
| tmat4& operator/=(const T& rhs) |
| { |
| m_[0] /= rhs; |
| m_[1] /= rhs; |
| m_[2] /= rhs; |
| m_[3] /= rhs; |
| m_[4] /= rhs; |
| m_[5] /= rhs; |
| m_[6] /= rhs; |
| m_[7] /= rhs; |
| m_[8] /= rhs; |
| m_[9] /= rhs; |
| m_[10] /= rhs; |
| m_[11] /= rhs; |
| m_[12] /= rhs; |
| m_[13] /= rhs; |
| m_[14] /= rhs; |
| m_[15] /= rhs; |
| return *this; |
| } |
| |
| // Divide a copy of this by a scalar. Return the copy. |
| const tmat4 operator/(const T& rhs) |
| { |
| return tmat4(*this) /= rhs; |
| } |
| |
| // Use an instance of the ArrayProxy class to support double-indexed |
| // references to a matrix (i.e., m[1][1]). See comments above the |
| // ArrayProxy definition for more details. |
| ArrayProxy<T, 4> operator[](int index) |
| { |
| return ArrayProxy<T, 4>(&m_[index]); |
| } |
| const ArrayProxy<T, 4> operator[](int index) const |
| { |
| return ArrayProxy<T, 4>(const_cast<T*>(&m_[index])); |
| } |
| |
| private: |
| T m_[16]; |
| }; |
| |
| // Multiply a scalar and a matrix just like the member operator, but allow |
| // the scalar to be the left-hand operand. |
| template<typename T> |
| const tmat4<T> operator*(const T& lhs, const tmat4<T>& rhs) |
| { |
| return tmat4<T>(rhs) * lhs; |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is right-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec4<T> operator*(const tvec4<T>& lhs, const tmat4<T>& rhs) |
| { |
| T x((lhs.x() * rhs[0][0]) + (lhs.y() * rhs[1][0]) + (lhs.z() * rhs[2][0]) + (lhs.w() * rhs[3][0])); |
| T y((lhs.x() * rhs[0][1]) + (lhs.y() * rhs[1][1]) + (lhs.z() * rhs[2][1]) + (lhs.w() * rhs[3][1])); |
| T z((lhs.x() * rhs[0][2]) + (lhs.y() * rhs[1][2]) + (lhs.z() * rhs[2][2]) + (lhs.w() * rhs[3][2])); |
| T w((lhs.x() * rhs[0][3]) + (lhs.y() * rhs[1][3]) + (lhs.z() * rhs[2][3]) + (lhs.w() * rhs[3][3])); |
| return tvec4<T>(x, y, z, w); |
| } |
| |
| // Multiply a copy of a vector and a matrix (matrix is left-hand operand). |
| // Return the copy. |
| template<typename T> |
| const tvec4<T> operator*(const tmat4<T>& lhs, const tvec4<T>& rhs) |
| { |
| T x((lhs[0][0] * rhs.x()) + (lhs[0][1] * rhs.y()) + (lhs[0][2] * rhs.z()) + (lhs[0][3] * rhs.w())); |
| T y((lhs[1][0] * rhs.x()) + (lhs[1][1] * rhs.y()) + (lhs[1][2] * rhs.z()) + (lhs[1][3] * rhs.w())); |
| T z((lhs[2][0] * rhs.x()) + (lhs[2][1] * rhs.y()) + (lhs[2][2] * rhs.z()) + (lhs[2][3] * rhs.w())); |
| T w((lhs[3][0] * rhs.x()) + (lhs[3][1] * rhs.y()) + (lhs[3][2] * rhs.z()) + (lhs[3][3] * rhs.w())); |
| return tvec4<T>(x, y, z, w); |
| } |
| |
| // Compute the outer product of two vectors. Return the resultant matrix. |
| template<typename T> |
| const tmat4<T> outer(const tvec4<T>& a, const tvec4<T>& b) |
| { |
| tmat4<T> product; |
| product[0][0] = a.x() * b.x(); |
| product[0][1] = a.x() * b.y(); |
| product[0][2] = a.x() * b.z(); |
| product[0][3] = a.x() * b.w(); |
| product[1][0] = a.y() * b.x(); |
| product[1][1] = a.y() * b.y(); |
| product[1][2] = a.y() * b.z(); |
| product[1][3] = a.y() * b.w(); |
| product[2][0] = a.z() * b.x(); |
| product[2][1] = a.z() * b.y(); |
| product[2][2] = a.z() * b.z(); |
| product[2][3] = a.z() * b.w(); |
| product[3][0] = a.w() * b.x(); |
| product[3][1] = a.w() * b.y(); |
| product[3][2] = a.w() * b.z(); |
| product[3][3] = a.w() * b.w(); |
| return product; |
| } |
| |
| // |
| // Convenience typedefs. These are here to present a homogeneous view of these |
| // objects with respect to shader source. |
| // |
| typedef tmat2<float> mat2; |
| typedef tmat3<float> mat3; |
| typedef tmat4<float> mat4; |
| |
| typedef tmat2<double> dmat2; |
| typedef tmat3<double> dmat3; |
| typedef tmat4<double> dmat4; |
| |
| typedef tmat2<int> imat2; |
| typedef tmat3<int> imat3; |
| typedef tmat4<int> imat4; |
| |
| typedef tmat2<unsigned int> umat2; |
| typedef tmat3<unsigned int> umat3; |
| typedef tmat4<unsigned int> umat4; |
| |
| typedef tmat2<bool> bmat2; |
| typedef tmat3<bool> bmat3; |
| typedef tmat4<bool> bmat4; |
| |
| namespace Mat4 |
| { |
| |
| // |
| // Some functions to generate transformation matrices that used to be provided |
| // by OpenGL. |
| // |
| mat4 translate(float x, float y, float z); |
| mat4 scale(float x, float y, float z); |
| mat4 rotate(float angle, float x, float y, float z); |
| mat4 frustum(float left, float right, float bottom, float top, float near, float far); |
| mat4 ortho(float left, float right, float bottom, float top, float near, float far); |
| mat4 perspective(float fovy, float aspect, float zNear, float zFar); |
| mat4 lookAt(float eyeX, float eyeY, float eyeZ, float centerX, float centerY, float centerZ, float upX, float upY, float upZ); |
| |
| } // namespace Mat4 |
| } // namespace LibMatrix |
| #endif // MAT_H_ |
