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+//
+// 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_
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-14 09:50:33 +0000