bluecore/engine/Math/Matrix.h

#ifndef BLUECORE_MATRIX_H
#define BLUECORE_MATRIX_H

// system includes
#include <algorithm>
#include <cmath>

// local includes
#include "Scalar.h"
#include "Vector.h"
#include "Quaternion.h"

namespace BlueCore
{
	template <class T>
	class Matrix3x3Template
	{
	public:
		T m[9];

		/**
		 * default constructor
		 */
		inline Matrix3x3Template()
		{
			identity();
		}


		/**
		 * constructor from array
		 */
		template <class S>
		inline Matrix3x3Template( const S a[9] )
		{
			m[0] = static_cast<T>(a[0]);
			m[1] = static_cast<T>(a[1]);
			m[2] = static_cast<T>(a[2]);

			m[3] = static_cast<T>(a[3]);
			m[4] = static_cast<T>(a[4]);
			m[5] = static_cast<T>(a[5]);

			m[6] = static_cast<T>(a[6]);
			m[7] = static_cast<T>(a[7]);
			m[8] = static_cast<T>(a[8]);
		}
		

		/**
		 * copy constructor
		 */
		template <class S>
		inline Matrix3x3Template( const Matrix3x3Template<S> &a )
		{
			m[0] = static_cast<T>(a.m[0]);
			m[1] = static_cast<T>(a.m[1]);
			m[2] = static_cast<T>(a.m[2]);

			m[3] = static_cast<T>(a.m[3]);
			m[4] = static_cast<T>(a.m[4]);
			m[5] = static_cast<T>(a.m[5]);

			m[6] = static_cast<T>(a.m[6]);
			m[7] = static_cast<T>(a.m[7]);
			m[8] = static_cast<T>(a.m[8]);
		}


		/**
		 * constructor from heading and up vectors
		 */
		inline Matrix3x3Template(
			const Vector3Template<T> &h,
			const Vector3Template<T> &u )
		{
			Vector3Template<T> a, b, c;
			c = h.unit();
			a = h.crossProduct( u ).unit();
			b = c.crossProduct( a ).unit();
			
			m[0]  = a.x;
			m[1]  = b.x;
			m[2]  = c.x;
			
			m[3]  = a.y;
			m[4]  = b.y;
			m[5]  = c.y;
			
			m[6]  = a.z;
			m[7]  = b.z;
			m[8]  = c.z;
		}
		

		/**
		 * contructor from euler angles
		 */
		inline Matrix3x3Template( T a, T e, T t )
		{
			T ch = cos( a );
			T sh = sin( a );
			T ca = cos( e );
			T sa = sin( e );
			T cb = cos( t );
			T sb = sin( t );
			
			m[0]  = ch * ca;
			m[1]  = sh*sb - ch*sa*cb;
			m[2]  = ch*sa*sb + sh*cb;

			m[3]  = sa;
			m[4]  = ca*cb;
			m[5]  = -ca*sb;

			m[6]  = -sh*ca;
			m[7]  = sh*sa*cb + ch*sb;
			m[8] = -sh*sa*sb + ch*cb;
		}
		
				
		/**
		 * contructor from quaternion
		 */
		template <class S>
		inline Matrix3x3Template( const QuaternionTemplate<S> &q )
		{
			T	xx = static_cast<T>(q.x*q.x),
				xy = static_cast<T>(q.x*q.y),
				xz = static_cast<T>(q.x*q.z),
				xw = static_cast<T>(q.x*q.w),
				
				yy = static_cast<T>(q.y*q.y),
				yz = static_cast<T>(q.y*q.z),
				yw = static_cast<T>(q.y*q.w),
				
				zz = static_cast<T>(q.z*q.z),
				zw = static_cast<T>(q.z*q.w);

			m[0] = 1 - yy - yy - zz - zz;
			m[1] = xy + xy + zw + zw;
			m[2] = xz + xz - yw - yw;

			m[3] = xy + xy - zw - zw;
			m[4] = 1 - xx - xx - zz - zz;
			m[5] = yz + yz + xw + xw;
			
			m[6] = xz + xz + yw + yw;
			m[7] = yz + yz - xw - xw;
			m[8] = 1 - xx - xx - yy - yy;
		}
		

		/**
		 * set matrix to identity matrix
		 */
		inline void identity()
		{
			m[0] = static_cast<T>(1);
			m[1] = static_cast<T>(0);
			m[2] = static_cast<T>(0);
			
			m[3] = static_cast<T>(0);
			m[4] = static_cast<T>(1);
			m[5] = static_cast<T>(0);
			
			m[6] = static_cast<T>(0);
			m[7] = static_cast<T>(0);
			m[8] = static_cast<T>(1);
		}


		/**
		 * get transposed matrix
		 */
		inline Matrix3x3Template<T> transposed() const
		{
			Matrix3x3Template<T> a;
			
			a.m[0] = m[0]; a.m[3] = m[1]; a.m[6] = m[2];
			a.m[1] = m[3]; a.m[4] = m[4]; a.m[7] = m[5];
			a.m[2] = m[6]; a.m[5] = m[7]; a.m[8] = m[8];
			
			return a;
		}


		/**
		 * transpose
		 */
		inline void transpose()
		{
			swap( m[3], m[1] );
			swap( m[6], m[2] );
			swap( m[7], m[5] );
		}
		

		/**
		 * determinate
		 */
		inline T determinant() const
		{
			return ( m[0]*m[4]*m[8] + m[1]*m[5]*m[6] + m[2]*m[3]*m[7] )
				- ( m[6]*m[4]*m[2] + m[7]*m[5]*m[0] + m[8]*m[3]*m[1] );
		}

		inline Matrix3x3Template<T> inverted()
		{
			T det = determinant();
			T one_over_det = 1.0f / det;

			Matrix3x3Template<T> result;
			result.m[0] = +(m[4] * m[8] - m[5] * m[7]) * one_over_det;
			result.m[1] = -(m[1] * m[8] - m[2] * m[7]) * one_over_det;
			result.m[2] = +(m[1] * m[5] - m[2] * m[4]) * one_over_det;
			result.m[3] = -(m[3] * m[8] - m[5] * m[6]) * one_over_det;
			result.m[4] = +(m[0] * m[8] - m[2] * m[6]) * one_over_det;
			result.m[5] = -(m[0] * m[5] - m[2] * m[3]) * one_over_det;
			result.m[6] = +(m[3] * m[7] - m[4] * m[6]) * one_over_det;
			result.m[7] = -(m[0] * m[7] - m[1] * m[6]) * one_over_det;
			result.m[8] = +(m[0] * m[4] - m[1] * m[3]) * one_over_det;

			return result;
		}
		

		/**
		 * add/assign operator
		 */
		template <class S>
		inline Matrix3x3Template<T> &operator += (
			const Matrix3x3Template<S> &a )
		{
			m[0] += static_cast<T>(a.m[0]);
			m[1] += static_cast<T>(a.m[1]);
			m[2] += static_cast<T>(a.m[2]);
			
			m[3] += static_cast<T>(a.m[3]);
			m[4] += static_cast<T>(a.m[4]);
			m[5] += static_cast<T>(a.m[5]);
			
			m[6] += static_cast<T>(a.m[6]);
			m[7] += static_cast<T>(a.m[7]);
			m[8] += static_cast<T>(a.m[8]);
	
			return *this;
		}	
	

		/**
		 * matrix multiplication
		 */
		template <class S> 
		inline Matrix3x3Template<T> operator * ( const Matrix3x3Template<S> &a )
		{
			Matrix3x3Template<T> result;

			result.m[0] = m[0] * static_cast<T>(a.m[0])
				+ m[3] * static_cast<T>(a.m[1])
				+ m[6] * static_cast<T>(a.m[2]);
				
			result.m[1] = m[1] * static_cast<T>(a.m[0])
				+ m[4] * static_cast<T>(a.m[1])
				+ m[7] * static_cast<T>(a.m[2]);
				
			result.m[2] = m[2] * static_cast<T>(a.m[0])
				+ m[5] * static_cast<T>(a.m[1])
				+ m[8] * static_cast<T>(a.m[2]);


			result.m[3] = m[0] * static_cast<T>(a.m[3])
				+ m[3] * static_cast<T>(a.m[4])
				+ m[6] * static_cast<T>(a.m[5]);
				
			result.m[4] = m[1] * static_cast<T>(a.m[3])
				+ m[4] * static_cast<T>(a.m[4])
				+ m[7] * static_cast<T>(a.m[5]);
				
			result.m[5] = m[2] * static_cast<T>(a.m[3])
				+ m[5] * static_cast<T>(a.m[4])
				+ m[8] * static_cast<T>(a.m[5]);


			result.m[6] = m[0] * static_cast<T>(a.m[6])
				+ m[3] * static_cast<T>(a.m[7])
				+ m[6] * static_cast<T>(a.m[8]);
				
			result.m[7] = m[1] * static_cast<T>(a.m[6])
				+ m[4] * static_cast<T>(a.m[7])
				+ m[7] * static_cast<T>(a.m[8]);
				
			result.m[8] = m[2] * static_cast<T>(a.m[6])
				+ m[5] * static_cast<T>(a.m[7])
				+ m[8] * static_cast<T>(a.m[8]);
			
			return result;
		}
		

		/**
		 * matrix vector multiplication
		 */
		template <class S>
		Vector3Template<T> operator * ( const Vector3Template<S>& a )
		{
			return Vector3Template<T>(
				m[0] * static_cast<T>(a.x)
				+ m[3] * static_cast<T>(a.y)
				+ m[6] * static_cast<T>(a.z),
				m[1] * static_cast<T>(a.x)
				+ m[4] * static_cast<T>(a.y)
				+ m[7] * static_cast<T>(a.z),
				m[2] * static_cast<T>(a.x)
				+ m[5] * static_cast<T>(a.y)
				+ m[8] * static_cast<T>(a.z) );
		}

		/**
		 * matrix scalar multiplication
		 */
		template <class S>
		Matrix3x3Template<T> operator * ( const S a )
		{
			Matrix3x3Template<T> result;

			result.m[0] = m[0] * static_cast<T>(a);
			result.m[1] = m[1] * static_cast<T>(a);
			result.m[2] = m[2] * static_cast<T>(a);
			result.m[3] = m[3] * static_cast<T>(a);
			result.m[4] = m[4] * static_cast<T>(a);
			result.m[5] = m[5] * static_cast<T>(a);
			result.m[6] = m[6] * static_cast<T>(a);
			result.m[7] = m[7] * static_cast<T>(a);
			result.m[8] = m[8] * static_cast<T>(a);

			return result;
		}

		friend std::ostream &operator << ( std::ostream& os, Matrix3x3Template<T> m )
		{
			os << "( " << m.m[0] << ", " << m.m[1] << ", " << m.m[2] << " )" << std::endl;
			os << "( " << m.m[3] << ", " << m.m[4] << ", " << m.m[5] << " )" << std::endl;
			os << "( " << m.m[6] << ", " << m.m[7] << ", " << m.m[8] << " )" << std::endl;
			return os;
		}

	};
	
	typedef Matrix3x3Template<float> Matrix3x3Float;
	typedef Matrix3x3Template<double> Matrix3x3Double;
	typedef Matrix3x3Template<Scalar> Matrix3x3;


	template <class T>
	class Matrix4x4Template
	{

	public:

		T m[16];

		/**
		 * default constructor
		 */
		inline Matrix4x4Template()
		{
			identity();
		}
		
		inline void identity()
		{
			m[0] = static_cast<T>(1);
			m[1] = static_cast<T>(0);
			m[2] = static_cast<T>(0);
			m[3] = static_cast<T>(0);
			
			m[4] = static_cast<T>(0);
			m[5] = static_cast<T>(1);
			m[6] = static_cast<T>(0);
			m[7] = static_cast<T>(0);
			
			m[8] = static_cast<T>(0);
			m[9] = static_cast<T>(0);
			m[10] = static_cast<T>(1);
			m[11] = static_cast<T>(0);
			
			m[12] = static_cast<T>(0);
			m[13] = static_cast<T>(0);
			m[14] = static_cast<T>(0);
			m[15] = static_cast<T>(1);
		}		
		
		
		/**
		 * constructor from array
		 */
		inline Matrix4x4Template( const T a[16] )
		{
			m[0]  = a[0];  m[1]  = a[1];  m[2]  = a[2];  m[3]   = a[3];
			m[4]  = a[4];  m[5]  = a[5];  m[6]  = a[6];  m[7]   = a[7];
			m[8]  = a[8];  m[9]  = a[9];  m[10] = a[10]; m[11]  = a[11];
			m[12] = a[12]; m[13] = a[13]; m[14] = a[14]; m[15]  = a[15];
		}

		/**
		 * constructor from 3x3 matrix, add. element are set to zero
		 */
		inline Matrix4x4Template( const Matrix3x3Template<T> &a )
		{
			m[0]  = a[0];
			m[1]  = a[1];
			m[2]  = a[2];
			m[3]  = static_cast<T>(0);
			
			m[4]  = a[3];
			m[5]  = a[4];
			m[6]  = a[5];
			m[7]  = static_cast<T>(0);
			
			m[8]  = a[6];
			m[9]  = a[7];
			m[10] = a[8];
			m[11] = static_cast<T>(0);
			
			m[12] = static_cast<T>(0);
			m[13] = static_cast<T>(0);
			m[14] = static_cast<T>(0);
			m[15] = static_cast<T>(1);
		}
		
		/**
		 * constructor from 3x3 rotation matrix and translation vector
		 */
		inline Matrix4x4Template(
			const Matrix3x3Template<T> &a,
			const Vector3Template<T> &b )
		{
			m[0]  = a[0];
			m[1]  = a[1];
			m[2]  = a[2];
			m[3]  = static_cast<T>(0);
			
			m[4]  = a[3];
			m[5]  = a[4];
			m[6]  = a[5];
			m[7]  = static_cast<T>(0);
			
			m[8]  = a[6];
			m[9]  = a[7];
			m[10] = a[8];
			m[11] = static_cast<T>(0);
			
			m[12] = b.x;
			m[13] = b.y;
			m[14] = b.z;
			m[15] = static_cast<T>(1);
		}
		

		/**
		 * copy constructor
		 */
		inline Matrix4x4Template( const Matrix4x4Template<T> &a )
		{
			m[0]  = a.m[0];
			m[1]  = a.m[1];
			m[2]  = a.m[2];
			m[3]  = a.m[3];

			m[4]  = a.m[4];
			m[5]  = a.m[5];
			m[6]  = a.m[6];
			m[7]  = a.m[7];

			m[8]  = a.m[8];
			m[9]  = a.m[9];
			m[10] = a.m[10];
			m[11] = a.m[11];

			m[12] = a.m[12];
			m[13] = a.m[13];
			m[14] = a.m[14];
			m[15] = a.m[15];
		}


		/**
		 * constructor from quaternion
		 */
		inline Matrix4x4Template( const QuaternionTemplate<T> &q )
		{
			m[0] = 1 - 2*q.y*q.y - 2*q.z*q.z;
			m[1] = 2*q.x*q.y - 2*q.z*q.w;
			m[2] = 2*q.x*q.z + 2*q.y*q.w;
			m[3] = static_cast<T>(0);
			
			m[4] = 2*q.x*q.y + 2*q.z*q.w;
			m[5] = 1 - 2*q.x*q.x - 2*q.z*q.z;
			m[6] = 2*q.y*q.z - 2*q.x*q.w;
			m[7] = static_cast<T>(0);
			
			m[8] = 2*q.x*q.z - 2*q.y*q.w;
			m[9] = 2*q.y*q.z + 2*q.x*q.w;
			m[10] = 1 - 2*q.x*q.x - 2*q.y*q.y;
			m[11] = static_cast<T>(0);

			m[12] = static_cast<T>(0);
			m[13] = static_cast<T>(0);
			m[14] = static_cast<T>(0);
			m[15] = static_cast<T>(1);
		}


		/**
		 * constructor from quaternion and translation vector
		 */
		inline Matrix4x4Template(
			const QuaternionTemplate<T> &q,
			const Vector3Template<T> &a  )
		{
			m[0] = 1 - 2*q.y*q.y - 2*q.z*q.z;
			m[1] = 2*q.x*q.y - 2*q.z*q.w;
			m[2] = 2*q.x*q.z + 2*q.y*q.w;
			m[3] = static_cast<T>(0);
			
			m[4] = 2*q.x*q.y + 2*q.z*q.w;
			m[5] = 1 - 2*q.x*q.x - 2*q.z*q.z;
			m[6] = 2*q.y*q.z - 2*q.x*q.w;
			m[7] = static_cast<T>(0);
			
			m[8] = 2*q.x*q.z - 2*q.y*q.w;
			m[9] = 2*q.y*q.z + 2*q.x*q.w;
			m[10] = 1 - 2*q.x*q.x - 2*q.y*q.y;
			m[11] = static_cast<T>(0);

			m[12] = a.x;
			m[13] = a.y;
			m[14] = a.z;
			m[15] = static_cast<T>(1);
		}

					
		/**
		 * constructor from heading, up and translation vectors
		 */
		inline Matrix4x4Template(
			const Vector3Template<T> &h,
			const Vector3Template<T> &u,
			const Vector3Template<T> &t )
		{
			Vector3Template<T> a, b, c;
			c = h.unit();
			a = h.crossProduct( u ).unit();
			b = c.crossProduct( a ).unit();
			
			m[0]  = a.x;
			m[1]  = b.x;
			m[2]  = c.x;
			m[3]  = static_cast<T>(0);
			
			m[4]  = a.y;
			m[5]  = b.y;
			m[6]  = c.y;
			m[7]  = static_cast<T>(0);
			
			m[8]  = a.z;
			m[9]  = b.z;
			m[10] = c.z;
			m[11] = static_cast<T>(0);
			
			m[12] = t.x;
			m[13] = t.y;
			m[14] = t.z;
			m[15] = static_cast<T>(1);
		}


		/**
		 * contructor from euler angles
		 */
		inline Matrix4x4Template(
			T a,
			T e,
			T t,
			const Vector3Template<T> &tr )
		{
			T ch = cos( a );
			T sh = sin( a );
			T ca = cos( e );
			T sa = sin( e );
			T cb = cos( t );
			T sb = sin( t );
			
			m[0]  = ch * ca;
			m[1]  = sh*sb - ch*sa*cb;
			m[2]  = ch*sa*sb + sh*cb;
			m[3]  = static_cast<T>(0);
			
			m[4]  = sa;
			m[5]  = ca*cb;
			m[6]  = -ca*sb;
			m[7]  = static_cast<T>(0);
			
			
			m[8]  = -sh*ca;
			m[9]  = sh*sa*cb + ch*sb;
			m[10] = -sh*sa*sb + ch*cb;
			m[11] = static_cast<T>(0);
			
			m[12] = tr.x;
			m[13] = tr.y;
			m[14] = tr.z;
			m[15] = static_cast<T>(1);
		}


		/**
		 * transpose this matrix
		 */
		inline void transpose()
		{
			std::swap( m[4], m[1] );
			std::swap( m[8], m[2] );
			std::swap( m[12], m[3] );

			std::swap( m[9], m[6] );
			std::swap( m[13], m[7] );
			std::swap( m[14], m[11] );
		}
	

		/**
		 * get transposed matrix
		 */
		inline Matrix4x4Template<T> transposed()
		{
			Matrix4x4Template<T> a;
			
			a.m[0] = m[0]; a.m[4] = m[1]; a.m[8] = m[2]; a.m[12] = m[3];
			a.m[1] = m[4]; a.m[5] = m[5]; a.m[9] = m[6]; a.m[13] = m[7];
			a.m[2] = m[8]; a.m[6] = m[9]; a.m[10] = m[10]; a.m[14] = m[11];
			a.m[3] = m[12]; a.m[7] = m[13]; a.m[11] = m[14]; a.m[15] = m[15];
			
			return a;
		}		


		/**
		 * matrix multiplication
		 */
		template <class S> 
		inline Matrix4x4Template<T> operator * ( const Matrix4x4Template<S> &a )
		{
			Matrix4x4Template<T> result;
			
			result.m[0] = m[0] * static_cast<T>(a.m[0])
				+ m[4] * static_cast<T>(a.m[1])
				+ m[8] * static_cast<T>(a.m[2])
				+ m[12] * static_cast<T>(a.m[3]);
				
			result.m[1] = m[1] * static_cast<T>(a.m[0])
				+ m[5] * static_cast<T>(a.m[1])
				+ m[9] * static_cast<T>(a.m[2])
				+ m[13] * static_cast<T>(a.m[3]);
				
			result.m[2] = m[2] * static_cast<T>(a.m[0])
				+ m[6] * static_cast<T>(a.m[1])
				+ m[10] * static_cast<T>(a.m[2])
				+ m[14] * static_cast<T>(a.m[3]);

			result.m[3] = m[3] * static_cast<T>(a.m[0])
				+ m[7] * static_cast<T>(a.m[1])
				+ m[11] * static_cast<T>(a.m[2])
				+ m[15] * static_cast<T>(a.m[3]);


			result.m[4] = m[0] * static_cast<T>(a.m[4])
				+ m[4] * static_cast<T>(a.m[5])
				+ m[8] * static_cast<T>(a.m[6])
				+ m[12] * static_cast<T>(a.m[7]);
				
			result.m[5] = m[1] * static_cast<T>(a.m[4])
				+ m[5] * static_cast<T>(a.m[5])
				+ m[9] * static_cast<T>(a.m[6])
				+ m[13] * static_cast<T>(a.m[7]);
				
			result.m[6] = m[2] * static_cast<T>(a.m[4])
				+ m[6] * static_cast<T>(a.m[5])
				+ m[10] * static_cast<T>(a.m[6])
				+ m[14] * static_cast<T>(a.m[7]);

			result.m[7] = m[3] * static_cast<T>(a.m[4])
				+ m[7] * static_cast<T>(a.m[5])
				+ m[11] * static_cast<T>(a.m[6])
				+ m[15] * static_cast<T>(a.m[7]);


			result.m[8] = m[0] * static_cast<T>(a.m[8])
				+ m[4] * static_cast<T>(a.m[9])
				+ m[8] * static_cast<T>(a.m[10])
				+ m[12] * static_cast<T>(a.m[11]);
				
			result.m[9] = m[1] * static_cast<T>(a.m[8])
				+ m[5] * static_cast<T>(a.m[9])
				+ m[9] * static_cast<T>(a.m[10])
				+ m[13] * static_cast<T>(a.m[11]);
				
			result.m[10] = m[2] * static_cast<T>(a.m[8])
				+ m[6] * static_cast<T>(a.m[9])
				+ m[10] * static_cast<T>(a.m[10])
				+ m[14] * static_cast<T>(a.m[11]);

			result.m[11] = m[3] * static_cast<T>(a.m[8])
				+ m[7] * static_cast<T>(a.m[9])
				+ m[11] * static_cast<T>(a.m[10])
				+ m[15] * static_cast<T>(a.m[11]);


			result.m[12] = m[0] * static_cast<T>(a.m[12])
				+ m[4] * static_cast<T>(a.m[13])
				+ m[8] * static_cast<T>(a.m[14])
				+ m[12] * static_cast<T>(a.m[15]);
				
			result.m[13] = m[1] * static_cast<T>(a.m[12])
				+ m[5] * static_cast<T>(a.m[13])
				+ m[9] * static_cast<T>(a.m[14])
				+ m[13] * static_cast<T>(a.m[15]);
				
			result.m[14] = m[2] * static_cast<T>(a.m[12])
				+ m[6] * static_cast<T>(a.m[13])
				+ m[10] * static_cast<T>(a.m[14])
				+ m[14] * static_cast<T>(a.m[15]);

			result.m[15] = m[3] * static_cast<T>(a.m[12])
				+ m[7] * static_cast<T>(a.m[13])
				+ m[11] * static_cast<T>(a.m[14])
				+ m[15] * static_cast<T>(a.m[15]);
			
			return result;			
		}
		
		/**
		 * matrix multiplication
		 */
/*
		template <class S> 
		inline Matrix4x4Template<T> operator *= ( const Matrix4x4Template<S> &a )
		{
			Matrix4x4Template<T> result;
			
			result.m[0] = m[0] * static_cast<T>(a.m[0])
				+ m[4] * static_cast<T>(a.m[1])
				+ m[8] * static_cast<T>(a.m[2]);
				+ m[12] * static_cast<T>(a.m[3]);
				
			result.m[1] = m[1] * static_cast<T>(a.m[0])
				+ m[5] * static_cast<T>(a.m[1])
				+ m[9] * static_cast<T>(a.m[2]);
				+ m[13] * static_cast<T>(a.m[3]);
				
			result.m[2] = m[2] * static_cast<T>(a.m[0])
				+ m[6] * static_cast<T>(a.m[1])
				+ m[10] * static_cast<T>(a.m[2]);
				+ m[14] * static_cast<T>(a.m[3]);

			result.m[3] = m[3] * static_cast<T>(a.m[0])
				+ m[7] * static_cast<T>(a.m[1])
				+ m[11] * static_cast<T>(a.m[2]);
				+ m[15] * static_cast<T>(a.m[3]);


			result.m[4] = m[0] * static_cast<T>(a.m[4])
				+ m[4] * static_cast<T>(a.m[5])
				+ m[8] * static_cast<T>(a.m[6]);
				+ m[12] * static_cast<T>(a.m[7]);
				
			result.m[5] = m[1] * static_cast<T>(a.m[4])
				+ m[5] * static_cast<T>(a.m[5])
				+ m[9] * static_cast<T>(a.m[6]);
				+ m[13] * static_cast<T>(a.m[7]);
				
			result.m[6] = m[2] * static_cast<T>(a.m[4])
				+ m[6] * static_cast<T>(a.m[5])
				+ m[10] * static_cast<T>(a.m[6]);
				+ m[14] * static_cast<T>(a.m[7]);

			result.m[7] = m[3] * static_cast<T>(a.m[4])
				+ m[7] * static_cast<T>(a.m[5])
				+ m[11] * static_cast<T>(a.m[6]);
				+ m[15] * static_cast<T>(a.m[7]);


			result.m[8] = m[0] * static_cast<T>(a.m[8])
				+ m[4] * static_cast<T>(a.m[9])
				+ m[8] * static_cast<T>(a.m[10]);
				+ m[12] * static_cast<T>(a.m[11]);
				
			result.m[9] = m[1] * static_cast<T>(a.m[8])
				+ m[5] * static_cast<T>(a.m[9])
				+ m[9] * static_cast<T>(a.m[10]);
				+ m[13] * static_cast<T>(a.m[11]);
				
			result.m[10] = m[2] * static_cast<T>(a.m[8])
				+ m[6] * static_cast<T>(a.m[9])
				+ m[10] * static_cast<T>(a.m[10]);
				+ m[14] * static_cast<T>(a.m[11]);

			result.m[11] = m[3] * static_cast<T>(a.m[8])
				+ m[7] * static_cast<T>(a.m[9])
				+ m[11] * static_cast<T>(a.m[10]);
				+ m[15] * static_cast<T>(a.m[11]);


			result.m[12] = m[0] * static_cast<T>(a.m[12])
				+ m[4] * static_cast<T>(a.m[13])
				+ m[8] * static_cast<T>(a.m[14]);
				+ m[12] * static_cast<T>(a.m[15]);
				
			result.m[13] = m[1] * static_cast<T>(a.m[12])
				+ m[5] * static_cast<T>(a.m[13])
				+ m[9] * static_cast<T>(a.m[14]);
				+ m[13] * static_cast<T>(a.m[15]);
				
			result.m[14] = m[2] * static_cast<T>(a.m[12])
				+ m[6] * static_cast<T>(a.m[13])
				+ m[10] * static_cast<T>(a.m[14]);
				+ m[14] * static_cast<T>(a.m[15]);

			result.m[15] = m[3] * static_cast<T>(a.m[12])
				+ m[7] * static_cast<T>(a.m[13])
				+ m[11] * static_cast<T>(a.m[14]);
				+ m[15] * static_cast<T>(a.m[15]);
			
			m = result.m;
			
			return *this;			
		}
	*/			
		/**
		 * matrix vector multiplication
		 */
		Vector3Template<T> operator * ( const Vector3Template<T> &a )
		{
			Vector3Template<T> result;
			
			result.x = m[0] * a.x + m[4] * a.y + m[8] * a.z + m[12];
			result.y = m[1] * a.x + m[5] * a.y + m[9] * a.z + m[13];
			result.z = m[2] * a.x + m[6] * a.y + m[11] * a.z + m[14];
			
			return result;
		}

		T *data()
		{
			return &m[0];
		}
	};
	
	typedef Matrix4x4Template<float> Matrix4x4Float;
	typedef Matrix4x4Template<double> Matrix4x4Double;
	typedef Matrix4x4Template<Scalar> Matrix4x4;
	
} // namespace bc

#endif // BLUECORE_MATRIX_H