# QVM: Quaternions, Vectors, Matrices

### Quaternion, Vector and Matrix Types

#include <boost/qvm/quat.hpp>
#include <boost/qvm/vec.hpp>
#include <boost/qvm/mat.hpp>

    namespace boost
    {
        namespace qvm
        {
            //*** Quaternion, vector and matrix types ***

            template <class T>
            struct quat
            {
                T a[4];

                template <class R>
                operator R() const
                {
                    R r;
                    assign(r,*this);
                    return r;
                }
            };

            template <class Quaternion>
            struct quat_traits;

            template <class T>
            struct quat_traits< quat<T> >
            {
                typedef T scalar_type;

                template <int I> static scalar_type read_element( quat<T> const & x ) { return x.a[I]; }
                template <int I> static scalar_type & write_element( quat<T> & x ) { return x.a[I]; }
            };

            template <class T,int Dim>
            struct vec
            {
                T a[Dim];

                template <class R>
                operator R() const
                {
                    R r;
                    assign(r,*this);
                    return r;
                }
            };

            template <class Vector>
            struct vec_traits;

            template <class T,int Dim>
            struct vec_traits< vec<T,Dim> >
            {
                typedef T scalar_type;
                static int const dim=Dim;

                template <int I> static scalar_type read_element( vec<T,Dim> const & x ) { return x.a[I]; }
                template <int I> static scalar_type & write_element( vec<T,Dim> & x ) { return x.a[I]; }

                static scalar_type read_element_idx( int i, vec<T,Dim> const & x ) { return x.a[i]; }
                static scalar_type & write_element_idx( int i, vec<T,Dim> & x ) { return x.a[i]; }
            };

            template <class T,int Rows,int Cols>
            struct mat
            {
                T a[Rows][Cols];

                template <class R>
                operator R() const
                    {
                    R r;
                    assign(r,*this);
                    return r;
                    }
            };

            template <class Matrix>
            struct mat_traits;

            template <class T,int Rows,int Cols>
            struct mat_traits< mat<T,Rows,Cols> >
            {
                typedef T scalar_type;
                static int const rows=Rows;
                static int const cols=Cols;

                template <int Row,int Col> static scalar_type read_element( mat<T,Rows,Cols> const & x ) { return x.a[Row][Col]; }
                template <int Row,int Col> static scalar_type & write_element( mat<T,Rows,Cols> & x ) { return x.a[Row][Col]; }

                static scalar_type read_element_idx( int row, int col, mat<T,Rows,Cols> const & x ) { return x.a[row][col]; }
                static scalar_type & write_element_idx( int row, int col, mat<T,Rows,Cols> & x ) { return x.a[row][col]; }
            };
        }
    }

See also: Boost QVM | Synopsis