QVM: Quaternions, Vectors, Matrices

vec_traits

namespace
boost
{
    namespace
    qvm
    {
        template <class V>
        struct vec_traits
        {
            /*main template members unspecified*/
        };
        
        /*
        User-defined (possibly partial) specializations:
        
        template <>
        struct vec_traits<V>
        {
            static int const dim = /*user-defined*/;        
            typedef /*user-defined*/ scalar_type;        
        
            template <int I> static inline scalar_type read_element( Vector const & v );        
            template <int I> static inline scalar_type & write_element( Vector & v );        
        
            static inline scalar_type read_element_idx( int i, Vector const & v );        
            static inline scalar_type & write_element_idx( int i, Vector & v );        
        };
        */
    }
}

The vec_traits template must be specialized for (user-defined) vector types in order to enable vector and matrix operations defined in Boost QVM headers for objects of those types.

Note: vector types are not required to be copyable.

The main vec_traits template members are not specified. Valid specializations are required to define the following members:

dim: the expression vec_traits<Vector>::dim must evaluate to a compile-time integer constant greater than 0 that specifies the vector size.
scalar_type: the expression vec_traits<Vector>::scalar_type must be a value type which satisfies the scalar requirements.

In addition, valid specializations of the vec_traits template may define the following access functions as static members, where v is an object of type Vector, I is a compile-time integer constant, and i is a variable of type int:

read_element: the expression vec_traits<Vector>::read_element<I>(v) returns either a copy of or a const reference to the I-th element of v.
write_element: the expression vec_traits<Vector>::write_element<I>(v) returns mutable reference to the I-th element of v.
read_element_idx: the expression vec_traits<Vector>::read_element_idx(i,v) returns either a copy of or a const reference to the i-th element of v.
write_element_idx: the expression vec_traits<Vector>::write_element_idx(i,v) returns mutable reference to the i-th element of v.

It is illegal to call any of the above functions unless is_vec<Vector>::value is true. Even then, vector types are allowed to define only a subset of the access functions. The general requirements are:

At least one of read_element or write_element must be defined;
If read_element_idx is defined, read_element must also be defined;
If write_element_idx is defined, write_element must also be defined.

Below is an example of a user-defined 3D vector type, and its corresponding specialization of the vec_traits template:

#include <boost/qvm/vec_traits.hpp>

struct float3 { float a[3]; };

namespace boost
{
    namespace qvm
    {
        template <>
        struct vec_traits<float3>
        {
            static int const dim=3;
            typedef float scalar_type;

            template <int I> static inline scalar_type & write_element( float3 & v ) { return v.a[I]; }
            template <int I> static inline scalar_type read_element( float3 const & v ) { return v.a[I]; }

            static inline scalar_type & write_element_idx( int i, float3 & v ) { return v.a[i]; } //optional
            static inline scalar_type read_element_idx( int i, float3 const & v ) { return v.a[i]; } //optional
        };
    }
}