triangle.h

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#pragma once
 
#include "./experimental/geom/point.h"
#include "./experimental/geom/pose.h"
#include "./experimental/geom/simplex.h"
#include "./experimental/geom/vector.h"
 
namespace emlabcpp
{
 
template < std::size_t N >
using triangle = simplex< point< N >, 2 >;
 
inline point< 3 > get_triangle_sphere_center( triangle< 3 > const& tri )
{
        vector< 3 > const ab     = tri[0] - tri[1];
        vector< 3 > const ac     = tri[0] - tri[2];
        vector< 3 > const normal = normalized( cross_product( ab, ac ) );
        vector< 3 >       p_ab   = cross_product( normal, ab );
        vector< 3 >       p_ac   = cross_product( normal, ac );
        vector< 3 >       c_ac   = ( vector_cast( tri[0] ) + vector_cast( tri[2] ) ) / 2;
        vector< 3 >       c_ab   = ( vector_cast( tri[0] ) + vector_cast( tri[1] ) ) / 2;
 
        float k;
 
        k = p_ab[0] * ( c_ab[1] - c_ac[1] ) + p_ab[1] * ( c_ac[0] - c_ab[0] );
        //-------------------------------------------------------------------
        k /= ( p_ab[0] * p_ac[1] - p_ac[0] * p_ab[1] );
 
        return point_cast( c_ac + k * p_ac );
}
 
constexpr vector< 3 > normal_of( triangle< 3 > const& tri )
{
        return cross_product( tri[0] - tri[1], tri[0] - tri[2] );
}
 
constexpr triangle< 3 > transform( triangle< 3 > const& t, pose const& transformation )
{
        return triangle< 3 >{
            transform( t[0], transformation ),
            transform( t[1], transformation ),
            transform( t[2], transformation ) };
}
 
template < std::size_t N >
constexpr triangle< N > scale( triangle< N > const& t, point< N > const& scales )
{
        return triangle< N >{ t[0] * scales, t[1] * scales, t[2] * scales };
}
 
}  // namespace emlabcpp