typename viennagrid::result_of::coord< typename PointAccessorT::value_type >::type
volume_impl(PointAccessorT const accessor, ElementT const & cell, viennagrid::quadrilateral_tag)
{
typedef typename PointAccessorT::value_type PointType;
PointType const & p0 = accessor( vertices(cell)[0] );
PointType const & p1 = accessor( vertices(cell)[1] );
PointType const & p2 = accessor( vertices(cell)[2] );
PointType const & p3 = accessor( vertices(cell)[3] );
return spanned_volume(p0, p1, p3) + spanned_volume(p1, p2, p3); //sum up the two triangular parts
}
typename viennagrid::result_of::coord< typename PointAccessorT::value_type >::type
volume_impl(PointAccessorT const accessor, ElementT const & cell, viennagrid::triangle_tag)
{
typedef typename PointAccessorT::value_type PointType;
PointType const & p0 = accessor( vertices(cell)[0] );
PointType const & p1 = accessor( vertices(cell)[1] );
PointType const & p2 = accessor( vertices(cell)[2] );
return spanned_volume(p0, p1, p2);
}
bool is_inside_impl( PointAccessorT const accessor,
ElementT const & element, viennagrid::tetrahedron_tag,
spatial_point<CoordType, CoordinateSystem> const & p,
NumericConfigT numeric_config )
{
typedef spatial_point<CoordType, CoordinateSystem> PointType;
typedef typename viennagrid::result_of::coord<PointType>::type NumericType;
PointType const & a = accessor( viennagrid::vertices(element)[0] );
PointType const & b = accessor( viennagrid::vertices(element)[1] );
PointType const & c = accessor( viennagrid::vertices(element)[2] );
PointType const & d = accessor( viennagrid::vertices(element)[3] );
NumericType denom = static_cast<NumericType>(1) / spanned_volume(a,b,c,d);
NumericType A = spanned_volume(p,b,c,d) * denom;
NumericType B = spanned_volume(a,p,c,d) * denom;
NumericType C = spanned_volume(a,b,p,d) * denom;
NumericType D = spanned_volume(a,b,c,p) * denom;
NumericType abs_eps = absolute_tolerance<NumericType>(numeric_config);
return (A >= -abs_eps) && (B >= -abs_eps) && (C >= -abs_eps) && (D >= -abs_eps) && (A+B+C+D <= static_cast<NumericType>(1) + NumericType(2.0)*abs_eps);
}
typename viennagrid::result_of::coord< typename PointAccessorT::value_type >::type
volume_impl(PointAccessorT const accessor, ElementT const & cell, viennagrid::hexahedron_tag)
{
typedef typename PointAccessorT::value_type PointType;
PointType const & p0 = accessor( vertices(cell)[0] );
PointType const & p1 = accessor( vertices(cell)[1] );
PointType const & p2 = accessor( vertices(cell)[2] );
PointType const & p3 = accessor( vertices(cell)[3] );
PointType const & p4 = accessor( vertices(cell)[4] );
PointType const & p5 = accessor( vertices(cell)[5] );
PointType const & p6 = accessor( vertices(cell)[6] );
PointType const & p7 = accessor( vertices(cell)[7] );
//decompose hexahedron into six tetrahedra
return spanned_volume(p0, p1, p3, p4)
+ spanned_volume(p4, p1, p3, p7)
+ spanned_volume(p4, p1, p7, p5)
+ spanned_volume(p1, p2, p3, p7)
+ spanned_volume(p1, p2, p7, p5)
+ spanned_volume(p5, p2, p7, p6);
}
