---
name: "reference_element"
section: "6rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/reference_element"
---

# reference\_element(6rheolef)

reference element (rheolef-7.2)

## NAME

reference\_element - reference element (rheolef-7.2)

## DESCRIPTION

The **reference\_element** class defines all supported types of geometrical elements in zero, one, two and three dimensions. Each supported element is represented by a letter:

- •

  `p`: **point(6)** (dimension 0)

- •

  `e`: **edge(6)** (dimension 1)

- •

  `t`: **[triangle(6)](/triangle/6.md)** (dimension 2)

- •

  `q`: **quadrangle(6)** (dimension 2)

- •

  `T`: **tetrahedron(6)** (dimension 3)

- •

  `P`: **prism(6)** (dimension 3)

- •

  `H`: **hexahedron(6)** (dimension 3)

## IMPLEMENTATION

This documentation has been generated from file fem/geo\_element/reference\_element.h

```
class reference_element {
public:
// typedefs:
    typedef std::vector<int>::size_type size_type;
    typedef size_type                   variant_type;
    static const variant_type
        p = 0,
        e = 1,
        t = 2,
        q = 3,
        T = 4,
        P = 5,
        H = 6,
        max_variant = 7;
    static const size_type max_side_by_variant = 6;
// allocators/deallocators:
    reference_element (variant_type x = max_variant)
      : _x(x) { assert_macro (x >= 0 && x <= max_variant, "invalid type " << x); }
// initializers:
    void set_variant (variant_type x) { _x = x; }
    void set_variant (size_type n_vertex, size_type dim) { _x = variant (n_vertex, dim); }
    void set_name    (char name);
// accessors:
    variant_type variant() const { return _x; }
    char name() const { return _name[_x % max_variant]; }
    size_type dimension() const { return _dimension[_x]; }
    size_type size()     const { return _n_vertex[_x]; }
    size_type n_vertex() const { return _n_vertex[_x]; }
    size_type n_side() const { return dimension() > 0 ? n_subgeo (variant(), dimension()-1) : 0; }
    size_type n_edge() const { return n_subgeo(1); }
    size_type n_face() const { return n_subgeo(2); }
    size_type n_subgeo_by_variant (size_type subgeo_variant) const {
        return n_subgeo_by_variant(variant(), subgeo_variant); }
    size_type n_subgeo(size_type subgeo_dim) const { return n_subgeo (variant(), subgeo_dim); }
    reference_element subgeo (size_type subgeo_dim, size_type loc_isid) const {
        if (dimension() == 0) return reference_element(reference_element::p);
        if (dimension() == subgeo_dim) return *this;
        reference_element hat_S;
        size_type subgeo_n_vertex = subgeo_size (subgeo_dim, loc_isid);
        hat_S.set_variant (subgeo_n_vertex, subgeo_dim);
        return hat_S;
    }
    reference_element side (size_type loc_isid) const { return subgeo (dimension()-1, loc_isid); }
    size_type subgeo_size (size_type subgeo_dim, size_type loc_isid) const {
        return subgeo_n_node (_x, 1, subgeo_dim, loc_isid); }
    size_type subgeo_local_vertex(size_type subgeo_dim, size_type loc_isid, size_type loc_jsidvert) const {
        return subgeo_local_node (_x, 1, subgeo_dim, loc_isid, loc_jsidvert); }
    size_type local_subgeo_index2index_by_variant (size_type subgeo_variant, size_type i) const {
      return (variant() == P && subgeo_variant == q) ? i-2 : i; }
    // TODO: use template<class T> instead of Float
    const point_basic<Float>& vertex (size_type iloc) const;
    friend Float measure (reference_element hat_K);
    Float side_measure (size_type loc_isid) const;
    void side_normal (size_type loc_isid, point_basic<Float>& hat_n) const;
// helpers:
    static variant_type variant  (char name);
    static variant_type variant  (size_type n_vertex, size_type dim);
    static char         name     (variant_type variant) { return _name     [variant]; }
    static size_type dimension   (variant_type variant) { return _dimension[variant]; }
    static size_type n_vertex    (variant_type variant) { return _n_vertex [variant]; }
    static size_type n_node      (variant_type variant, size_type order);
    static size_type n_sub_edge    (variant_type variant);
    static size_type n_sub_face    (variant_type variant);
    static size_type n_subgeo      (variant_type variant, size_type subgeo_dim);
    static size_type subgeo_n_node (variant_type variant, size_type order, size_type subgeo_dim, size_type loc_isid);
    static size_type subgeo_local_node (variant_type variant, size_type order, size_type subgeo_dim, size_type loc_isid, size_type loc_jsidnod);
    static variant_type first_variant_by_dimension (size_type dim) {
                return _first_variant_by_dimension[dim]; }
    static variant_type  last_variant_by_dimension (size_type dim) {
                return _first_variant_by_dimension[dim+1]; }
    static size_type first_inod_by_variant (variant_type variant, size_type order, variant_type subgeo_variant);
    static size_type  last_inod_by_variant (variant_type variant, size_type order, variant_type subgeo_variant)
       { return first_inod_by_variant (variant, order, subgeo_variant+1); }
    static size_type first_inod (variant_type variant, size_type order, size_type subgeo_dim)
       { return first_inod_by_variant (variant, order, first_variant_by_dimension(subgeo_dim)); }
    static size_type  last_inod (variant_type variant, size_type order, size_type subgeo_dim)
       { return first_inod_by_variant (variant, order,  last_variant_by_dimension(subgeo_dim)); }
    static void init_local_nnode_by_variant (size_type order, std::array<size_type,reference_element::max_variant>& loc_nnod_by_variant);
    static size_type n_subgeo_by_variant (size_type variant, size_type subgeo_variant)
      { return _n_subgeo_by_variant [variant] [subgeo_variant]; }
```

```
};
```

## AUTHOR

Pierre  Saramito  \<Pierre.Saramito@imag.fr\>

## COPYRIGHT

Copyright   (C)  2000-2018  Pierre  Saramito  \<Pierre.Saramito@imag.fr\> GPLv3+: GNU GPL version 3 or later  \<http://gnu.org/licenses/gpl.html\>. This  is  free  software:  you  are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.