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prism

reference element

## Description

The prism reference_element is

        K = { 0 < x < 1 and 0 < y < 1-x and -1 < z < 1 }

                x2

                3 ---- 5
             '  | .    |
          4 .  '|      |
          |     |      |
          |     |      |
          |     0 . . .2    x1
          |  '    .
          1 .  '

        x0

The orientation is such that trihedral (01, 02, 03) is direct and all faces, see from exterior, are in the direct sens. See

        P. L. Georges,
        Generation automatique de maillages,
        page 24, coll RMA, 16, Masson, 1994.

This three-dimensional reference_element is then transformed, after the Piola geometrical application, as a prism in a 3D physical space, as a geo_element.

Curved high order transformed geo_element Pk prisms (k >= 1) are supported for 2D or 3D geometries.

## Implementation

This documentation has been generated from file fem/geo_element/prism.icc

const size_t dimension = 3;
const Float measure = 1;
const size_t n_vertex = 6;
const point vertex [n_vertex] = {
point( 0, 0,-1 ),
point( 1, 0,-1 ),
point( 0, 1,-1 ),
point( 0, 0, 1 ),
point( 1, 0, 1 ),
point( 0, 1, 1 ) };
const size_t n_face = 5;
const size_t face [n_face][4] = {
{ 0, 2, 1, size_t(-1) },
{ 3, 4, 5, size_t(-1) },
{ 0, 1, 4, 3 },
{ 1, 2, 5, 4 },
{ 0, 3, 5, 2 } };
const size_t n_edge = 9;
const size_t edge [n_edge][2] = {
{ 0, 1 },
{ 1, 2 },
{ 2, 0 },
{ 0, 3 },
{ 1, 4 },
{ 2, 5 },
{ 3, 4 },
{ 4, 5 },
{ 5, 3 } };

## Description

The prism reference_element is

        K = { 0 < x < 1 and 0 < y < 1-x and -1 < z < 1 }

                x2

                3 ---- 5
             '  | .    |
          4 .  '|      |
          |     |      |
          |     |      |
          |     0 . . .2    x1
          |  '    .
          1 .  '

        x0

The orientation is such that trihedral (01, 02, 03) is direct and all faces, see from exterior, are in the direct sens. See

        P. L. Georges,
        Generation automatique de maillages,
        page 24, coll RMA, 16, Masson, 1994.

This three-dimensional reference_element is then transformed, after the Piola geometrical application, as a prism in a 3D physical space, as a geo_element.

Curved high order transformed geo_element Pk prisms (k >= 1) are supported for 2D or 3D geometries.

## Implementation

This documentation has been generated from file fem/geo_element/prism.icc

const size_t dimension = 3;
const Float measure = 1;
const size_t n_vertex = 6;
const point vertex [n_vertex] = {
point( 0, 0,-1 ),
point( 1, 0,-1 ),
point( 0, 1,-1 ),
point( 0, 0, 1 ),
point( 1, 0, 1 ),
point( 0, 1, 1 ) };
const size_t n_face = 5;
const size_t face [n_face][4] = {
{ 0, 2, 1, size_t(-1) },
{ 3, 4, 5, size_t(-1) },
{ 0, 1, 4, 3 },
{ 1, 2, 5, 4 },
{ 0, 3, 5, 2 } };
const size_t n_edge = 9;
const size_t edge [n_edge][2] = {
{ 0, 1 },
{ 1, 2 },
{ 2, 0 },
{ 0, 3 },
{ 1, 4 },
{ 2, 5 },
{ 3, 4 },
{ 4, 5 },
{ 5, 3 } };