.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH tetrahedron 7rheolef "rheolef-6.5" "rheolef-6.5" "rheolef-6.5"
.\" label: /*Class:tetra
.SH NAME
\fBtetrahedron\fP - Tetraedron reference element
.\" skip: @cindex tetrahedron
.\" skip: @cindex reference element
.\" skip: @pindex gmsh
.\" skip: @pindex msh2geo
.SH DESCRIPTION

The tetrahedron reference element is
.\" begin_example
.Sp
.nf
        K = { 0 < x < 1 and 0 < y < 1-x and 0 < z < 1-x-y }
.Sp
.fi
.\" end_example
.\" begin_example
.Sp
.nf
                       z
                     .
                   ,/
                  /
                3
              ,/|`\\
            ,/  |  `\\
          ,/    '.   `\\
        ,/       |     `\\
      ,/         |       `\\
     0-----------'.--------2 --> y
      `\\.         |      ,/
         `\\.      |    ,/
            `\\.   '. ,/
               `\\. |/
                  `1
                     `\\.
                       ` x
.Sp
.fi
.\" end_example
Curved high order Pk tetrahedra (k >= 1) in 3d geometries are supported.
These tetrahedra have additional edge-nodes, face-nodes
and internal volume-nodes.
.SH THESE NODES ARE NUMBERED AS
 first vertex, then edge-node, following
the edge numbering order and orientation, then face-nodes following the face numbering
order and orientation, and finally the face internal nodes,
following the tetrahedron lattice.
See below for edges and faces numbering and orioentation.
.\" begin_example
.Sp
.nf
                3
              ,/|`\\
            ,/  |  `\\
          ,7    '.   `9
        ,/       |     `\\
      ,/         8       `\\
     0--------6--'.--------2
      `\\.         |      ,/
         `\\.      |    ,5
            `4.   '. ,/
               `\\. |/
                  `1
               P2
.Sp
.fi
.\" end_example
.SH NUMBERING

The orientation is such that triedra (01, 02, 03) is direct,
and all faces, see from exterior, are in the direct sens.  References:
P. L. Georges, "Generation automatique de maillages",
page 24-, coll RMA, 16, Masson, 1994.
Notice that the edge-nodes and face-nodes numbering slighly differ from
those used in the \fBgmsh\fP mesh generator when using high-order elements.
This difference is handled by the \fBmsh2geo\fP mesh file converter (see msh2geo(1)).
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
const size_t dimension = 3;
const Float  measure = Float(1.)/Float(6.);
const size_t n_vertex = 4;
const point vertex [n_vertex] = {
        point( 0, 0, 0 ),
        point( 1, 0, 0 ),
        point( 0, 1, 0 ),
        point( 0, 0, 1 ) };
const size_t  n_face = 4;
const size_t face [n_face][3] = {
        { 0, 2, 1 },
        { 0, 3, 2 },
        { 0, 1, 3 },
        { 1, 2, 3 } };
const size_t  n_edge = 6;
const size_t edge [n_edge][2] = {
        { 0, 1 },
        { 1, 2 },
        { 2, 0 },
        { 0, 3 },
        { 1, 3 },
        { 2, 3 } };
.Sp
.fi
.\" end_example

.\" LENGTH = 1
.SH SEE ALSO
msh2geo(1)