NAME

       tetrahedron - Tetraedron reference element

DESCRIPTION

       The tetrahedron reference element is

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

                              z
                            .
                          ,/
                         /
                       3
                     ,/|`\
                   ,/  |  `\
                 ,/    '.   `\
               ,/       |     `\
             ,/         |       `\
            0-----------'.--------2 --> y
             `\.         |      ,/
                `\.      |    ,/
                   `\.   '. ,/
                      `\. |/
                         `1
                            `\.
                              ` x

       Curved high order Pk tetrahedra (k >= 1) in 3d geometries are supported.  These tetrahedra
       have additional edge-nodes, face-nodes and internal volume-nodes.

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.

                       3
                     ,/|`\
                   ,/  |  `\
                 ,7    '.   `9
               ,/       |     `\
             ,/         8       `\
            0--------6--'.--------2
             `\.         |      ,/
                `\.      |    ,5
                   `4.   '. ,/
                      `\. |/
                         `1
                      P2

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 gmsh mesh generator when using high-
       order  elements.   This  difference  is  handled  by  the msh2geo mesh file converter (see
       msh2geo(1)).

IMPLEMENTATION

       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 } };

SEE ALSO

       msh2geo(1)