.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH triangle 7rheolef "rheolef-6.7" "rheolef-6.7" "rheolef-6.7"
.\" label: /*Class:triangle
.SH NAME
\fBtriangle\fP - Triangle reference element
.\" skip: @cindex triangle
.\" skip: @cindex reference element
.SH DESCRIPTION

The triangle reference element is
.\" begin_example
.Sp
.nf
        K = { 0 < x < 1 and 0 < y < 1-x }
.Sp
.fi
.\" end_example
.SH NUMBERING

.\" begin_example
.Sp
.nf
      y
.PP
      2
      | +
      |   +
      |     +
      |       +
      0---------1   x
.Sp
.fi
.\" end_example
Curved high order Pk triangles (k >= 1), in 2d or 3d geometries, are supported.
These triangles have additional edge-nodes and face-nodes.
.SH THESE NODES ARE NUMBERED AS
 first vertex, then edge-node, following
the edge numbering order and orientation, and finally the face internal nodes,
following the triangle lattice.
See below for edge numbering and orientation.
.\" begin_example
.Sp
.nf
      2               2               2
      | +             | +             | +
      |   +           7   6           9   8
      5     4         |     +        10 14  7
      |       +       8   9   5      11 12 13 6
      |         +     |         +     |         +
      0-----3-----1   0---3---4---1   0--3--4--5--1
            P2              P3              P4
.Sp
.fi
.\" end_example
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
const size_t dimension = 2;
const Float  measure = 0.5;
const size_t n_vertex = 3;
const point vertex [n_vertex] = {
        point(0, 0),
        point(1, 0),
        point(0, 1) };
const size_t  n_edge = 3;
const size_t edge [n_edge][2] = {
        { 0, 1 },
        { 1, 2 },
        { 2, 0 } };
.Sp
.fi
.\" end_example