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

# triangle(6rheolef)

reference element (rheolef-7.2)

## NAME

triangle - reference element (rheolef-7.2)

## DESCRIPTION

The triangle **reference\_element(6)** is `K = [0,1]`.

```
    K = { 0 < x0 < 1 and 0 < x1 < 1-x0 }
    x1
    2
    | +
    |   +
    |     +
    |       +
    0---------1  x0
```

 This two-dimensional **reference\_element(6)** is then transformed, after the Piola geometrical application, as a triangle in a 2D or 3D physical space, as a **geo\_element(6)**.

Curved high order transformed **geo\_element(6)** Pk triangle (k \>= 1) are supported for 2D or 3D geometries. In these cases, the nodes of an high-order triangle are numbered as:

Note that high-order triangles have additional edge-nodes and face-nodes. These nodes are numbered as: first vertices, then edge-nodes, following the edge numbering order and orientation, and finally the face internal nodes, following the triangle lattice.

```
  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
```

## IMPLEMENTATION

This documentation has been generated from file fem/geo\_element/triangle.icc

```
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 } };
```

## 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.