quadrangle(6rheolef)

📦
version 7.2 · 4 versions
, in debian trixie, ubuntu noble, ubuntu questing

💖 quadrangle — reference element 💖

okay bestie, so this is a page from the rheolef manual, version 7.2 — and yes, that's quadrangle(6rheolef) if you're keeping score. it's giving geometry girl summer and i am obsessed. let's get into it 🎀

✨ NAME ✨

quadrangle — the reference element (rheolef-7.2) 🦋

🌸 DESCRIPTION 🌸

so the quadrangle reference_element(6) is literally just K = [-1,1]^2. that's it. that's the girl. 💅

           x1

           3---------2
           |         |
           |         |
           |         |
           |         |
           0---------1--->  x0

this two-dimensional reference_element(6) then gets transformed — after the Piola geometrical application — into a quadrangle in a 2D or 3D physical space, and that's what we call a geo_element(6). periodt. ✨

curved high order Pk quadrangles (k >= 1), in 2D or 3D geometries, are supported 👑. these quadrangles have extra edge-nodes and face-nodes. the way these nodes are numbered is: first the vertex, then the edge-node, following the edge numbering order and orientation, and finally the face internal nodes, following the quadrangle lattice. no cap, that's the whole system:

           3-----6-----2   3---9---8---2
           |           |   |           |
           |           |  10  14  15   7
           7     8     5   |           |
           |           |  11  12  13   6
           |           |   |           |
           0-----4-----1   0---4---5---1
                 P2              P3

🛠️ IMPLEMENTATION 🛠️

this documentation has been generated from file fem/geo_element/quadrangle.icc 🫶

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

💜 AUTHOR 💜

Pierre Saramito <Pierre.Saramito@imag.fr> — an icon, fr fr 🌟

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.

okay so real talk, bestie: there is NO WARRANTY, to the extent permitted by law. that's not me being dramatic, that's the actual text. slay responsibly. 💀

and that's the whole page, angel 💖 this was rheolef, Version 7.2, and we were looking at quadrangle(6rheolef). go forth and quadrangulate 🌈✨🦋

📦 where this page comes from