Determine Vertex-to-Element Information

**MESH_VTOE**,
a MATLAB program which
uses ETOV, the element-to-vertex connectivity information, to construct
VTOE, the vertex-to-element connectivity, for a 2D mesh.

The mesh is assumed to consist of E_NUM elements, each of which is defined by E_ORDER vertices, provided in ETOV, an E_ORDER by E_NUM array.

The desired VTOE information gives, for each vertex, a list of the elements in which it occurs. It is essentially an "inverse" to ETOV, but since the number of elements that any vertex can participate in will vary, the storage for VTOE must use a scheme typically used for sparse arrays.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**MESH_VTOE** is available in
a MATLAB version.

MESH_BANDWIDTH, a MATLAB program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

MESH_DISPLAY, a MATLAB program which plots the nodes and elements of a polygonal mesh, with optional numbering.

MESH_ETOE, a MATLAB program which uses ETOV, the mesh element-to-vertex connectivity, to construct ETOE, the element-to-element connectivity.

MESH_IO, a MATLAB library which reads or writes MESH files defining a finite element mesh.

MESH_TO_XML, a MATLAB program which reads information defining a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding XML file for input to DOLFIN or FENICS.

NEIGHBORS_TO_METIS_GRAPH, a MATLAB program which reads a triangle mesh neighbor file created by TRIANGULATION_TRIANGLE_NEIGHBORS and writes a modified version of the same data suitable for input to the mesh partitioning program METIS.

QUAD_MESH, a MATLAB library which handles meshes of quadrilaterals over a 2D region;

TRIANGULATION_BOUNDARY_NODES, a MATLAB program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

TRIANGULATION_DISPLAY, a MATLAB program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;

TRIANGULATION_TRIANGLE_NEIGHBORS, a MATLAB program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.

TRIG_TO_NEIB, a C program which reads "NODE" and "ELE" files (a format prescribed by the triangle program), describing a triangulation, and produces a file defining the neighbor triangles of each element; the program can also produce information about the Voronoi diagram. The program is by Lili Ju.

VORONOI_NEIGHBORS, a MATLAB program which is given a set of points in the plane and determines the Voronoi adjacency structure, that is, which points share an edge of the Voronoi diagram.

**BOXY** is a mesh using 16 triangles and 13 nodes.

- boxy_elements.png, a plot of the mesh.
- boxy_elements.txt, the ETOV information;
- boxy_nodes.txt, the vertex coordinates.
- boxy_test.m
- boxy_test.txt, the output file.

**POOL** is a mesh using 18 quadrilaterals and 28 nodes.

- pool_elements.png, a plot of the mesh.
- pool_elements.txt, the ETOV information;
- pool_nodes.txt, the vertex coordinates.
- pool_test.m.
- pool_test.txt, the output file.

You can go up one level to the MATLAB source codes.