A Simple Mesh Generator in Matlab

• Published in: SIAM review Vol. 46; no. 2; pp. 329 - 345
• Main Authors: Persson, Per-Olof, Strang, Gilbert
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.2004
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Circles; Computer science; control theory; systems; Coordinate systems; Data smoothing; Distance functions; Education; Exact sciences and technology; Geometry; Grid generation; Mathematical analysis; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Pattern recognition. Digital image processing. Computational geometry; Rectangles; Sciences and techniques of general use; Software; Studies; Triangles; Triangulation; Graphics; Scientific computation; Applied mathematics; Linear structure; Mesh generator; Computer graphics; Delaunay triangulation; Linear relation; Computing; MATLAB
• ISSN: 0036-1445; 1095-7200
• DOI: 10.1137/S0036144503429121

Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires a choice of meshpoints (vertex nodes) and a triangulation. We want to offer a short and simple Matlab code, described in more detail than usual, so the reader can experiment (and add to the code) knowing the underlying principles. We find the node locations by solving for equilibrium in a truss structure (using piecewise linear force-displacement relations) and reset the topology by the Delaunay algorithm. The geometry is described implicitly by its distance function. In addition to being much shorter and simpler than other meshing techniques, our algorithm typically produces meshes of very high quality. We discuss ways to improve the robustness and the performance, but our aim here is simplicity. Readers can download (and edit) the codes from http://math.mit.edu/~persson/mesh.