A Simple Mesh Generator in Matlab

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 usu...

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Bibliographic Details
Published inSIAM review Vol. 46; no. 2; pp. 329 - 345
Main Authors Persson, Per-Olof, Strang, Gilbert
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.2004
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Online AccessGet full text
ISSN0036-1445
1095-7200
DOI10.1137/S0036144503429121

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Abstract 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.
AbstractList 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.
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. [PUBLICATION ABSTRACT]
Author Persson, Per-Olof
Strang, Gilbert
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  surname: Strang
  fullname: Strang, Gilbert
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15775084$$DView record in Pascal Francis
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Issue 2
Keywords Graphics
Scientific computation
Applied mathematics
Linear structure
Mesh generator
Computer graphics
Delaunay triangulation
Linear relation
Computing
MATLAB
Language English
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Snippet Creating a mesh is the first step in a wide range of applications, including scientific computing and computer graphics. An unstructured simplex mesh requires...
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SubjectTerms 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
Title A Simple Mesh Generator in Matlab
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