MESH2D is a MATLAB / OCTAVE-based unstructured mesh-generator for two-dimensional polygonal geometries, providing a range of relatively simple, yet effective two-dimensional meshing algorithms. MESH2D includes variations on the "classical" Delaunay refinement technique, a new "Frontal"-Delaunay refinement scheme, a non-linear mesh optimisation method, and auxiliary mesh and geometry pre- and post-processing facilities.
Algorithms implemented in MESH2D are "provably-good" - ensuring convergence, geometrical and topological correctness, and providing guarantees on algorithm termination and worst-case element quality bounds. Support for user-defined "mesh-spacing" functions and "multi-part" geometry definitions is also provided, allowing MESH2D to handle a wide range of complex domain types and user-defined constraints. MESH2D typically generates very high-quality output, appropriate for a variety of finite-volume and/or finite-element type applications.
MESH2D has undergone several transformations in its lifetime, having been first released in 2006 as an extension of the DISTMESH algorithm of Persson and Strang, before being updated in 2017 to its current form.
As of MESH2D release 3.0.0, the code has been completely rewritten, and is now based on a simplified version of my JIGSAW mesh-generation algorithm (a C++ code). MESH2D aims to provide a straightforward MATLAB / OCTAVE implementation of these Delaunay-based triangulation and mesh optimisation techniques.
MESH2D is a pure MATLAB / OCATVE package, consisting of a core library + associated utilities:
MESH2D::
├── MAIN-DIR. -- core MESH2D library functions. See REFINE2, SMOOTH2 and TRIDEMO, etc.
├── aabb-tree -- support for fast spatial indexing, via tree-based data-structures.
├── mesh-file -- support for mesh file text serialisation.
└── poly-data -- geometry data for example problems, image cache, etc.
After downloading and unzipping the current repository, navigate to the installation directory within MATLAB / OCTAVE and run the set of examples contained in tridemo.m:
tridemo( 0); % a very simple example to get everything started.
tridemo( 1); % investigate the impact of the "radius-edge" threshold.
tridemo( 2); % Frontal-Delaunay vs. Delaunay-refinement refinement.
tridemo( 3); % explore impact of user-defined mesh-size constraints.
tridemo( 4); % explore impact of "hill-climbing" mesh optimisations.
tridemo( 5); % assemble triangulations for "multi-part" geometries.
tridemo( 6); % assemble triangulations with "internal" constraints.
tridemo( 7); % investigate the use of "quadtree"-type refinement.
tridemo( 8); % explore use of custom, user-defined mesh-size functions.
tridemo( 9); % larger-scale problem, mesh refinement + optimisation.
tridemo(10); % medium-scale problem, mesh refinement + optimisation.
For OCTAVE users, performance can be improved by compiling elements of the MESH2D library. Running compile.m within the MESH2D installation directory will complete the build process (note: requires a -dev installation of OCTAVE).
If you make use of MESH2D in your work, please include a reference to the following:
@misc{MESH2D,
title = {MESH2D: Delaunay-based mesh generation in MATLAB},
author = {Darren Engwirda},
note = {https://github.com/dengwirda/mesh2d},
year = {2017},
}
If you make use of MESH2D please include a reference to the following! MESH2D is designed to provide a simple and easy-to-understand implementation of Delaunay-based mesh-generation techniques. For a much more advanced, and fully three-dimensional mesh-generation library, see the JIGSAW package. MESH2D makes use of the AABBTREE and FINDTRIA packages to compute efficient spatial queries and intersection tests.
[1] - Darren Engwirda, Locally-optimal Delaunay-refinement and optimisation-based mesh generation, Ph.D. Thesis, School of Mathematics and Statistics, The University of Sydney, September 2014.