DistMesh

The DistMesh was designed to be a simple MATLAB code for generation of unstructured triangular and tetrahedral meshes.

One reason that the code is short and simple is that the geometries are specified by Signed Distance Functions. These give the shortest distance from any point in space to the boundary of the domain. The sign is negative inside the region and positive outside. A simple example is the unit circle in 2-D, which has the distance function d=r-1, where r is the distance from the origin. For more complicated geometries the distance function can be computed by interpolation between values on a grid, a common representation for level set methods.

For the actual mesh generation, DistMesh uses the Delaunay triangulation routine in MATLAB and tries to optimize the node locations by a force-based smoothing procedure. The topology is regularly updated by Delaunay.

The boundary points are only allowed to move tangentially to the boundary by projections using the distance function. This iterative procedure typically results in very well-shaped meshes.

Our aim with this code is simplicity, so that everyone can understand the code and modify it according to their needs. The code is not entirely robust (that is, it might not terminate and return a well-shaped mesh), and it is relatively slow.

However, our current research shows that these issues can be resolved in an optimized C++ code, and we believe our simple MATLAB code is important for demonstration of the underlying principles.