A nonuniform triangulation algorithm for planar domains with holes

We consider the problem of the generation of an adaptive triangulation on a planar domain with holes, where the desired local mesh size is defined by a given map l. For the solution of this problem, we propose a modification of the PolyFront algorithm [3]. PolyFront generates a near-uniform triangulation of a two dimensional domain with holes. It is based on a normal offsetting technique, where a domain is triangulated starting from a discretization of its boundary and constructing the mesh layer by layer going towards the interior of the domain. In particular, starting from a polygonal approximation of the boundary of the domain, the PolyFront algorithm constructs a sequence of polygons inside the domain and the region between two consecutive polygons is triangulated by using some vertices selected on the edges of these polygons. By changing the construction of these polygons and the choice of the triangulation vertices on their edges, we can obtain a nonuniform grid according to the size map l.