Geometry independence for a meshing engine for 2D manifolds

The ‘meshing engine’ of the title is a software component that generates unstructured triangular meshes of two-dimensional triangles for a variety of contexts. The mesh generation is based on the well-known technique of iterative Delaunay refinement, for which the Euclidean metric is intrinsic. The meshing engine is to be connected to applications specific host programs which can use a geometry that is different from the intrinsic geometry of the mesh, i.e. locally, the Euclidean plane. An application may require a surface mesh for embedding in a three-dimensional geometry, or it might use a Riemannian metric to specify a required anisotropy in the mesh, or both. We focus on how the meshing engine can be designed to be independent of the embedding geometry of a host program but conveniently linked to it. A crucial tool for these goals is the use of an appropriate local co-ordinate system for the triangles as seen by the meshing engine. We refer to it as the longest edge co-ordinate system. Our reference to ‘linking’ the meshing engine and host system is both general and technical in the sense that the example meshes provided in the paper have all been generated by the same object code of a prototype of such a meshing engine linked to host programs defining different embedding geometries