Connectivity Oblivious Merging of Triangulations

Simplicial meshes are extremely useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, which tends to make the numerical simulations unstable. In this paper we propose an alternative technique for updating simplicial meshes that undergo geometric and topological changes. We exploit the property that a Weighted Delaunay Triangulation (WDT) can be used to implicitly define the connectivity of a mesh. Instead of explicitly maintaining connectivity information, we simply keep a collection of weights associated with each vertex. This approach allows for a simple way to merge triangulations, which we illustrate with examples in 2D and 3D.