Refinement and hierarchical coarsening schemes for triangulated surfaces

We present a refinement and a coarsening (also simplification or decimation) algorithm for the adaptive representation of bivariate functions. The algorithms have proved to be efficient tools in numerical methods such as finite element method or image processing, [Pla00, Sua01b]. In this paper we particularize the algorithms and apply to the generation of levels of detail of terrain models. The refinement algorithm is very simple and of linear complexity in the number of vertices, and proceeds uniformly or locally in triangular meshes. The coarsening algorithm shows a complexity of O(logn) and obtains an adaptive hierarchical representation of the input terrain. We provide the most important features of the algorithms as well as the application to generate levels of detail of regions in the Gran Canaria island, an island where the topography is of great irregularity. Several experimental data are presented, including times of the meshes generated, rendering times, error evolution, suitability of the meshes and size of the generated meshes. The algorithms have been tested for VRML visualization showing a real time generation of levels of detail, and this fact is showed in the numerical experiments