A combined geometrical and topological simplification hierarchy for terrain analysis

Abstract

We consider the problem of modeling a terrain from both a geometric and a morphological point of view for efficient and effective terrain analysis on large data sets. We devise and implement a simplification hierarchy for a triangulated terrain, where the terrain is represented as a triangle mesh and its morphology is described by a discrete Morse gradient field defined on the basis on the elevation values given at the vertices of the mesh. The discrete Morse gradient is attached to the triangles, edges and vertices of the mesh. We define a new edge-contraction operator for the edges of the triangle mesh, which does not change the behavior of the gradient flow and does not create new critical points, and we apply it to the original full-resolution mesh in combination with a topological simplification operator which eliminates critical simplices in pair. We build the simplification hierarchy based on suitably combining such operators and we evaluate it experimentally.