Computing Large Planar Regions in Terrains
Katharina M. Lange, Rahul Ray, Michiel Smid, Ulrich Wendt · Electronic Notes in Theoretical Computer Science · 2001
We consider the problem of computing the largest region in a terrain that is approximately contained in some two-dimensional plane. We reduce this problem to the following one. Given an embedding of a degree-3 graph G on the unit sphere S 2, whose vertices are weighted, compute a connected subgraph of maximum weight that is contained in some spherical disk of a fixed radius. We given an algorithm that solves this problem in O(n2 log n (log log n)3) time, where n denotes the number of vertices of G or, alternatively, the number of faces of the terrain. We also give a heuristic that can be used to compute sufficiently large regions in a terrain that are approximately planar. We discuss a web-based implementation of this heuristic, and show some results for terrains representing three-dimensional (topographical) images of fracture surfaces of metals obtained by confocal laser scanning microscopy.