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Abstract:
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 S2, 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.
