Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Direct construction of polynomial surfaces from dense range images through region growing
ACM Transactions on Graphics (TOG)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Translating a Planar Object to Maximize Point Containment
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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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 give 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 an implementation of this heuristic, and show some experimental results for terrains representing three-dimensional (topographical) images of fracture surfaces of metals obtained by confocal laser scanning microscopy.