| ACS Algorithms for Complex Shapes with Certified Numerics and Topology Spherical approximation of convex shapes (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413 Given points in convex position in three dimensions, we want to find an approximating convex surface consisting of spherical patches, such that all points are within some specified tolerance bound ε of the approximating surface. We describe a greedy algorithm which constructs an approximating surface whose spherical patches are associated to the faces of an inscribed polytope formed from a subset of the input points. We show that deciding whether an approximation with not more than a given number of spherical patches exists is NP-hard by a reduction from planar 3SAT. 1 | |||||||||||||||
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