Kevin Buchin, Simon Plantinga, Günter Rote, Astrid Sturm, and Gert
Convex approximation by spherical patches
In: Abstracts of the 23rd European Workshop on Computational Geometry,
Graz, March 2007, pp. 26–29.
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 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. We
show that deciding whether an approximation with not more than a given number
of spherical patches exists is NP-hard.
Last update: April 13, 2010.