Pii: S0925-7721(01)00044-x

On the development of the intersection of a plane with a polytope

Define a “slice” curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy’s arm lemma to permit nonconvex “openings” of a planar convex chain.

Pii: S0925-7721(01)00015-3

In this paper we present a heuristic to reconstruct nonsmooth curves with multiple components. Experiments with several input data reveals the effectiveness of the algorithm in contrast with the other competing algorithms.  2001 Elsevier Science B.V. All rights reserved.

Pii: S0925-7721(01)00068-2

Reconstruction of polygons from visibility information is known to be a difficult problem in general. In this paper, we consider a special case: reconstruction of orthogonal polygons from horizontal and vertical visibility information and show that this reconstruction can be performed in O(n logn) time.  2002 Elsevier Science B.V. All rights reserved.

Polygonal chains cannot lock in 4d

We prove that, for all dimensions d 4, every simple open polygonal chain may be straightened, and every simple closed polygonal chain may be convexi ed. Both can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of \moves." These results contrast to those known for d = 3, where open and closed chains can be \locked."

Convexity recognition of the union of polyhedra