Pii: S0925-7721(01)00012-8

The point in polygon problem for arbitrary polygons

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even-odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

Orienting Polyhedral Parts by Pushing

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.

Rotational polygon overlap minimization and compaction

An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1, P2, P3, . . . , Pk in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any perturbation of the polygons increases the overlap. Overlap minimization is modified to create a p...

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.