Pii: S0925-7721(00)00019-5

Delaunay conforming iso-surface, skeleton extraction and noise removal

Union and split operations on dynamic trapezoidal maps

We propose here algorithms to perform two new operations on an arrangement of line segments in the plane, represented by a trapezoidal map: the split of the map along a given vertical line D, and the union of two trapezoidal maps computed in two vertical slabs of the plane that are adjacent through a vertical line D. The data structure is a modiied Innuence graph, still allowing dynamic inserti...

More planar two-center algorithms

This paper considers the planar Euclidean two-center problem: given a planar n-point set S, nd two congruent circular disks of the smallest radius covering S. The main result is a deter-ministic algorithm with running time O(n log 2 n log 2 log n), improving the previous O(n log 9 n) bound of Sharir and almost matching the randomized O(n log 2 n) bound of Eppstein. If a point in the intersectio...

Pii: S0925-7721(00)00010-9

We improve previous lower bounds on the number of simple polygonizations, and other kinds of crossing-free subgraphs, of a set of N points in the plane by analyzing a suitable configuration. We also prove that the number of crossing-free perfect matchings and spanning trees is minimum when the points are in convex position.  2000 Elsevier Science B.V. All rights reserved.

Converting triangulations to quadrangulations

We study the problem of converting triangulated domains to quadrangulations, under a variety of constraints. We obtain a variety of characterizations for when a triangulation (of some structure such as a polygon, set of points, line segments or planar subdivision) admits a quadrangulation without the use of Steiner points, or with a bounded number of Steiner points. We also investigate the effe...