Fast reconstruction of Delaunay triangulations

Fast reconstruction of delaunay triangulations

We present a new O(n) algorithm to compute good orders for the point set of a Delaunay triangulation of n points in the plane. Such a good order makes reconstruction in O(n) time with a simple algorithm possible. In contrast to the algorithm of Snoeyink and van Kreveld [1], which is based on independent sets, our algorithm uses a breadth rst search (BFS) to obtain these orders. Both approaches ...

Linear-Time Reconstruction of Delaunay Triangulations with Applications

Many of the computational geometers' favorite data structures are pla-nar graphs, canonically determined by a set of geometric data, that take (n log n) time to compute. Examples include 2-d Delaunay triangulation, trapezoidations of segments, and constrained Voronoi diagrams, and 3-d convex hulls. Given such a structure, one can determine a permutation of the data in O(n) time such that the da...

Restricted Constrained Delaunay Triangulations

We introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...

Blocking Delaunay triangulations

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex posit...

Higher Order Delaunay Triangulations