Constrained higher order Delaunay triangulations

Constrained higher order Delaunay triangulations

We extend the notion of higher-order Delaunay triangulations to constrained higherorder Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nk log n log k, n log n)) time. We show that the completion of a set of useful order-k Delaunay edges may have order 2k − 2, which is worst-case optimal. We give an algorithm for the lowest-ord...

Higher Order Delaunay Triangulations

Towards a Definition of Higher Order Constrained Delaunay Triangulations

When a triangulation of a set of points and edges is required, the constrained Delaunay triangulation is often the preferred choice because of its well-shaped triangles. However, in applications like terrain modeling, it is sometimes necessary to have flexibility to optimize some other aspect of the triangulation, while still having nicely-shaped triangles and including a set of constraints. Hi...

Optimal Higher Order Delaunay Triangulations of Polygons

This paper presents an algorithm to triangulate polygons optimally using order-k Delaunay triangulations, for a number of quality measures. The algorithm uses properties of higher order Delaunay triangulations to improve the O(n) running time required for normal triangulations to O(kn log k + kn log n) expected time, where n is the number of vertices of the polygon. An extension to polygons wit...

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...