Higher order Delaunay triangulations

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...

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...

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...

Drainage reality in terrains with higher-order Delaunay triangulations

Terrains are often modeled by triangulations. One of the criteria that a triangulation should have is “nice shape” triangles. Delaunay triangulation is a good way to formalize nice shape. Another criterion is reality of drainage in terrains. Natural terrains do not have many local minima and have drainage lines in the bottom of valleys. To achieve these characteristics, higher-order Delaunay tr...