We present a definition of a pointed Delaunay pseudotriangulation of a simple polygon. We discuss why our definition is reasonable. Our approach will be motivated from maximal locally convex functions, and extends the work of Aichholzer et al.[1]. Connections between the polytope of the pointed pseudotriangulations and the Delaunay pseudo-triangulation will be given.

A b s t r a c t. Chew and Dobkin et. al. have shown that the Delaunay triangulation and its variants are sparse approximations of the complete graph, in that the shortest distance between two sites within the triangulation is bounded by a constant multiple of their Euclidean separation. In this paper, we show that other classical triangulation algorithms, such as the greedy triangulation, and m...

Skeleton is an important 1-D descriptor of polygon and a useful tool for advanced geometric algorithms. However the skeleton that most existing algorithms investigated is the longest one, which is not intended in all circumstances. This paper proposes an algorithm for extracting hierarchically optimal skeleton network of polygons. The algorithm incorporates length, angularity and area of associ...

This paper describes the derivation of an empirically ee-cient parallel two-dimensional Delaunay triangulation program from a theoretically eecient CREW PRAM algorithm. Compared to previous work, the resulting implementation is not limited to datasets with a uniform distribution of points, achieves signiicantly better speedups over good serial code, and is widely portable due to its use of MPI ...

We describe the implementation of algorithms to construct and maintain threedimensional dynamic Delaunay triangulations with kinetic vertices using a threesimplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vert...

This paper presents in detail how the techniques described in my previous work [Kallmann et al., 2003] can be used for efficiently computing collision-free paths in a triangulated planar environment. The method is based on a dynamic Constrained Delaunay Triangulation (CDT) where constraints are the obstacles in the planar environment. The main advantage of relying on a triangulated domain is th...

This paper introduces a visibility relation v (and the strong visibility relation ⩕ v) on proximal Delaunay meshes. A main result in this paper is that the visibility relation v is equivalent to Wallman proximity. In addition, a Delaunay triangulation region endowed with the visibility relation v has a local Leader uniform topology.

Isotropic tetrahedron meshes generated by Delaunay refinement algorithms are known to contain a majority of well-shaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicity. The solution which explicitly perturbs the slivers through random vertex relocation and ...

Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering technique that confirms most bi-cells whose...