Random sampling of a cylinder yields a not so nasty Delaunay triangulation

Dense point sets have sparse Delaunay triangulations: or "... but not too nasty"

Dense Point Sets Have Sparse Delaunay Triangulations ∗ or “ . . . But Not Too Nasty ” Jeff

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R3 with spread ∆ has complexity O(∆3). This bound is tight in the worst case for all ∆ = O( √ n). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to re...

Variable Radii Poisson - Disk Sampling extended version

We introduce three natural and well-defined generalizations of maximal Poisson-disk sampling. The first is to decouple the disk-free (inhibition) radius from the maximality (coverage) radius. Selecting a smaller inhibition radius than the coverage radius yields samples which mix advantages of Poisson-disk and uniform-random samplings. The second generalization yields hierarchical samplings, by ...

Sets Have Sparse Delaunay Triangulations ∗ or “ . . . But Not Too Nasty ”

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R3 with spread ∆ has complexity O(∆3). This bound is tight in the worst case for all ∆ = O( √ n). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to re...

Self-delaunay Meshes for Surfaces

In the Euclidean plane, a Delaunay triangulation can be characterized by the requirement that the circumcircle of each triangle be empty of vertices of all other triangles. For triangulating a surface S in R3, the Delaunay paradigm has typically been employed in the form of the restricted Delaunay triangulation, where the empty circumcircle property is defined by using the Euclidean metric in R...