## Nice Point Sets Can Have Nasty Delaunay Triangulations (2001)

Venue: | In Proc. 17th Annu. ACM Sympos. Comput. Geom |

Citations: | 49 - 5 self |

### BibTeX

@INPROCEEDINGS{Erickson01nicepoint,

author = {Jeff Erickson},

title = {Nice Point Sets Can Have Nasty Delaunay Triangulations},

booktitle = {In Proc. 17th Annu. ACM Sympos. Comput. Geom},

year = {2001},

pages = {96--105}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the complexity of Delaunay triangulations of sets of points in IR 3 under certain practical geometric constraints. The spread of a set of points is the ratio between the longest and shortest pairwise distances. We show that in the worst case, the Delaunay triangulation of u points in IR 3 with spread A has complexity il(min{A 3 , uA, u2}) and O (min{A 4, u2}). For the case A = D(v/), our lower bound construction consists of a grid-like sample of a right circular cylinder with constant height and radius. We also construct a family of smooth connected surfaces such that the Delaunay triangulation of any good point sample has near-quadratic complexity.