Cardinality Bounds for Triangulations with Bounded Minimum Angle

We consider bounding the cardinality of an arbitrary triangulation with smallest angle : We show that if the local feature size (i.e. distance between disjoint vertices or edges) of the triangulationis within a constant factor of the local feature size of the input, then N < O(1= )M where N is the cardinality of the triangulation and M is the cardinality of any other triangulation with smallest angle at least : Previous results 7, 8] had an O(1= 1= ) dependence. Our O(1= ) dependence is tight for input with a large length to height ratio, in which triangles may be oriented along the long dimension.

• Type: Conference
• Year: 1994
• Where: CCCG
• Authors: Scott A. Mitchell
• Keywords: Cardinality, CCCG 1994, CCCG 2007, Local Feature Size, Smallest Angle