Local Order Types

Abstract

This thesis considers past research on the order type of point configurations and introduces a variation on this concept: the local order type. The regular order type is a mapping that assigns to each ordered triple of points the orientation of these three points: positive, neutral or negative. The local order type is a similar mapping but only considers a subset of all triples. In order to decide which triples are included in the order type, a triple selection method must be chosen. We present six different methods and some of their properties. For one of these variations, the Delaunay order type, we give algorithms to compare and enumerate them. For the extended Delaunay order type we present similar but incomplete algorithms, that can be completed by solving two open problems.