Constructing Order Type Graphs using an Axiomatic Approach
Abstract
A given order type in the plane can be represented by a point set. However, it might be difficult to recognize the orientations of some point triples. Recently, Aichholzer ηl abh19 introduced exit graphs for visualizing order types in the plane. We present a new class of geometric graphs, called OT-graphs, using abstract order types and their axioms described in the well-known book by Knuth k92. Each OT-graph corresponds to a unique order type. We develop efficient algorithms for recognizing OT-graphs and computing a minimal OT-graph for a given order type in the plane. We provide experimental results on all order types of up to nine points in the plane including a comparative analysis of exit graphs and OT-graphs.
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