Describing and Calculating of Geometry Adjacency Relation with Voronoi Tessellation

Abstract

Geometry adjacency relation is a new important spatial relationship and can help many fields of Geographic Information System (GIS). This paper described the geometry adjacency relation with topology and metric based on Voronoi model. (i) The geometry adjacency relation is an equivalence relation for an object set is proved, and more it is represented by Voronoi adjacency graph (VAG). (ii) A local computing method (V2) of geometry adjacency upon on VAG is proposed, which takes distance as a foundational operator to ensure influence neighbors. (iii) A prototype application of the V2 method to three queries of geometry adjacency is briefly discussed.