Mathematically provable correct implementation of integrated 2D and 3D representations

Abstract

The concept of the 'Regular Polytope' has been designed to facilitate the search for a rigorous closed algebra for the query and manipulation of the representations of spatial objects within the finite precision of a computer implementation. It has been shown to support a closed, complete and useful algebra of connectivity, and support a topology, without assuming the availability of infinite precision arithmetic. This paper explores the practicalities of implementing this approach both in terms of the database schema and in terms of the algorithmic implementation of the connectivity and topological predicates and functions. The problem domains of Cadastre and Topography have been chosen to illustrate the issues.