Calculation for Multidimensional Topological Relations in 3D Cadastre Based on Geometric Algebra

Abstract

Maintaining topological consistency is a crucial issue for 3D cadastral modeling as this helps to represent the cadastral boundary clearly and accurately. As a result, 3D cadastral data models are mainly built on the basis of topological models that allow topology to be expressed clearly. However, topological models in Euclidean space cannot directly represent objects’ geometric information. As geometric information is important in 3D spatial analysis, 3D cadastral data models based on topological models cannot realize topological calculation and analysis. Previous research has proved that geometric and topological information for cadastral objects can be integrated and represented by conformal geometric algebra (CGA) expressions. This paper aims to realize 3D topological analysis in the cadastral field using CGA’s advantages in geometric relations computation. A calculation framework is designed on the basis of the outer product to achieve the purpose of multidimensional unity for 3D cadastral topological analysis in this paper. A calculation framework of topological relations between a boundary point (or a boundary line) and a cadastral parcel is developed. A total of 13 types of topological relations between a boundary point and a cadastral parcel and 48 types of topological relations between a boundary line and a cadastral parcel are obtained. The study indicates that the advantages of CGA in multidimensional unified representation and calculation can be used to solve problems encountered by topological models in Euclidean space.