A novel computation method for line-line topological relations based on conformal geometric algebra

Abstract

Topological relations computation is an important component of spatial analysis and reasoning. In the framework of Euclidean space, topological relations computation is mainly based on computational geometry methods, and it is hard to unify the computation for spatial objects of different dims. But with the birth of conformal geometric algebra (CGA), on one hand, classical geometry can be unified to a simple homogeneous algebraic framework, and with the concise and general algebraic language of CGA for geometric modeling, the classical geometry objects can be simply unified represented by the novel CGA. On the other hand, with the CGA providing fast and robust algebraic processing method for the geometric calculation, it is very easy for classical geometry's computation. This paper aims to provide a novel computation method for line-line topological relations based on CGA. It can be divided into the following two steps. First, using CGA to represent the classical geometry of line. Second, using CGA to calculate line-line topological relations. The computing process shows that the CGA can simplify the computation of line-line topological relations, and the calculation is robust and effective.