ABSTRACT
There is a need for a robust, simple set of tools for deriving topology from geometric co-ordinates, or validating whether the stated topology reflects the underlying geometry. This objective is distinct from the aims of solid modelling where the emphasis is more on the dynamic creation of models by addition, deletion or movement of points, lines, planes and volumes. This chapter discusses one possible set of geometric calculations that can be used to determine topology. It explains these calculations in three-dimensional space, where both the geometry and the topology are more complex than in two-dimensional space. The most complicated interaction between topological primitives is the intersection of cells. The importance of determining efficient and reliable algorithms for lower dimensional topological primitives can be seen from the fact that the higher dimensional algorithms use the lower dimensional algorithms repeatedly.
