Simplicial sets and triangular patches

This work fits into the domain of topology-based geometric modeling. An assembling of non-overlapping patches can be interpreted as a subdivision of a geometric object into cells of different dimensions and a combinatorial structure can be associated with it. More precisely, our study deals with the manipulation of simplicial sets imbedded on triangular patches. We give the definition and properties of simplicial sets and triangular Bezier spaces and discuss the relationship between these two entities. The advantages of this approach are developed and some construction operations for the manipulation of this structure are presented