Simplicial diffeomorphisms Original Research Article

In this paper we will present a theory for simplicial diffeomorphims, that is, diffeomorphisms that preserve the incidence relations of a simplicial complex. Simplicial diffeomorphisms can be regarded as curvilinear barycentric coordinates. Using the combination of piecewise linear functions on complexes with simplicial diffeomorphisms, we also propose a new representation of curves and surfaces (and hypersurfaces, in general) that is simultaneously implicit and parametric.