Simplicial diffeomorphisms

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.

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► What happens with barycentric coordinates when the linear precision property is relaxed?
► The answer can be viewed as a non-linear warping over a simplicial complex.
► We call this warping a Simplicial Diffeomorphism (SD).
► The composition of SD's with piecewise linear functions results in curved patches.
► We show how to model complex hypersurfaces gluing such curved patches.