| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 441262 | Computer Aided Geometric Design | 2010 | 12 Pages |
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.
Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (41 K)Download as PowerPoint slideResearch highlights► 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.
