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Computer Aided Geometric Design
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Computer Aided Geometric Design
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Mean value coordinates for arbitrary planar polygons
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A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design
Efficient mesh deformation using tetrahedron control mesh
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MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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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.