A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Polar forms for geometrically continuous spline curves of arbitrary degree
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Transfinite Surface Interpolation
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Geometric Design with Trimmed Surfaces
Geometric Modelling, Dagstuhl, Germany, 1993
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Transfinite mean value interpolation in general dimension
Journal of Computational and Applied Mathematics
From Computer Aided Design to wavelet BEM
Computing and Visualization in Science
Pointwise radial minimization: Hermite interpolation on arbitrary domains
SGP '08 Proceedings of the Symposium on Geometry Processing
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Interpolation to boundary data on the simplex
Computer Aided Geometric Design
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We propose an approach for constructing a transfinite interpolation where the domain of definition is a convex polytope. For multifaceted domains which are not of tensor product type, it is difficult to directly generalize the usual approach of transfinite interpolation which blends opposite faces and which then substracts that by a mixed term. Therefore, we suggest a short formula which uses topologic entities of the convex domain. Our formula uses some projection operator onto the faces of the polytope. Both representations (V-setting and H-setting) of a polytope are used. We show also that the transfinite interpolation is stable under affine transformations. As a supplement to the theoretical demonstrations, we show some interesting practical illustrations.