Variational Constructions Using Algebraic Curves and Surfaces

Kdy? 22.5.2012 12:00
Kde? ZČU / FAV / KIV
Kategorie

doc. RNDr. Pavel Chalmovianský, PhD.

Fakulta matematiky, fyziky a informatiky
Univerzita Komenského
Bratislava, Slovensko

We discuss certain constructions of variational design. They are applied to modify/approximate curves/surfaces with respect to the given criteria such as distance to the set of fixed point and/or set of fixed normals at these points. For the modeling/approximation, we use mostly algebraic curves/surfaces often represented in rational form. The applications covered by these constructions are filling holes in point clouds, approximate parameterization of plane/spatial curves, non-linear subdivision scheme. In these constructions, we consider also singular points of algebraic curves/surfaces and state several properties of such points not only due to their significant influence during the optimization process on the run of the optimization. It seems to be a difficult task to understand the structure of singularities even in low dimensional cases and low degree algebraic varieties. We discuss several notions and give visual examples for them.

Přednáška proběhne v místnosti UK417.

Evropská unie, ESF, MŠMT, OP Vzdělávání pro konkurenceschopnost, ZČU

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