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Geometrically continuous splines on surfaces of arbitrary topology

Banff International Research Station for Mathematical Innovation and Discovery

We study the space of geometrically continuous splines, or piecewise polynomial functions, on topological surfaces. These surfaces consist of a collection of rectangular and triangular patches together with gluing data that identifies pairs of polygonal edges. A spline is said to be G1-geometrically continuous on a topological surface if they are C1-continoous functions across the edges after the composition by a transition map. In the talk we will describe the required compatibility conditions on the transition maps so that the C1-smoothness is achieved, and give a formula for a lower bound on the dimension of the G1 spline space. In particular, we will show that this lower bound gives the exact dimension of the space for a sufficiently large degree of the polynomials pieces. We will also present some examples to illustrate the construction of basis functions for splines of small degree on particular topological surfaces. *This is a joint work with Bernard Mourrain and Raimundas Vidunas.

Mathematics; Algebraic geometry; Computer science; Applied computer science

video/mp4

Author affiliation: RICAM Austrian Academy of Sciences

2017-02-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60565

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/