[Forschungsseminar-BSV] Research Seminar 'Computer Graphics, Image Processing, and Visualization'

[Tom Liebmann]

I N V I T A T I O N

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to the Research Seminar 'Computer Graphics, Image Processing, and
Visualization'

    on Wednesday, February 6th, 2019, at 1:15 PM,
    in Room P-701 in the Paulinum, Augustusplatz.

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A talk will be given by

    Eugene Zhang
    Oregon State University

and is entitled

    "Interactive Design and Visualization of Branched Covering Spaces".

Abstract:

   Branched covering spaces are a mathematical concept which originates
   from complex analysis and topology and has applications in tensor
   field topology and geometry remeshing. Given a manifold surface and
   an N-way rotational symmetry field, a branched covering space is a
   manifold surface that has an N-to-1 map to the original surface
   except at the ramification points, which correspond to the
   singularities in the rotational symmetry field.

   Understanding the notion and mathematical properties of branched
   covering spaces is important to researchers in tensor field
   visualization and geometry processing, and their application areas.
   In this paper, we provide a framework to interactively design and
   visualize the branched covering space (BCS) of an input mesh surface
   and a rotational symmetry field defined on it. In our framework, the
   user can visualize not only the BCSs but also their construction
   process. In addition, our system allows the user to design the
   geometric realization of the BCS using mesh deformation techniques
   as well as connecting tubes. This enables the user to verify
   important facts about BCSs such as that they are manifold surfaces
   around singularities, as well as the Riemann-Hurwitz formula which
   relates the Euler characteristic of the BCS to that of the original
   mesh. Our system is evaluated by student researchers in scientific
   visualization and geometry processing as well as faculty members in
   mathematics at our university who teach topology. We include their
   evaluations and feedback in the paper.

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On behalf of Professor Scheuermann all those interested are cordially
invited to attend.

Yours sincerely
Tom Liebmann