Interactive Design and Visualization of Branched Covering Spaces
Event date:  December 10, 2018 4:00 PM  to 5:00 PM

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.



Eugene Zhang received the PhD degree in computer science from the Georgia Institute of Technology in 2004. He is currently a Professor with Oregon State University, where he is a member in the School of Electrical Engineering and Computer Science. During part of 2011 and 2012, he was a guest professor with the Free University of Berlin and the Max-Planck-Institute in informatics. His research interests include computer graphics, scientific visualization, geometric modeling, and computational topology. He received the National Science Foundation CAREER award in 2006. He has also served as a program co-chair for CAD/CG 2013. He is a senior member of the IEEE and the ACM.





University of Stuttgart, Powerwall Room, VISUS, cellar

The talk will be transmitted to Konstanz.