Colloquium Computer Science - Lucia Romani, University of Bologna

Title: Exploiting Catmull-Clark subdivision to build interpolatory basic limit functions with raised smoothness everywhere

Abstract:

Subdivision schemes are a special class of iterative methods for generating smooth surfaces via the recursive application of local refinement rules to a given coarse initial mesh. One of the most famous subdivision schemes is the one proposed by Catmull and Clark (Computer-Aided Design, 1978) to generalize bicubic uniform B-spline surfaces to quadrilateral meshes of arbitrary topology. Although, in the regular regions, the limit surfaces generated by the Catmull-Clark scheme have continuous second derivatives, this property is not maintained at extraordinary vertices where they are only C 1 . The goal of this talk is to introduce a strategy that exploits the basic limit functions of the Catmull-Clark scheme to construct compactly supported fundamental functions for local interpolation that are C 2 at extraordinary vertices and C 3 everywhere else.

Short bio:

Lucia Romani is Full Professor of Numerical Analysis at the Mathematics Department of the University of Bologna (Italy). Professor Romani received her Ph.D. in Computational Mathematics from the University of Padua (Italy) in 2004 and spent the years between 2007 and 2018 at the Mathematics Department of the University of Milano-Bicocca (Italy). Her research interests mainly deal with geometric modelling and approximation theory, with a special focus on splines, subdivision schemes and their applications. She is author of over 70 peer- reviewed scientific papers and has participated in numerous national and international conferences as invited or plenary speaker. For some years now Professor Romani has been Associate Editor of the Elsevier journal Computer Aided Geometric Design and Co-Editor-in-Chief of the Elsevier journal of Computational and Applied Mathematics. She also industriously participates in the activities of SIAM and Solid Modeling Association. For the two-year period 2023-2024 she will be Vice Chair of the SIAM activity group on Geometric Design, and in the years 2021-2022 she was Program Director of the same group.