Polyhedral-net Splines for Geometry and Engineering Analysis

Speaker: Prof. Jorg Peters, University of Florida

Abstract: Control nets of splines are embedded graphs whose node x y z values scale basis functions  and whose edges define adjacency and support of the functions. The talk will illustrate this concept and focus on a new family of Polyhedral-net splines (PnS) the generalizes classical tensor-product (quad-grid layout) splines: By allowing non-grid patterns in the control net, PnS enables the modeling and parameterization of well-shaped free-form surfaces. As the talk demonstrates, the PnS surfaces have everywhere, except where not wanted, baked-in differentiability, for example curvature continuity; and PnS are fully compatible with industrial design standards allowing interplay with tools ranging from Blender to the NURBS step format. Moreover, the same PnS functions can be leveraged for engineering analysis. The talk will show how to solve the (second order) heat equation or the (fourth order, time-dependent) Cahn-Hilliard process on PnS free-form surfaces with PnS elements.

Biography: Dr. Jorg Peters is a Professor of Computer and Information Sciences at the University of Florida. His research focuses on representing, analyzing, and computing with geometry. He has developed tools for free-form modeling and design using spline, Bézier, subdivision, and implicit representations. He leads the TIPS project, enabling surgeon-educators to author virtual reality simulations with force feedback.He earned his Ph.D. in Computer Sciences from the University of Wisconsin in 1990 under advisor Carl de Boor. Dr. Peters held positions at IBM T. J. Watson Research Center and Rensselaer Polytechnic Institute before joining Purdue University were he received a National Young Investigator Award in 1994 and was tenured. In 1998, he joined the University of Florida where he is a full professor. Dr. Peters received the John Gregory Award in 2014, the highest award in geometric design. In 2024, he was elected Fellow of the Solid Modeling Association, and in 2025, he received the Bézier Award. He has served as Editor-in-Chief of the journal Graphical Models (GMOD) and as editor of ACM Transactions on Graphics. He currently serves as associate editor for journals including Computer Aided Geometric Design (CAGD), Applied Numerical Mathematics (APNUM), Computers & Mathematics with Applications (CAMWA), and Computer-Aided Design (CAD). He has chaired the SIAM Interest Group on Geometric Design. Dr. Peters and his students have developed tools such as BézierView, TIPS, and Polyhedral-Net Splines.

Host: Prof. Kai Hormann