Beyond Bézier: New Curve Modelling Techniques by Prof Kai Hormann

Abstract

Bézier and rational Bézier curves are indispensable for CAGD due to their numerous favourable properties and the fact that they provide the user with intuitive tools for editing their shape. In the first part of this talk, we explore the barycentric form of rational Bézier curves and the additional editing possibilities that it offers. In the second part, we will learn about GL-k curves, which provide a novel way to control high-degree polynomial curves via a control polygon that is closer to the curve than the Bézier control polygon, thus offering more intuitive shape control.

Biography

Kai Hormann is a full professor in the Faculty of Informatics at the Università della Svizzera italiana (USI) in Lugano. His research focusses on the mathematical foundations of geometry processing algorithms and their applications in computer graphics and related fields. In particular, he is working on generalized barycentric coordinates, subdivision of curves and surfaces, barycentric rational interpolation, and dynamic geometry processing. Professor Hormann has published over 100 highly cited papers in the professional literature and is an associate editor for the journals "Computer Aided Geometric Design" and "IEEE Transactions on Visualization and Computer Graphics". He served as chair of the SIAM Activity Group on Geometric Design in 2017/2018 and has been entrusted with the chairmanship of the steering board of the international conference Geometric Modeling and Processing (GMP) since 2017. In June 2024, he received the John A. Gregory Award for his fundamental contributions to and the lifetime impact on the field of geometric modeling, and in October 2025, he became an SMA Fellow, honouring his distinguished record of research, accomplishment, and publication in areas of solid modeling.