Jorg Peters, the 2025 Pierre Bézier Award Recipient
- Personal Website: https://www.cise.ufl.edu/~jorg/
The 2025 SMA Bézier Award is awarded to Professor Jorg Peters in recognition of his outstanding contributions to original theory and tools for the constructive design of free-form surfaces and volumes – in spline, Bézier, subdivision and implicit form – and to solving differential equations on such surfaces and in volumes.
Over the past decades, Peters’ work has contributed original theory and tools for the construction and design of manifolds (with over 6000 google citations) – in spline, Bézier, subdivision and implicit representations – with particular emphasis on making the difficult irregular and singular configurations as easy to work with as the classical, regular case. Peters’ lower bound proofs and efficient algorithms for smooth manifolds have settled a number of hard open problems in constructive theory; and their efficient use in geometric computing, computer graphics and engineering analysis found significant application in practice.
As an example of use in practice, as reported by Tom Grandine, Peters’ pixel-accurate display of trimmed splines on the GPU is now used by Boeing Corp. as their main quality control visualization tool. Peters’ pixel-accurate rendering revealed unknown oscillations in the outer surface and showed gaps due to trimming (not visualization) accuracy. Pixel-accurate rendering relies on Peters’ concept and algorithms for constructing a subdividable linear efficient equispaced function enclosure (SLEEVE), that minimizes the max-norm distance between splines and a two-sided piecewise linear enclosure.
Peters’ joint work with U. Reif (1000 citations) established the standard for the theory of subdivision surface algorithms. The fundamental analytic techniques were collected in the 2008 Springer monograph Subdivision Surfaces. The work shows that the limit of subdivision surfaces can only be understood through the differential geometry of a nested sequence of spline rings — and not naively as the refinement of a control net. The widely-used Catmull-Clark subdivision has shape-deficiencies and refines at a non-uniform speed near the extraordinary points. Peters’ latest joint work with K. Karciauskas on evolving guide subdivision generates “class A” high-quality subdivision surfaces at the same cost as the classical solutions. Moreover, guided subdivision algorithms offer more uniform refinement and have directly served as finite elements for engineering analysis.
Peters’ work on Polyhedral-net Splines, a finite, CAD-compatible alternative to subdivision algorithms, is available as an ACM algorithm package, commercially, for high-end design, and provides finite elements for computing on such domains.