### Thomas W. Sederberg, the 2013 Pierre Bézier Award Recipient

The Bézier award committee has chosen to award the 2013 Bézier Award to Thomas W. Sederberg for his pioneering contributions to solid and physical modeling ranging from algebraic techniques and FFD to subdivision and T-splines.

Thomas W. Sederberg was introduced to geometric modeling at Brigham Young University during his masters degree research on surface reconstruction from contour lines. His PhD thesis at Purdue University applied tools from classical algebraic geometry to computer aided geometric design. That thesis showed how to compute an exact implicit equation for Bézier curves and surfaces, and revealed that the implicit equation for a generic bicubic patch is degree 18, so two generic bicubic patches intersect in a curve of algebraic degree 324. He next invented piecewise algebraic surfaces, a technique for creating low-degree implicit surfaces suitable for free-form design. Piecewise algebraic surfaces are defined using trivariate Bézier solids, a tool he also used in Free-Form Deformation. The Bézier representation was also central to his invention of the method of Bézier-clipping, a series of algorithms for robustly computing intersections.

A problem with implicitization is that the early methods, based on multivariate resultants, fail for surfaces that have base points, which many do. He solved this problem by inventing a method called “moving surfaces” that can elegantly implicitize a surface with base points. Applying this method to curves led to his discovery of the so-called mu-basis for parametric curves.

His innovation of non-uniform Catmull-Clark surfaces provided a surface representation that is a superset of both Catmull-Clark surfaces and non-uniform bicubic B-spline surfaces. His 2003 invention of T-Splines allows for local refinement of a spline surface of arbitrary topology. A subsequent paper presented a method for representing the union of two NURBS models as a single watertight T-spline. He co-founded a company to commercialize T-splines, which was acquired by Autodesk in December 2011. Because T-splines provide local refinement and watertight models, they have proven to be ideal for isogeometric analysis, which avoids the need for meshing.