Friday, November 5

Tight Enclosures for Splines Via Their Control Net: Theory & Applications

1:45 PM-3:45 PM
Room: Rio Grande Ballroom

B-spline and Bernstein-Bézier representations of curves and surfaces owe much of their appeal and practical relevance for geometric design to the fact that they are closely mimicked by their control net. While the characterization of variation diminuition and convergence under subdivision decades ago has given important qualitative assurances for relying on the control net to reason about nonlinear geometry, until recently, no sharp, quantitative bounds existed to tightly and efficiently bound the distance of spline curves or surfaces from their control net. Yet such quantitative bounds are crucial for efficient rendering, intersection testing, optimal subdivision, and path planning. The speakers will give an overview over the recent results and their potential impact on practice.

Organizer: Jorg Peters
University of Florida

The order of speakers, titles. and authors have been updated.

1:45-2:10 On the Distance Between Splines and Their Control Polygon
Ulrich Reif, University of Stuttgart, Germany
2:15-2:40 Range Separation Bounds for the Distance Between a Spline and Its Control Polygon
Jorg Peters, Organizer; and David Lutterkort, Purdue University, West Lafayette
2:45-3:10 Bounds Applications: Bounded Smoothing of Polyhedra
David Lutterkort, Purdue University; and Jorg Peters, Organizer
3:15-3:40 Non-Algebraic Systems and the Convex Hull Property of L-Splines
Joachim Gaukel and Ulrich Reif, University of Stuttgart, Germany

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Created LMH, 5/18/99; Last Updated MMD, 8/2/99