Thursday, November 9

Pythagorean-Hodograph Curves

Polynomial and rational Bezier- and B-spline forms are commonly used in computer-aided design (CAD) systems for curve and surface design. However, the ``offsets'' to general polynomial and rational parametric curves (which arise in applications such as tolerance analysis and numerical-control machining) do not in general admit exact rational representations, and must therefore be approximated in existing CAD systems. The Pythagorean-hodograph (PH) curves are a special class of parametric curves that provide, among other things, the significant advantage of having rational offsets. Polynomial and rational PH curves have recently been subject to intensive research, and they have successfully been used in curve design. The speakers will describe new developments in this field, including the extension to surfaces.

Organizer: Gudrun Albrecht
Universitat Kaiserslautern, Germany

10:30 A Bird's-Eye View of New Developments Concerning Pythagorean-Hodograph Curves
Rida T. Farouki, University of Michigan, Ann Arbor
11:00 Generalizing Pythagorean-Hodograph Curves by Reparametrization
Wei Lu, Zhejiang University, People's Republic of China
11:30 Rational Pythagorean Hodograph Rosettes and Ovaloids of Constant Width
Rachid Ait Haddou and Luc Biard, Laboratoire LMC-IMAG, France
12:00 Construction of C2 Pythagorean-Hodograph Interpolating Splines by the Homotopy Method
Gudrun Albrecht, Organizer and Rida T. Farouki, University of Michigan, Ann Arbor

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