Thursday, November 9
MS9
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
8/28/95