Degree Reduction for NURBS Symbolic Computation on Curves

Author

Chen, Xianming ; Riesenfeld, Richard F. ; Cohen, Elaine

Author_Institution

Sch. of Comput., Utah Univ.

fYear

2006

fDate

14-16 June 2006

Firstpage

28

Lastpage

28

Abstract

Symbolic computation of NURBS plays an important role in many areas of NURBS-based geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider include zero curvatures and critical curvatures of plane curves, various ruled surfaces related to space curves, and point/curve bisectors and curve/curve bisectors

Keywords

computational geometry; curve fitting; splines (mathematics); surface fitting; symbol manipulation; NURBS symbolic computation; critical curvature; curve-curve bisector; degree reduction strategy; geometric computation; geometric design; plane curve; point-curve bisector; rational B-splines; space curve; zero curvature; Polynomials; Shape; Solid modeling; Spline; Surface reconstruction; Surface topography; NURBS symbolic computation; binormal; bisector curve; bisector surface; critical curvature; degree reduction; evolute; focal curve; normal scroll; rectifying developable; scroll; tangent developable; torsion; zero curvature;

fLanguage

English

Publisher

ieee

Conference_Titel

Shape Modeling and Applications, 2006. SMI 2006. IEEE International Conference on

Conference_Location

Matsushima

Print_ISBN

0-7695-2591-1

Type

conf

DOI

10.1109/SMI.2006.10

Filename

1631207