Degree Reduction for NURBS Symbolic Computation on Curves

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 r...

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Bibliographic Details
Main Authors: Chen, X., Riesenfeld, R.F., Cohen, E.
Format: Conference Proceeding
Language:English
Subjects:
binormal
bisector curve
bisector surface
critical curvature
degree reduction
evolute
focal curve
normal scroll
NURBS symbolic computation
Polynomials
rectifying developable
scroll
Shape
Solid modeling
Spline
Surface reconstruction
Surface topography
tangent developable
torsion
zero curvature
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Summary: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
DOI:10.1109/SMI.2006.10