Degree Reduction for NURBS Symbolic Computation on Curves

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IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06)

Matsushima, Japan

June 14-June 16

ISBN: 0-7695-2591-1

	ASCII Text	x
	Xianming Chen, Richard F. Riesenfeld, Elaine Cohen, "Degree Reduction for NURBS Symbolic Computation on Curves," Shape Modeling and Applications, International Conference on, pp. 28, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06), 2006.

	BibTex	x
	@article{ 10.1109/SMI.2006.10, author = {Xianming Chen and Richard F. Riesenfeld and Elaine Cohen}, title = {Degree Reduction for NURBS Symbolic Computation on Curves}, journal ={Shape Modeling and Applications, International Conference on}, volume = {0}, year = {2006}, isbn = {0-7695-2591-1}, pages = {28}, doi = {http://doi.ieeecomputersociety.org/10.1109/SMI.2006.10}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - CONF JO - Shape Modeling and Applications, International Conference on TI - Degree Reduction for NURBS Symbolic Computation on Curves SN - 0-7695-2591-1 SP EP A1 - Xianming Chen, A1 - Richard F. Riesenfeld, A1 - Elaine Cohen, PY - 2006 KW - NURBS symbolic computation KW - degree reduction KW - zero curvature KW - critical curvature KW - torsion KW - evolute KW - focal curve KW - tangent developable KW - normal scroll KW - binormal scroll KW - rectifying developable KW - bisector curve KW - bisector surface VL - 0 JA - Shape Modeling and Applications, International Conference on ER -

Xianming Chen, University of Utah, USA

Richard F. Riesenfeld, University of Utah, USA

Elaine Cohen, University of Utah, USA

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SMI.2006.10

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.

Index Terms:

NURBS symbolic computation, degree reduction, zero curvature, critical curvature, torsion, evolute, focal curve, tangent developable, normal scroll, binormal scroll, rectifying developable, bisector curve, bisector surface

Citation:

Xianming Chen, Richard F. Riesenfeld, Elaine Cohen, "Degree Reduction for NURBS Symbolic Computation on Curves," smi, pp.28, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06), 2006

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