A Study of the Parametric Uniform B-spline Curve and Surface Representations

Brian A. Barsky

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-83-118

1983

This publication is archived. It is kept only for reference purposes, so it is no longer being updated and may not meet accessibility standards. If you need this content in a different format, please email webteam@eecs.berkeley.edu.

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1983/Archive/CSD-83-118.pdf

This paper explains the parametric uniform B-spline curve and surface representations. The parametric representation is discussed, the properties of the B-spline representation are described, and a detailed derivation of the B-spline basis functions is presented. Various end conditions and boundary conditions are described in order to enable the B-spline user to select which of the many options would be appropriate for a particular application. Efficient algorithms are designed and analyzed for B-spline basis function evaluation, and for the evaluation and perturbation of both B-spline curves and surfaces. Finally, difference techniques to accomplish this are also developed.

BibTeX citation:

@techreport{Barsky:CSD-83-118,
    Author= {Barsky, Brian A.},
    Title= {A Study of the Parametric Uniform B-spline Curve and Surface Representations},
    Year= {1983},
    Month= {May},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/1983/5671.html},
    Number= {UCB/CSD-83-118},
    Abstract= {This paper explains the parametric uniform B-spline curve and surface representations. The parametric representation is discussed, the properties of the B-spline representation are described, and a detailed derivation of the B-spline basis functions is presented. Various end conditions and boundary conditions are described in order to enable the B-spline user to select which of the many options would be appropriate for a particular application. Efficient algorithms are designed and analyzed for B-spline basis function evaluation, and for the evaluation and perturbation of both B-spline curves and surfaces. Finally, difference techniques to accomplish this are also developed.},
}

EndNote citation:

%0 Report
%A Barsky, Brian A. 
%T A Study of the Parametric Uniform B-spline Curve and Surface Representations
%I EECS Department, University of California, Berkeley
%D 1983
%@ UCB/CSD-83-118
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/1983/5671.html
%F Barsky:CSD-83-118