# 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

May 1983

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1983/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}, Institution = {EECS Department, University of California, Berkeley}, Year = {1983}, Month = {May}, URL = {http://www.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://www.eecs.berkeley.edu/Pubs/TechRpts/1983/5671.html %F Barsky:CSD-83-118