Abstract
The cubicB-spline representation provides the local interaction properties and the sufficient order of continuity required in free-form curve and surface modelling in CAD. Basic problems are nevertheless encountered when applyingB-splines to interpolation, where they have global behavior. In this paper, we present theB2-spline formulation, a superset of theB-splines with local interpolation properties. Besides providing the local interpolation access, theB2-spline interaction operations can also be used directly as aB-spline modelling interface. Modelling aplications are discussed especially with the skinning method for interpolating surfaces through curve networks.
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References
Barsky BA (1981) The beta-spline: a local representation based on shape parameters and fundamental geometric measures. PhD dissertation, Dept of Computer Science, University of Utah
Barsky BA (1982) End conditions and boundary conditions for uniformB-spline curve and surface representations. Computers in Industry 3(1/2):17–29
Böhm W (1980) Inserting new knots intoB-spline curves. CAD 12(4):199–201
Catmull E, Clark J (1978) Recursively generatedB-spline surfaces on arbitrary topological meshes. CAD 10(6):350–355
Cohen E, Lyche T, Riesenfeld R (1980) DiscreteB-splines and subdivision techniques in computer-aided geometric design and computer graphics. Comput Graph Image Proc 14(2):87–111
DeBoor C (1978) A practical guide to splines. Springer, New York Berlin Heidelberg Tokyo
Faux ID, Prett MJ (1979) Computational geometry for design and manufacture. Ellis Horwood/Halstead Press, Chichester
Fournier A, Barsky BA (1985) Geometric continuity with interpolating Bézier curves. In: Magnenat-Thalmann N, Thalmann D (eds) Computer Generated Images. Springer, New York Berlin Heidelberg Tokyo pp 153–158
Riesenfeld RF (1973) Applications ofB-spline approximation to geometric problems of computer aided design. PhD dissertation, Dept of Systems and Information Science, Syracuse University
Tiller W (1983) RationalB-splines for curve and surface representation. IEEE Comput Graph Appl 3(6):61–69
Varady T (1985) Integration of free-form surfaces into volumetric modeller. Dissertation, Hungarian Academy of Sciences
Woodward CD (1987a) Cross-sectional design ofB-spline surfaces. Comp Graph 11(2):193–201
Woodward CD (1987b) Skinning techniques for interactiveB-spline surface interpolation. CAD (to be published)
Woodward CD (1987c) Video presentation at CG International '87, Japan
Wu S-C, Abel JF, Greenberg DP (1977) An interactive computer graphics approach to surface presentation. CACM 20(10):703–712
Yamaguchi F (1978) A new curve fitting method using a CRT display. Comput Graph Image Proc 7(3):425–437
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Woodward, C.D. B2-splines: a local representation for cubic spline interpolation. The Visual Computer 3, 152–161 (1987). https://doi.org/10.1007/BF01962896
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DOI: https://doi.org/10.1007/BF01962896