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Publication Type	Technical report
School or College	College of Engineering
Department	Computing, School of
Creator	Barsky, Brian A., 1954-
Title	Beta-spline: a local representation based on shape parameters and fundamental geometric measures
Date	1981-12
Description	Abstract: A mathematical technique for curve and surface representation has been developed which reflects an underlying geometric, as opposed to algebraic nature. Elementary differential geometry concepts are reviewed and the unit tangent and curvature vectors are used as fundamental geometric measures replacing parametric derivative vectors in the continuity constraints. In addition to being more appropriate, the use of these geometric measures adds degrees of freedom which can be captured to provide further control of shape. This control is via shape parameters, beta1 and beta2, which have the property that beta1=1 indicates continuity of the parametric first derivative vector and beta1=1 with beta2=0 indicates continuity of the parametric first and second derivative vectors. The geometrical interpretation of these shape parameters and their relation to the mathematical modeling of tension is also presented. In addition to inherent tension capability, the Beta-spline representation has local control; that is, the capability of modifying one portion of the shape without altering the remainder of the shape. The combination of the geometric nature of this technique with shape control via the shape parameters as well as the presence of local control capability forms a powerful representation which will be useful in computer graphics and computer aided geometric design and modeling.
Type	Text
Publisher	University of Utah
Subject	beta-spline; geometric curves; geometric surfaces; shape parameters
Subject LCSH	Curves--Computer simulation; Surfaces--Computer simulation; Computer-aided design; Computer graphics--Research; Three-dimensional imaging--Research
Language	eng
Series	University of Utah Computer Science Technical Report
Relation is Part of	ARPANET
Format Medium	application/pdf
Format Extent	238,152,680 bytes
File Name	Barsky-The_Beta_Spline.pdf
Conversion Specifications	Original scanned with Kirtas 2400 and saved as 400 ppi uncompressed TIFF. PDF generated by LIMB™ for CONTENTdm display
ARK	ark:/87278/s64f49w4
Setname	ir_computersa
ID	105814
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4

Page Metadata

Title	Page 199
Setname	ir_computersa
ID	105795
OCR Text	Show 183 195. Hamilton, M. L. and Weiss, A. D. "An Approach to Computer-Aided Preliminary Ship Design", Tech. Report No. EWSL-™-228, M.I.T., Cambridge, Massachusetts, January 1965. 196. Hanson, Richard J. "Constrained Least Squares Curve Fitting to Discrete Data Using B-splines: A User's Guide", Numerical Mathematics Divsion, Sandia Laboratories, Albuquerque, New Mexico, February 1979. 197. HarriS, M. "SPLIFIT: An Interactive Graphics Curve Fitting Computer Program Utilizing Spline Functions", Report No. PA-TR-4677, Picatinny Arsenal, Dover, N.J., January 1974. 198. Hart, W. B. "Glider Fuselage Design with the Aid of Computer Graphics", Computer-Aided Design, Vol. 3, No.2, 1971, pp. 3-8. 199. Hart, W. B. "Current and Potential Applications to Industrial Design and Manufacture". In Proceedings of Curved Surfaces in Engineering, Churchill College, edited by Brown, I. J., IPC Science and Technology Press, Ltd., Cambridge, England, 15-17th March 1972. 200. Hart, W. B. "The Application of Computer-Aided Design Techniques to Glassware and Mould Design", Computer-Aided Design, VoL 4, No.2, 1972, pp , 57-66. 201. Hartley, P. J. and Judd, C. J. "Parametrisation of Bezier-Type B-spline Curves and Surfaces", Computer-Aided Design, Vol. 10, No.2, March 1978, pp. 130-134. 202. Hartley, P. J. and Judd, C. J. "Parametrization and Shape of Bspline Curves for CAD", Computer-Aided Design, VoL 12, No.5, September 1980, pp. 235-238. 203. Hartley, P. J. and Judd, C. J. "Curve and Surface Representations for Bezier B-spline Systmes". In Proceedings of the CAD80 Conference, IPC Science and Technology Press, Ltd., Guildford, England, March 1980, pp. 226-236. 204. Hatvany, Joseph; Newman, William M.; and Sabin, Malcolm A. "World Survey of Computer-Aided Design", Computer-Aided Design, Vol. 9, No.2, April 1977, pp. 79-98. 205. Hayes, Jeffrey G. "Available Algorithms for Curve and Surface Fitting", Report No. NPL-DNACS-39, Division of Numerical Analysis and Computing, National Physical Laboratory, Teddington, Middlesex, England, 1973 •
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105795