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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

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Title	Page 198
Setname	ir_computersa
ID	105794
OCR Text	Show 182 184. Gould, S. S. "Surface Programs for Numerical Control". 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. 185. Gouraud, Henri. Computer Display of Curved Surfaces, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, June 1971. Also Tech. Report No. UTEC-CSc-71-113, Department of Computer SCience, University of Utah and in IEEE Transactions on Computers, Vol. C-20, June 1971, p. 623-629 •• 186. Green, P. J. and Sibson, R. "Computing Dirichlet Tessellations in the Plane", The Computer Journal, Vol. 21, No.2, April 1978, pp. 168-173. - 187. Gregory, John A. "Symmetric Smooth Interpolation on Triangles", Tech. Report No. T/34, Brunel University, Uxbridge, Middlesex, 1973. 188. Gregory, John A. "Smooth Interpolation without Twist Constraints.". In Computer Aided Geometric Design, edited by Barnhill, Robert E. and Riesenfeld, Richard F., Academic Press, New York, 1974, pp. 71-87. 189. Gregory, John A. Piecewise Interpolation Theory for Functions of Two Variables, Ph.D. Thesis, Brunel University, Uxbridge, Middlesex, 1975. 190. Gregory, John A. "A C1 Triangular Interpolation Patch for Computer-Aided Geometric Design", Computer Graphics and Image Processing, Vol. 13, No.1, May 1980, pp. 80-87. 191. Gylys, V. B. "Evaluation of Sculptured Surface Techniques", lIT Research Institute, 1967. 192. Haber, Robert; Abel, John F.; and Greenberg, Donald P. "A Computer-Aided Design System for Funicular Network Structures". In Proceedings of the Third International Conference and Exhibition on Computers in Engineering and Building Design, IPC Science and Technology Press, Ltd., Guildford, England, 1978, pp. 212-222. 193. Haber, Robert; Mutryn, Thomas A.; Abel, John F.; and Greenberg, Donald P. "Computer-Aided Design of Framed Dome Structures with Interactive Graphics", Computer-Aided Design, VoL 9, No.3, July 1977, pp. 157-164. 194. Haber, Robert; Shepard, Mark; Abel, John F.; Gallagher, Richard H.; and Greenberg, Donald P. "A Generalized Graphic Preprocessor for Two-Dimensional Finite Element Analysis". In Proceedings of SIGGRAPH '78, ACM, August 1978, pp. 323-329.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105794