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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 200
Setname	ir_computersa
ID	105796
OCR Text	Show 184 206. Hayes, Jeffrey G. "New Shapes from Bicubic Splines", Report No. V.58, Division of Numerical Analysis and Computing, National Physical Laboratory, Teddington, Middlesex, England, September 1914. 201. Hayes, Jeffrey G. "Data-Fitting Algorithms Available, in Preparation, and in Prospect for the NAC Library", Report No. NPLDNACS- 5118, Division of Numerical Analysis and Computing, National Physical Laboratory, Teddington, Middlesex, England, 1918. 208. Hayes, J. G. and Halliday, J. "The Least-Squares Fitting of Cubic Spline Surfaces to General Data Sets", !l.. Inst. Maths. Applics., Vol. 14, 1914, pp. 89-103. 209. Hazony, Y. "Algorithms for Parallel Processing Curve and Surface Definition with Q-splines", Computers and Graphics, Vol. 4, No. 3-4, 1919, pp. 165-16. 210. Herron, Gary J. Triangular and Multisided Patch Schemes, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, 1919. 211 • . Hinds, J. K. and Kuan, L. P. "Surfaces De fined by Curve Transformations". In Proceedings of the Fifteenth Numerical Control Society Annual Meeting and Technical conference, April 1918, pp. 325- 340. 212. Horn, Bertram. "Circle Generators for Display Devices", Computer Graphics and Image Processing, Vol. 5, 1916, pp. 280-288. 213. Hosaka, M. and Kimura, F. "Synthesis Methods of Curves and Surfaces in Interactive CAD". In Proceedings of the International Conference Interactive Techniques in Computer Aided DeSign, IEEE Computer SOCiety, Bologna, 21 - 23 September 1918, pp. 151-156. 214. Hughes, G. and Hankins, H. "Precision Hardware Circular-Arc Generation for Computer Graphic-Display Systems Using Line SegmentData", Proceedings of the IEEE, Vol. 120, No.2, February 1913, pp. 206-212. 215. Ichida, K.; Yoshimoto, F.; and Kiyono, T. "Curve Fitting by a One Pass Method with a Piecewise Cubic Polynomial", ACM Transactions 􁪽􋵍 Mathematical Software, Vol. 3, 1911, pp. 164-114.--- 216. Jiachang, S. "A Class of Matrix Methods for Surface Representation". In Proceedings of the CAD80 Conference, IPC Science and Technology Press, Ltd., Guildford, England, March 1980, pp. 251- 254.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105796