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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 192
Setname	ir_computersa
ID	105788
OCR Text	Show 176 116. Coons, Steven A. "Constrained Least Squares", Computers and Graphics, Vol. 3, 1978, pp. 43-47. 117. Coons, Steven A. and Herzog, Bertram. "Surfaces for ComputerAided Aircraft Design, Paper 67-895". In American Institute of Aeronautics and Astronautics, 1967. 118. Cox, Morris G. and Hayes, Jeffrey G. "Curve Fitting: A Guide and Suite of Programs for the Non-specialist User", Report No. NPLDNACS- 26, National Physical Laboratory, Teddington, Middlesex, England, 1973. 119. Creutz, Guenter and Schubert, Christian. "An Interactive Line Creation Method Using B-splines", Computers and Graphics, Vol. 5, No. 2-4, 1980, pp. 69-78. 120. Danielsson, Per-Erik. "Incremental Curve Generation", IEEE Transactions 􁪽􋵃 Computers, Vol. C-19, No.9, September 1970, pp. 783- 793. 121. Danielsson, Per-Erik. "Comments on Circle Generator for Display Devices", Computer Graphics and Image Processing, Vol. 7, No.2, April 1978, pp. 300-301. 122. DATASAAB. "FORMEL.A General Description", Reg. No. 917-E, SAAB Aktiebolag 58188, Linkoping, Sweden, 1965. 123. Dimsdale, B. "Bicubic Patch Bounds", Comp. & Maths. with 􁪽􋴮. , Vol. 3, No.2, 1977, pp , 95-104. 124. Dimsdale, B. and Burkley, R. M. "Bicubic Patch Surfaces for High-Speed Numerical Control Processing", IBM􁪽􋴮. Res. and Develop., 1976, pp. 358-367. 125. Dimsdale, B. and Johnson, K. "Multiconic Surfaces", IBM 􁪽􋴮. Res. and Develop., Vol. 19, No.6, 1975, pp. 523-529. 126. Dokken, Tor and Ulfsby, Stig. "Specifications of the Modules for Sculptured Surfaces", GPM Report No.5, Central Institute for Industrial Research, 1979. 127. Dollries, J. F. "Three-Dimensional Surface Fit and Numerically Controlled Machining from a Mesh of Points", Technical Information Series Report No. R63FPD319, General Electric Company, 1963. 128. Done, G. T. S. "Interpolation of Mode Shapes: A Matrix Scheme Using Two-Way Spline Curves", The Aeronautical Quarterly, November 1965, pp. 333-349.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105788