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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 189
Setname	ir_computersa
ID	105785
OCR Text	Show 173 80. Brewer, John A. and Anderson, David C. "Visual Interaction with Overhauser Curves and Surfaces". In Proceedings of SIGGRAPH '77, ACM, July 1977, pp. 132-137. 81. Brodlie, K. W. (editor). Mathematical Methods in Computer Graphics and Design, Academic Press, New York, 1979. 82. Brown, Bruce E. Modeling of Solids for Three-Dimensional Finite Element Analysis, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, June 1974. 83. Brown, James H. Conformipg and Nonconforming Finite Element Models for Curved Regions, Ph.D. Thesis, University of Dundee, Scotland, June 1976. 84. Brueckner, I. "Construction of Bezier Points of Quadilaterals from Those of Triangles", Computer-Aided Design, Vol. 12, No.1, January 1980, pp. 21-24. 85. Calu, Johan V. J. Implementation of Surface Interpolation for Computer Graphics, Master's Thesis, University of Utah, Salt Lake-City, Utah, December 1974. 86. Carpenter, Loren C. "Computer Rendering of Fractal Curves and Surfaces", Communications of the ACM. To appear. 87. Catmull, Edwin E. ! Subdivision Algorithm for Computer Display of Curved Surfaces, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, December 1974. Also Tech. Report No. UTEC-CSc-74-133, Department of Computer Science, University of Utah. 88. Catmull, Edwin E. "Computer Display of Curved Surfaces". In Proceedings of the IEEE Conference on Computer Graphics, Pattern Recospition, and Data Structure, LoS-Angeles, 14 - 16 May 1975, pp. 11-17. 89. Catmull, Edwin E. and Clark, James H. "Recursively Generated Bspline Surfaces on Arbitrary Topological Meshes", Computer-Aided Design, Vol. 10, No.6, November 1978, pp. 350-355. -- 90. Catmull, Edwin E. and Rom, Raphael J. "A Class of Local Interpolating Splines". In Computer Aided Geometric Design, edited by Barnhill, Robert E. and Riesenfeld, Richard F., Academic Press, New York, 1974, pp. 317-326. 91. Cerny, H. F. "F-curve and F-surface Layout", Document No. D2- 23924-1, Boeing Company, Seattle, Washington, March 1965.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105785