Page 202

Contents | 202 of 217

Download PDF | | Reference URL | Gallery View | Parent Record

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 202
Setname	ir_computersa
ID	105798
OCR Text	Show 186 228. Lane, Jeffrey M. Shape Operators for Computer Aided Geometric Design, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, June 1977. 229. Lane, Jeffrey M. and Carpenter, Loren C. "A Generalized Scan Line Algorithm for the Computer Display of Curved Surfaces", Computer Graphics and Image Processing, Vol. 11, No.3, November 1979, pp. 290- 297. 230. Lane, Jeffrey M.; Carpenter, Loren C.; Whitted, J. Turner; and Blinn, James F. "Scan Line Methods for Displaying Parametrically Defined Surfaces", Communications of the ACM, Vol. 23, No.1, January 1980, pp. 23-34. - - - 231. Lane, Jeffrey M. and Riesenfeld, Richard F. "The Application of Total Positivity to Computer Aided Curve and Surface Design", Tech. Report No. UUCS-79-115, Department of Computer Science, University of Utah, Salt Lake City, Utah, October 1979. 232. Lane, Jeffrey M. and Riesenfeld, Richard F. "A Theoretical Development for the Computer Generation of Piecewise Polynomial Surfaces", IEEE Transactions 􁪽􋵐 Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No.1, January 1980, pp. 35-46. 233. Lane, Jeffrey M. and Riesenfeld, Richard F. "A Geometric Proof of the Variation Diminishing Property of B-spline Approximation", Journal of Approximation Theory. To appear. 234. Lavick, J. J. "Computer-Aided Design at McDonnell Douglas.". In Advanced Computer Graphics -- Economics, Techniques and Applications, edited by Parslow, R. D. and Green, R. E., Plenum Press, London and New York, 1971. 235. Lawson, C. L. "Generation of a Triangular Grid with Application to Contour Plotting", Technical Memorandum No. 299, Jet Propulsion Laboratory, Pasadena, California, 1972. 236. Lawson, C. L. "C1 Compatible Interpolation Over a Triangle", Computing Memorandum No. 407, Jet Propulsion Laboratory, Pasadena, California, 1976. 237. Lawson, C. L. "Software for C1 Surface Interpolation". In Mathematical Software III, edited by Rice, John R., Academic Press, New York, 1977, pp. 161=194. 238. Lee, T. M. P. "A Class of Surfaces for Computer Display". In Proceedings of the Spring Joint Computer Conference, AFIPS Press, Montvale, N.J., 1969, pp. 309-319.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105798