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Publication Type	technical report
School or College	College of Engineering
Department	Computing, School of
Creator	O'Dell, Connie Lynn
Title	Approximating data with parametric B-splines for computer aided design
Date	1985-12
Description	This thesis addresses some of the difficulties that can be encountered when approximation is used as a design tool. In many cases, it is most intuitive for a designer to specify points on or near a desired contour, and approximate them with a curve. Merely computing some approximation to a set of data points is not difficult; the difficulty lies in producing an approximation that has the same general shape as the desired contour, and behaves reasonably between the data points. The smoothness and shape of a parametric approximation is affected by many factors, including the parameterization of the data points, the number of knots used and their locations, and the metric that is minimized to produce the final approximation. The interrelationships of these factors, and their effect on the resulting approximation, will be discussed. Existing methods for estimating parameters and knots will be compared to newly developed methods, which have been designed to overcome limitations of previous methods. Finally, the synthesis of these methods into an integrated approach will be explored. An approximation process has been developed which automatically determines an appropriate parametrization and knot vector, so that, with minimal user input, a discrete set of data points can be transformed into a continuous parametric B-spline curve that has the desired shape.
Type	Text
Subject	computer graphics; computer-aided design; approximation theory; B-splines
Language	eng
Bibliographic Citation	O'Dell, C. L. (1985). Approximating data with parametric B-splines for computer aided design. UUCS-85-119.
Series	University of Utah Computer Science Technical Report
Relation is Part of	ARPANET
Format Medium	application/pdf
Format Extent	33,847,742 bytes
File Name	ODell-Approximating_Data.pdf
Conversion Specifications	Original scanned with Kirtas 2400 and saved as 400 ppi uncompressed TIFF. PDF generated by Adobe Acrobat Pro X for CONTENTdm display
ARK	ark:/87278/s6pv8mnb
Setname	ir_computersa
ID	98881
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6pv8mnb

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Title	Page 94
Setname	ir_computersa
ID	98880
OCR Text	Show 82 13. lchida, K., Kiyono, T. and Yoshimoto, F., ·curve Fitting by a One- Pass Method With a Piecewise Cubic Polynomial," ACM Transactions on Mathematical Software, Vol. 3, No. 2, June, 1977, pp. 164-174. 14. Jupp, D. L. B., "Approximation to Data By Splines with Free Knots,., SlAM J. Numer. Anal., Vol. 15, No. 2, April, 1978, pp. 328-343. 15. Lawton, W. H. and Sylvestre, E. A., "Elimination of Linear Parameters in Nonlinear Regression," Technometrics, Vol. 13, No. 3, August, 1971 , pp. 461-467. 16. Manning, J. R., "Continuity Conditions for Spline Curves," The Computer Journal, Vol. 17, No. 2, May, 1974, pp. 181-183. 17. Marin, S. P., "An Approach to Data Parametrization in Parametric Cubic Spline Interpolation Problems," Journal Of Approximation Theory, Vol. 41 , No. 64, May, 1984, pp. 64-68. 18. Pavlidis, T., "Curve Fitting with Conic Splines," ACM Transactions on Graphics, Vol. 2, No. 1, January, 1983, pp. 1-31 . 19. Plass, M. and Stone, M., "Curve-Fitting with Piecewise Parametric Cubics," Computer Graphics, Peter Tanner, ed., ACM/SIGGRAPH, Detroit, Michigan, July 1983, pp. 229-239. 20. Powell, M. J. D., Curve Fitting By Splines in One Variable, Athlone Press, London, 1970, pp. 65-83, . 21. Reinsch, C. H., "Smoothing by Spline Functions," Numer. Math., Vol. 10, 1967, pp. 177-183. 22. Schoenberg, I. J., "Spline Functions and the Problem of Graduation," Proc. Nat. Acad. Sci., Vol. 52, 1965, pp. 947-950. 23. Whittaker, E. T., "On a New Method of Graduation," Proc. Edinburgh Math. Soc., Vol. 41, 1923, pp. 63-75.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6pv8mnb/98880