Page 188

Contents | 188 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 188
Setname	ir_computersa
ID	105784
OCR Text	Show 172 67. Birkhoff, Garrett; and Gordon, William J. "The Draftsman's and Related Equations", Journal of Approximation Theory, Vol. 1, No.2, 1968, pp. 1199-208. 68. Blinn, James F. "Models of Light Reflection for Computer Synthesized Pictures". In Proceedings of SIGGRAPH '77, ACM, July 1977, pp. 192-198. 69. Blinn, James F. Computer Diselay of Curved Surfaces, Ph.D. Thesis, University of Utah, Salt Lake City, Utah, December 1978. Also Tech. Report No. 1060-126, Jet Propulsion Laboratory, Pasadena, California. 70. Blinn, James F. "Simulation of Wrinkled Surfaces". In Proceedings of SIGGRAPH '78, ACM, August 1978, pp. 286-292. 71. Blinn, James F. and Newell, Martin E. "Texture and Reflection in Computer Generated Images", Communications of the ACM, Vol. 19, No. 10, October 1976, pp. 542-547. 72. Bloor, M. S.; de Pennington, A.; and Woodwark, J. R. "RISP: Bridging the Gap between Conventional Surface Elements". In Proceedings of the CAD78 Conference, Brighton, IPC Science and Technology Press, Ltd., Guildford, England, 1978. 73. Boehm, Wolfgang. "Parameterdarstellung, Kubisher und Bikubisher Splines", Computing, Vol. 17, 1976, pp. 87-92. 74. Boehm, Wolfgang. "Ueber die Konstruktion von B-Spline-Kurven", Computing, Vol. 18, No.2, 1977, pp. 161-167. 75. Boehm, Wolfgang. "Cubic 􁪽􋵳spline Curves and Surfaces in Computer-Aided Geometric Design", Computing, Vol. 19, No.1, 1977, pp. 29-34. 76. Boehm, Wolfgang. "Inserting New Knots into &spline Curves", Computer-Aided Desigg, Vol. 12, No.4, July 1980, pp. 199-201. 77. Boere, H. The Design of Surfaces with the Coons' Method, Ph.D. Thesis, Technical University of Delft, The Netherlands, November 1970. 78. Bolton, K. M. "Biarc Curves", Computer-Aided Design, Vol. 7, No.2, 1975, pp. 89-92. 79. Bresenham, J. E. "A Linear Algorithm for Incremental Digital Display of Circular Arcs", Communications of the ACM, Vol. 20, No.2, February 1977, pp. 100-106.
Reference URL	https://collections.lib.utah.edu/ark:/87278/s64f49w4/105784