Beta-spline: a local representation based on shape parameters and fundamental geometric measures

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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
Date Created 2016-11-18
Date Modified 2016-11-18
ID 105814
Reference URL
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