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Brian A. Barsky, "Rational BetaSplines for Representing Curves and Surfaces," IEEE Computer Graphics and Applications, vol. 13, no. 6, pp. 2432, November/December, 1993.  
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@article{ 10.1109/38.252550, author = {Brian A. Barsky}, title = {Rational BetaSplines for Representing Curves and Surfaces}, journal ={IEEE Computer Graphics and Applications}, volume = {13}, number = {6}, issn = {02721716}, year = {1993}, pages = {2432}, doi = {http://doi.ieeecomputersociety.org/10.1109/38.252550}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  MGZN JO  IEEE Computer Graphics and Applications TI  Rational BetaSplines for Representing Curves and Surfaces IS  6 SN  02721716 SP24 EP32 EPD  2432 A1  Brian A. Barsky, PY  1993 VL  13 JA  IEEE Computer Graphics and Applications ER   
The rational Betaspline representation, which offers the features of the rational form as well as those of the Betaspline, is discussed. The rational form provides a unified representation for conventional freeform curves and surfaces along with conic sections and quadratic surfaces, is invariant under projective transformation, and possesses weights, which can be used to control shape in a manner similar to shape parameters. Shape parameters are an inherent property of the Betaspline and provide intuitive and natural control over shape. The Betaspline is based on geometric continuity, which provides an appropriate measure of smoothness in computeraided geometric design. The Betaspline has local control with respect to vertex movement, is affine invariant, and satisfies the convex hull property. The rational Betaspline enjoys the benefit of all these attributes. The result is a general, flexible representation, which is amenable to implementation in modern geometric modeling systems.
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