NDLI: AHT Bézier Curves and NUAHT B-Spline Curves

Content Provider	Springer Nature Link
Author	Xu, Gang Wang, Guo Zhao
Copyright Year	2007
Abstract	In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric (AHT) Bézier curves and non-uniform algebraic hyperbolic trigonometric (NUAHT) B-spline curves of order n, which are generated over the space span {sin t, cos t, sinh t, cosh t, 1, t,...,t $^{ n − 5}$}, n ⩾ 5. The two kinds of curves share most of the properties as those of the Bézier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
Starting Page	597
Ending Page	607
Page Count	11
File Format	PDF
ISSN	10009000
Journal	Journal of Computer Science and Technology
Volume Number	22
Issue Number	4
e-ISSN	18604749
Language	English
Publisher	Springer US
Publisher Date	2007-09-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	CAD/CAM AHT Bézier curve NUAHT B-spline curves transcendental curves Computer Science Software Engineering Theory of Computation Data Structures, Cryptology and Information Theory Artificial Intelligence (incl. Robotics) Information Systems Applications (incl.Internet)
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computer Science Applications Software Hardware and Architecture

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