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Mathematical Problems in Engineering
Volume 2014, Article ID 242469, 7 pages
Research Article

A Geometric Modeling Method Based on TH-Type Uniform B-Splines

Jin Xie1,2

1Department of Mathematics and Physics, Hefei University, Hefei 230601, China
2Department of Mathematics and Physics, University of La Verne, La Verne, CA 91750, USA

Received 26 January 2014; Accepted 24 May 2014; Published 15 June 2014

Academic Editor: Vassilios C. Loukopoulos

Copyright © 2014 Jin Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A geometric modeling method based on TH-type uniform B-splines which are composed of trigonometric and hyperbolic polynomial with parameters is introduced in this paper. The new splines possess many important properties of quadratic and cubic B-splines. Taking different values of the parameters, one can not only locally adjust the shape of the curves, but also change the type of some segments of a curve between trigonometric and hyperbolic functions as well. The given curves can also interpolate directly control polygon locally by selecting special parameters. Moreover, the introduced splines can represent some quadratic curves and transcendental curves with selecting proper control points and parameters.