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Mathematical Problems in Engineering
Volume 2016, Article ID 7067408, 9 pages
Research Article

Cubic Trigonometric Nonuniform Spline Curves and Surfaces

1School of Mathematics and Statistics, Central South University, Changsha 410083, China
2School of Science, East China University of Technology, Nanchang 330013, China

Received 29 September 2015; Revised 9 January 2016; Accepted 11 January 2016

Academic Editor: Ofer Hadar

Copyright © 2016 Lanlan Yan. 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 class of cubic trigonometric nonuniform spline basis functions with a local shape parameter is constructed. Their totally positive property is proved. The associated spline curves inherit most properties of usual polynomial -spline curves and enjoy some other advantageous properties for engineering design. They have continuity at single knots. For equidistant knots, they have continuity and continuity for particular choice of shape parameter. They can express freeform curves as well as ellipses. The associated spline surfaces can exactly represent the surfaces of revolution. Thus the curve and surface representation scheme unifies the representation of freeform shape and some analytical shapes, which is popular in engineering.