Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters
Received date: 2016-11-08
Revised date: 2016-12-14
Online published: 2017-05-30
A spline curve with shape parameters is an important method in design. In existing methods, however, shapes parameters are either global or local, and only parameter continuity are considered. To modify and blending the curves, an algebraic-trigonometric spline curve, called ATB-spline, is constructed with two kinds of shape parameters satisfying geometric continuity. This curve not only has the properties of ordinary trigonometric polynomials, but also has global and local properties. When the two kinds of shape parameters are taken in a given range, the ATB-spline curves with two kinds of shape parameters satisfy geometric continuity of the frst order; when the shape parameter of the two adjacent curves is given a special value, the ATB-spline curve with two kinds of shape parameters can satisfy continuity of the different properties. The rotation surface is constructed based on the property of the curve. Blending of the two kinds of shape parameters on the surface of the rotating surface is given together with an example. In addition, this curve can accurately represent conic curves. The above results indicate that curves constructed with this method are practical and effective.
LIU Hua-yong, LI Lu, ZHANG Da-ming, WANG Huan-bao . Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters[J]. Journal of Applied Sciences, 2017 , 35(3) : 383 -393 . DOI: 10.3969/j.issn.0255-8297.2017.03.012
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