Two Kinds of Trigonometric Spline Curves with Shape Parameter

Author

Yan, LanLan ; Liang, JiongFeng ; Wu, GuoGen

Author_Institution

Coll. of Math. & Inf. Sci., East China Inst. of Technol., Fuzhou, China

Volume

1

fYear

2009

fDate

4-5 July 2009

Firstpage

549

Lastpage

552

Abstract

Two kinds of trigonometric spline curves with shape parameter are presented in this paper. The trigonometric spline curves are constructed with three consecutive control points for each curve segment. The given curves posses many properties of the quadratic B-spline curve. Meanwhile, they have many better properties than the quadratic B-spline curve. The first kind of curve is continuous with equidistant knot vector, and it is continuous with special shape parameter. The second kind of curve is continuous with equidistant knot vector. The shape parameter can adjust the given curves´ shape with the same control polygon. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves can be closer to the control polygon than the quadratic B-spline curve. In the last, the trigonometric spline surfaces with shape parameter are also constructed and they have most properties of the corresponding trigonometric spline curves.

Keywords

computational geometry; curve fitting; splines (mathematics); control polygon; equidistant knot vector; quadratic B-spline curve; shape parameter; trigonometric spline curve; Application software; Computer graphics; Educational institutions; Information science; Mathematics; Polynomials; Shape control; Spline; Surface reconstruction; Surface topography; computer application; continuity; shape parameter; spline curve; trigonometric basis;

fLanguage

English

Publisher

ieee

Conference_Titel

Environmental Science and Information Application Technology, 2009. ESIAT 2009. International Conference on

Conference_Location

Wuhan

Print_ISBN

978-0-7695-3682-8

Type

conf

DOI

10.1109/ESIAT.2009.22

Filename

5200181