Three Kinds of Curves That Shape Can Adjust

Author

Liang, JiongFeng ; Yan, LanLan

Author_Institution

Coll. of Civil & Environ. Eng., East China Inst. of Technol., Fuzhou, China

Volume

2

fYear

2009

fDate

18-19 July 2009

Firstpage

356

Lastpage

359

Abstract

Three kinds of trigonometric bases are constructed in this paper. Based on these bases, three kinds of trigonometric spline curves with shape parameter are defined. As each piece of the curves is generated by three consecutive control points, they retain many properties of the quadratic B-spline curves, but they have higher order continuity than the quadratic B-spline curves. For equidistant knots, they have C² continuity under normal conditions, and they have C³ continuity under special conditions. Besides, the curves are closer to the control polygon than the quadratic B-spline curves when the shape parameters under special conditions. In the last, the trigonometric spline surfaces with shape parameter are constructed. They have most properties of the corresponding trigonometric spline curves.

Keywords

computational geometry; splines (mathematics); C² continuity; C³ continuity; control polygon; geometric modeling; quadratic B-spline curves; shape parameter; three consecutive control points; trigonometric bases; trigonometric spline curves; trigonometric spline surfaces; Educational institutions; Information processing; Information science; Mathematics; Polynomials; Shape control; Solid modeling; Spline; computer application; continuity; shape parameter; spline curve; trigonometric basis;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Processing, 2009. APCIP 2009. Asia-Pacific Conference on

Conference_Location

Shenzhen

Print_ISBN

978-0-7695-3699-6

Type

conf

DOI

10.1109/APCIP.2009.224

Filename

5197210