Curve construction based on five trigonometric blending functions

被引：47

作者：

Han, Xuli ^{[1
]}

Zhu, Yuanpeng ^{[1
]}

机构：

[1] Cent S Univ, Changsha 410083, Peoples R China

来源：

BIT NUMERICAL MATHEMATICS | 2012年 / 52卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Trigonometric blending functions; Trigonometric Bezier curves; Shape parameters; Trigonometric B-spline curves; Interpolation; DEGREE POLYNOMIAL SPLINES; SHAPE PARAMETER; TENSION PROPERTIES;

D O I：

10.1007/s10543-012-0386-0

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Five new trigonometric blending functions with two exponential shape parameters are given in this paper. Based on these blending functions, trigonometric B,zier curves analogous to the quartic B,zier curves, with two exponential shape parameters, are presented. The ellipses and parabolas can be represented exactly by using the trigonometric B,zier curves. Based on the blending functions, trigonometric B-spline curves with three local shape parameters and a global shape parameter are also constructed. The obtained spline curves can be C (2)a (c) FC (2k+3) (kaa"currency sign(+)) continuous by fixing some values of the shape parameters. Without solving a linear system, the spline curves can be also used to interpolate sets of points with C (2) continuity partly or entirely.

引用

页码：953 / 979

页数：27

共 17 条

[1] C1 and C2-continuous polynomial parametric LP splines (p ≥ 1) [J].