- · 《自动化技术与应用》征[08/03]
- · 《自动化技术与应用》投[08/03]
- · 《自动化技术与应用》数[08/03]
- · 《自动化技术与应用》栏[08/03]
- · 《自动化技术与应用》刊[08/03]
来稿应自觉遵守国家有关著作权法律法规，不得侵犯他人版权或其他权利，如果出现问题作者文责自负，而且本刊将依法追究侵权行为给本刊造成的损失责任。本刊对录用稿有修改、删节权。经本刊通知进行修改的稿件或被采用的稿件，作者必须保证本刊的独立发表权。 一、投稿方式： 1、 请从 我刊官网 直接投稿 。 2、 请 从我编辑部编辑的推广链接进入我刊投审稿系统进行投稿。 二、稿件著作权： 1、 投稿人保证其向我刊所投之作品是其本人或与他人合作创作之成果，或对所投作品拥有合法的著作权，无第三人对其作品提出可成立之权利主张。 2、 投稿人保证向我刊所投之稿件，尚未在任何媒体上发表。 3、 投稿人保证其作品不含有违反宪法、法律及损害社会公共利益之内容。 4、 投稿人向我刊所投之作品不得同时向第三方投送，即不允许一稿多投。 5、 投稿人授予我刊享有作品专有使用权的方式包括但不限于：通过网络向公众传播、复制、摘编、表演、播放、展览、发行、摄制电影、电视、录像制品、录制录音制品、制作数字化制品、改编、翻译、注释、编辑，以及出版、许可其他媒体、网站及单位转载、摘编、播放、录制、翻译、注释、编辑、改编、摄制。 6、 第5条所述之网络是指通过我刊官网。 7、 投稿人委托我刊声明，未经我方许可，任何网站、媒体、组织不得转载、摘编其作品。
The Cubic Trigonometric Automatic Interpola
作者:网站采编关键词:
摘要：IN geometric modeling,curves are usually constructed on the basis of ,trigonometric polynomials have received much attention within geometric examples are the trigonometric polynomial B′ezier curves[1]-[4],the trigonometric polynomial B-s
IN geometric modeling,curves are usually constructed on the basis of ,trigonometric polynomials have received much attention within geometric examples are the trigonometric polynomial B′ezier curves[1]-[4],the trigonometric polynomial B-spline curves[5]-[8],and the trigonometric Hermite spline curves[9],[10].Those trigonometric polynomial curves not only inherit similarities of the corresponding classical polynomial curves,but also have better performance ability in different aspects.
It is well known that the spline interpolation has a wide range of applications in geometric ,when the traditional cubic splines are used to construct C2interpolation curves,a linear equation system usually needs to be order to solve this problem,Su and Tan[11]and Yan and Liang[12]constructed two automatic interpolation splines on the basis of trigonometric main characteristic of these two splines is that they can automatically interpolate the given data points without solving equation are some deficiencies in these two splines,however,the shape of the spline presented in[11]cannot be adjusted when the data points and auxiliary points the spline presented in[12]can achieve shape adjustment when the data points and auxiliary points are fixed,it can only become G2interpolation main purpose of this paper is to present a class of cubic trigonometric automatic interpolation spline curves with two proposed spline curves can achieve shape adjustment by altering values of the two ,the proposed spline curves can automatically interpolate the given data points and be C2without solving equations system even if the interpolation conditions are ,the optimal automatic interpolation spline curves can be obtained by selecting proper values of the two parameters.
The rest of this paper is organized as Section II,the cubic trigonometric automatic interpolation spline curves with two parameters are constructed,and properties of interpolation spline curves are Section III,a method for determining the optimal automatic interpolation spline curves is presented,and some examples are given.A short conclusion is given in Section IV.
INTERPOLATIONSPLINECURVES
A.The Basis Functions
Firstly,the cubic trigonometric spline basis functions with two parameters are defined as follows.
Definition 1:For 0≤ t≤ 1,α,β ∈R,the following four functions about t are defined as cubic trigonometric spline basis functions,
where
By simple deduction,the cubic trigonometric spline basis functions defined as(1)have the following properties at the endpoints,
From(1),the cubic trigonometric spline basis functions have two free parameters α and β.Hence,various shapes of curves of the cubic trigonometric spline basis functions can be obtained by altering values of the parameters α and β.Fig.1 shows curves of the cubic trigonometric spline basis functions for different values of α and β,where α and β are taken as(α,β)=(-0.5,0.5)(marked with dotted lines),(α,β)=(0,0)(marked with solid lines),(α,β)=(0.5,-0.5)(marked with dashed lines).
of the proposed basis functions for different α and β.
and Properties of the CTAI-spline Curves
Depending on the cubic trigonometric spline basis functions,the cubic trigonometric automatic interpolation spline curves with two parameters can be defined as follows.
Definition 2:Given a series of data points(xi,yi)(i=0,1,...,n),set hi= xi+1-xi(i= 0,1,...,n-1),the following piecewise curves are called cubic trigonometric automatic interpolation spline curves(CTAI-spline curves for short),
where x∈[xi,xi+1](i=1,2,...,n-2),0,1,2,3)are the cubic trigonometric spline basis functions defined according to(1).
Theorem 1:The CTAI-spline curves defined as(5)have the following properties,
a)Automatic interpolation property:For given data points(xi,yi)(i=0,1,...,n),the CTAI-spline curves Si(x)(i=1,2,...,n-2)automatically interpolate all the given data points except(x0,y0)and(xn,yn),i.e.,
b)C2continuity:When hi(i=0,1,...,n-1)are equal to a constant h,the CTAI-spline curves Si(x)(i=1,2,...,n-2)are C2,i.e.,
Proof:a)By(2)and(5),we have
Equation(6)shows that the CTAI-spline curves Si(x)(i=1,2,...,n-2)automatically interpolate all the given data points except(x0,y0)and(xn,yn).
b)When hi(i=0,1,...,n-1)are equal to a constant h,by(3)and(5),we have
By(4)and(5),we have
From(6)-(8),we have
Equation(9)shows that the CTAI-spline curves Si(x)(i=1,2,...,n-2)are C2.
From Theorem 1,if two auxiliary points(x-1,y-1)and(xn+1,yn+1)are added to the given data points,the CTAI-spline curves Si(x)(i=0,1,...,n-1)interpolating all the data points(xi,yi)(i=0,1,...,n)would be naturally two auxiliary points can be added arbitrarily,and they only have effects on the starting and the end segments of the interpolation convenience,(x-1,y-1)and(xn+1,yn+1)can be taken as
文章来源：《自动化技术与应用》 网址: http://www.zdhjsyyy.cn/qikandaodu/2020/1005/475.html