Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

Yuanpeng Zhu,Xuli Han,Shengjun Liu

doi:10.1155/2014/857840

Yuanpeng Zhu, Xuli Han + Show 1 more

Open Access

https://doi.org/10.1155/2014/857840

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Abstract

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

Highlights

Constructing practical basis functions to generate free form curves and surfaces is an important topic of CAGD and computer graphics
The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters
The purpose of this paper is to present four new quartic rational Said-Ball-like basis functions with two-tensionshape parameters, which include the cubic Said-Ball basis functions

Summary

Introduction

Constructing practical basis functions to generate free form curves and surfaces is an important topic of CAGD (computer aided geometric design) and computer graphics. In [18, 19], two kinds of C2 cubic rational interpolation splines were proposed by Sarfraz for the visualization of monotonic data. The purpose of this paper is to present four new quartic rational Said-Ball-like basis functions with two-tensionshape parameters, which include the cubic Said-Ball basis functions. By using the new basis, a class of C1 continuous quartic rational Hermite interpolation spline with local tension shape parameters is constructed. The quartic rational Said-Ball-like basis functions are extended to a triangular domain.

Quartic Rational Said-Ball-Like Basis

Definition and Properties of the Quartic Rational SaidBall-Like Curve

C1 Quartic Rational Shape Preserving Interpolation Spline

Quartic Rational Said-Ball-Like Basis over a Triangular Domain

Conclusion