Approximations Of A Circle By Quartic Bézier Spline Curves

Bézier approximation method has a very important role in CAGD,which is simple and convenient when applied on the curve and surface construction.This paper presents two concrete approximation schemes of arcs by analyzing the roots of error function,and obtains two methods of Bézier spline curve approximating the circle.This paper mainly studies the approximation method of quartic Bézier curve approximation and the first way obtains the corresponding Bézier curve parameters by calculating the minimum value of the function_?m_[0a,₁x_]1)?,?to determines the roots of error function.This method not only ensures the continuity of curvature,but also improves the accuracy of circular approximation.The second approximation method is based on the reference[8]and combines the roots of the error function constructing the⁴Bézier spline curve with approximation order eight.This paper is divided into four chapters:The first chapter is the introduction,which mainly introduces the research status of arc approximation by Bézier curves and the main structure of this paper.The second chapter mainly introduces the basic knowledge of Bézier curve,including the expression and properties of Bézier curve,the simple introduction of four Bézier curves approaching the circular arc,and error function.The third chapter is the core of this paper.It introduces quartic Bézier curve spline approximation of a circle.In the first section,by selecting the roots of the error function to make the approximation error smaller,a better circular arc ap-proximation scheme is obtained.In the second section,on the basis of literature[8],the approximation curve with higher smoothness is obtained by using the same midpoint between the approximation curve and the arc.The fourth chapter gives the conclusion,analyzing the circular arc approxima-tion method and results,and puts forward the prospect.