Two parameters extension of quartic Bézier curve and its applications

Abstract

A set of quintic polynomial basis functions with two parameters are presented. Based on these basis functions, the quintic Bezier curve with two parameters which is called λμ -Bezier curves is defined. λμ -Bezier curves produces a closer fit to the guiding polygon than does the Bézier curves. We can attain local shape control of quintic λμ − B spline curve by modifying the shape parameters exactly to ensure two quintic λμ -Bezier curves segment satisfying C¹-continuity at the common endpoint without affecting other parts. Finally,we present a example to illustrate the validity of the modification methods.