5阶Bézier型曲线及其应用  

Bézier-type curve of 5 order and its applications

作　　者：车毅[1] 熊建[1] 

机构地区：[1]安徽审计职业学院基础部,合肥230601

出　　处：《阜阳师范学院学报（自然科学版）》2015年第1期9-12,共4页Journal of Fuyang Normal University(Natural Science)

基　　金：安徽省高校优秀青年人才基金重点项目(2013SQRL113ZD)资助

摘　　要：为了精确表示椭圆弧、圆弧等二次曲线及摆线、螺旋线等超越曲线,在非多项式空间{1,t,sin t,cos t,sin 2t}中,构造了一种5阶Bézier型基函数,其具有Bernstein基的类似性质,诸如非负性、规范性、对称性、端点性质等。由此基函数构造的5阶Bézier型曲线,具有Bézier曲线基本性质,诸如凸包性、对称性、几何不变性及端点插值和边界相切性质。给出了5阶Bézier型曲线C1连续及G1连续光滑拼接条件及在旋转曲面造型中的应用实例。试验表明,此造型方法是有效的,丰富了造型技术理论。To represent some quadric curves and transcendental curves,such as elliptic arc,circular arc,cycloid and helix,a new kind of Bézier-type basis functions of 5 order in the non-polynomial space { 1,t,sint,cost,sin2 t } are constructed. They share the most properties with Bernstein basis,such as non-negative,normative,symmetry,and endpoints nature. The Bézier-type curve of 5 order based on the new basis functions have similar properties as the Bézier curve,such as convex hull,symmetry,geometric invariance and endpoint interpolation and end edge tangent property. C^1 and G^1 link conditions of the curve and an example in surface of revolution modeling are presented. The result of experimentation shows that the modeling method is effective and enriches modeling theories.

关 键 词：5阶Bézier型基 5阶Bézier型曲线 拼接 二次曲线 超越曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]