通基于流形的封闭参数曲线构造理论

为了方便地构造真正意义上的光滑封闭参数曲线,以微分流形--圆为封闭参数曲线的定义域,以非均匀B样条为定义域上的基函数,设计了用于构造封闭参数曲线的控制顶点、控制顶点对应的参数值及节点矢量的确定方法和曲线上一点的三维坐标值计算方法;以作均匀有理B样条(NURBS)曲线常用的控制技术如夹直线段、在曲线上形成尖角等检验该算法与NURBS方法的兼容性.实验结果表明,该算法不仅实用可靠,而且比目前造型系统中的NURBS方法简单方便,完全与NURBS造型系统兼容.

Theory of constructing closed parametric curves based on manifold

Manifold based parametric curve was designed for constructing really good and closed curve expediently.A kind of differential manifold,circle,was defined as the parametric space and non-uniform B-splines defined on the unit circle were treated as base functions.A method of constructing knot vectors,control points and corresponding parameters were proposed.A method of getting coordinates for any point on curve were also proposed.Some NURBS control techniques,such as curves with embedded line,with sharp angle,and so on,were used to verify the proposed method's compatibility with non-uniform rational B-splines(NURBS).Some examples were used to compare the arithmetic with NURBS's.The results show that the method is not only simple,feasible and reliable but also compatible with CAD system using NURBS.