摘要
根据工程中对自由曲面曲线表示的几何要求,通过对NURBS曲线、曲面性质的研究,对于工程图中用于表示零件的基本线几何元素直线、圆弧和圆以及面几何元素平面、圆柱面、圆锥面和球面等表示对象,采用的不同控制顶点和节点矢量,从而得到其二次和三次NURBS的表示方法,并且导出了不同表示方法之间的关系.理论结果表明,这些表示方法形式简单,所表示的曲线曲面具有良好的凸包性和几何连续性,满足CAD工程实践的要求.
The characteristics of NURBS curves and surfaces are studed to meet demands in free curve and surface's presentation.Several methods of square and cubic NURBS's expression are presented to represent basic geometry elements of line and surface such as line,arc,circle,plan,cylinder,cone and sphere surface which are the details of engineering drawing.Besides,the connection of different representation methods has been conducted.Theoritical study show:those methods with simple forms can express curve and surface with good convex hull and parameter continuity which satisfies the demands of CAD processing.
出处
《西安工业学院学报》
2004年第4期311-315,共5页
Journal of Xi'an Institute of Technology
基金
陕西省教育厅自然科学基金(02JS33)
