NURBS曲线控制点几何关系在产品三维建模中的应用  

Application of geometric relationship of NURBS curve control points in product 3D modeling

作　　者：成振波[1] 柯善军[1] 

机构地区：[1]重庆理工大学车辆工程学院,重庆400054

出　　处：《机械设计》2016年第7期105-108,共4页Journal of Machine Design

基　　金：重庆市科学技术研究基础资助项目(KJ1500912)

摘　　要：为研究工业产品三维建模中的曲线及曲面拼接问题,通过分析贝塞尔曲线连续性的数学意义和成立条件,得出连续性与控制点位置之间的联系;计算并总结出贝塞尔曲线在G0,G1,G2连续时,相邻控制点几何关系的规律,该规律也适用于相邻NURBS曲线及曲面的连续性调节,并通过实例应用进行了验证。结论表明:曲线及曲面控制点的几何规律可用于预判、调节曲线及曲面的连续性,有助于设计师通过三维模型准确表达产品造型。I n order to research the problem of continuity among curves and surfaces, by analyzing the mathematic meaning and achieve condition of Bezier curve continuity,the relationship between the continuity and the position of control points could be concluded. The discipline of geometric relations between the adjacent control points were calculated and summarized when G0,G1 and G2 of Bezier curve were continuous. The discipline could be applied to the continuous adjustment of adjacent NURBS curves and surfaces. Conclusion showed that the geometry rules of control points of curve and surface could be used to predict and adjust the continuity of curve and surface, which could help designer to express accurately the product form through the 3D model.

关 键 词：产品设计 三维建模 CAID NURBS 曲面拼接 连续性 

分 类 号：TB391.7[一般工业技术—材料科学与工程]