自适应约束条件下过型值点的连续Bezier曲线设计方法  

Design method of continuous Bezier curve for passing modal points under adaptive constraints

作　　者：杨俊茹[1,2] 贾巧辉[1] 张道忠[3] 许宁[3] 

机构地区：[1]山东科技大学机械电子工程学院,山东青岛266510 [2]山东大学材料科学与工程学院,山东济南250061 [3]山东山大华天软件有限公司,山东济南250101

出　　处：《机械设计》2011年第10期19-23,共5页Journal of Machine Design

基　　金：国际科技合作资助项目(2009DFB10010);山东省优秀中青年科学家科研奖励基金资助项目(BS2009ZZ012);山东省自然科学基金资助项目(ZR2010EM013)

摘　　要：已知Bezier曲线型值点,利用三点圆弧近似方法获得曲线端点的自适应约束条件,根据Bezier曲线端点性质和C2连续条件建立曲线型值点与其控制点之间的关系,采用高斯顺序消去法反算出曲线控制点,从而获得过型值点的连续Bezier曲线。基于该设计方法进行了实例研究,其结果与专业三维CAD软件在同样条件下的设计结果具有较好的一致性。In case that the modal points on the Bezier curve were given,the adaptive constraints of the curve endpoints were obtained by using three-point arc approximation method.The relationship between the modal points of the curve and their control points was established according to the endpoint behavior and C^2 continuity of the Bezier curve.The control points in the curve were calculated reversely by the Gaussian elimination method in order,therefore the continuous Bezier curve passing modal points was designed in terms of control points.Based on the design method,an example investigation was carried out.The research result conformed well with the design result obtained by the professional 3D CAD software under the same condition.

关 键 词：BEZIER曲线 型值点 自适应约束条件 控制点 C2连续 

分 类 号：TH12[机械工程—机械设计及理论] TP39[自动化与计算机技术—计算机应用技术]