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

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.