四次拟Bézier旋转曲面的构造技术

New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters

为了方便解决传统旋转曲面计算复杂和形状难以调节的问题,研究了一种带多形状参数的四次拟Bézier旋转曲面的构造技术。首先,基于二元超限向量值有理插值函数的重要思想,利用带多形状参数的四次拟Bézier曲线作为母线进行旋转曲面的设计;其次,推导了生成整个四次拟旋转曲面的一个显式函数表达式。该方法生成的旋转曲面不仅计算简单而且具有良好的形状可调性,同时还保留了传统Bézier旋转曲面的许多几何特性。最后,对所设计的旋转曲面进行了形状与性质分析,并给出了形状控制参数对旋转曲面形状的影响规律。造型实例表明,所提方法不仅直观、高效,而且易于调整旋转曲面的局部形状,在各种旋转曲面的构造与外形设计中将得到十分广泛的应用。

To deal with the problems in adjusting and controlling shapes of rotation surfaces,a new efficient method for quick constructing rotary surfaces with local shape parameters is proposed.Following the essence of transfinite vectored rational interpolating function,the quartic quasi-Bézier rotary surfaces with multiple shape parameters are constructed and the explicit function for quartic quasi-Bézier rotary surfaces is presented.The so constructed surfaces inherit the outstanding properties of the Bézier rotary surfaces with good performance in adjusting local shapes by changing the shape parameters.Some properties of the quartic quasi-Bézier rotary surfaces and applications to surface design are discussed.