可展Bezier曲面的构造算法

Construction Algorithm of Developable Bezier Interpolation Patches

首先提出了一种由设计曲线和伴随曲线构造可展曲面的算法,并讨论了其依赖于设计曲线和匹配函数的几何性质及相应条件,在其基础上,研究了设计曲线和伴随曲线分别为n+1次,m+n+1次Bezier曲线的可展曲面构造方法,解决了任意次可展Bezier曲面的设计问题,最后以可展(3,4)次Bezier曲面为构造实例,证明了该算法的正确性和实用性.

An algorithm is proposed for constructing developable patches by using design curve and adjoint curve. The geometrical properties of the developable patches and corresponding conditions are discussed, which depend on design curve and matched function. The method of constructing the developable Bezier interpolation patches of (n+1,m+n+1) degree is investigated based on the algorithm. As an example, the developable Bezier interpolation patches of (3,4) degree are constructed, which proves that the algorithm is correct and effective.