可展有理Bezier曲面的设计与修正

Design and Modification of Developable Rational Bezier Surfaces

通过构造与给定有理Bezier曲线形状相似的曲线,构造出可展曲面,从而提出了一种用于可展有理Bezier曲面的设计与修正方法.并进一步根据需要给出约束平面,对于与约束平面相交的曲面片,将被其所在的曲面族中的一个与约束平面相切或插值于约束平面边界的曲面片所取代.该方法不需要重新计算曲面的控制点和权因子,减少了计算量.修正后的曲面片不穿过约束平面,且仍为可展的曲面片.数值实验表明该方法简单、快速、有效.

A method for design and modification of developable surfaces was presented by constructing a curve which was similar to the given rational Bezier curve. Furthermore, the constrained plane was given, and the surface patch which was intersected with the plane would be replaced with one of its surface family, which either was tangent to the plane or interpolated the point on its boundaries. The method did not need to calculate the new control points and their weights and then reduced the calculation. The modified surface would not intersect with the plane but would remain a developable surface. Numerical examples show that the method is simple, fast and efficient.