一种采用圆锥曲线进行自由造型的新方法

本文提出了一种采用二次Ｂ样条曲线和双二次Ｂ样条曲面通过映射交换来实现圆锥曲线和二次曲面造型的新方法．

On a New Method for Free Modeling with Conic Sections

UP to new, conic section design employs a shape factor to adjust shape of curve; such adjUstment is rather inconvenient. In this paper, the authors propose a convenient method for free modeling with conic sections, which, after a careful and extensive search, bas not been found by the authors in any paper in the open literature. In the authors' new method, shape of curve is adjUsted through varying one of the vertices of a polygon instead of a shape factor. Another advantage of the authors' new method is that the geometrically continuous joint between adjacent conic segments can be castly achieved. In the authors' new method, free modeling is achieved through mapping B-spline curves. It is obvious that what has been said about conic segments can be easily extended to quadric patches. The authors' new method works out quite well on a computer for conic segments.