C-B样条旋转曲面造型研究

论文提出利用C-B样条来构造工程中常见的旋转曲面。在介绍C-B样条曲线理论的基础上,讨论了圆及椭圆弧的C-B样条表示及用C-B样条构造旋转曲面体的建模方法。构造了形状可调,母线可以包含圆弧、椭圆弧等的旋转曲面。该方法结构简单,造型速度快,形状在一定范围内可调,表示圆弧、椭圆弧时,参数的几何意义明确。同时由于C-B样条和均匀B样条有相同的结构,该方法可以方便地应用于CAD/CAM建模系统。

Study on Surfaces of Revolution Modeling with C-B-Splines

A modeling scheme of revolution surfaces with C-B-splines for engineering is proposed. In this paper, the basic principles of the C-B-splines are introduced first. Then, the representation of elliptical arcs with C-B-splines, and the modeling of revolution surfaces of C-B-splines are discussed. At last, some samples of revolution surfaces constructed by C-B-splines are provided. Since C-B-splines are adopted, this scheme has adjustable shape parameters that have geometric meaning, and the generatrixes of the generated revolution surface can have exact elliptical and circlar arcs that are commonly used in engineering. With this scheme, the modeling process is simple and fast, the resulting shape of revolution surfaces is adjustable, and the parameter for selection has a definite geometric meaning when representing elliptical and circular arcs. Also, since both the C-B-splines and the B-splines have the same structure, this scheme is simple, and can be introduced to the CAD/CAM modeling system easily.