Abstract
This paper describes a new mathematical theory for generating a sculptured surface defined by B-spline, and the application of this theory to practical design and manufacturing. The initial curved surface is constructed easily by blending two or more outlines. When outlines are blended, special functions introduced in this paper and implied in the equation for curved surfaces, control the shape of surfaces globally. It is possible to control the shape of those locally too. This method is analogous to the way used in early work. Namely, adjusting vertices of the polygon is used to control the shape locally. The system applied this theory can generate easily a sculptured surface desired by designers.
