用变形模型整体构造B样条曲面方法研究

传统的造型方法都是基于纯粹的几何模型,通过几何上的型值点或边界曲线定义曲线或曲面,难于进行交互修改.基于物理模型的变形曲线、曲面造型方法将参数化几何描述方法与力学原理结合起来,使曲线曲面变形形态在一定程度上与弹性梁和薄壳相似.设计者可以通过施加于变形曲线曲面上的力或约束,或改变曲线曲面本身刚度来改变其局部或整体形状,克服了局部控制与总体光顺的矛盾.该造型方法已在光顺、N边域构造以及曲面的光滑拼接和过渡面构造等领域得到应用. 

Study on Global Construction of B-Spline Surface by Deformable Model

The surface modeling techniques in current CAD systems are generally based on the purely mathematical theories of parametrically described geometry. It is very difficult to design interactively fair surfaces which interpolate given data points or boundary curves. Physics based modeling techniques are based on physical laws. So the deformation has a great similarity to elastic beams and plates, this makes their behavior natural and fair. The designer can simply and intuitively sculpt the local or global shape by adjusting the applied forces, geometric constraints and physical parameters, therefor can mediate the contradictory of local shape manipulation and global fairness as well as convexity. This method has been used in fairing, N sided patch blending surfaces and joining surfaces.