准D-NURBS摆转曲面在曲面造型中的应用

Simplified Dynamic NURBS Swung Surfaces for Physics-based Shape design

提出了基于物理型面设计的准Ｄ－ＮＵＲＢＳ摆转曲面的概念。建立了用于表达具有对称性和拓扑变化的一大类物体的动态的、自由表面模型。这一新的模型是基于摆转ＮＵＲＢＳ曲面之上的，继承了其有用的截面设计特性。在基于物理的框架之内，具有曲面设计的几何特征。用弹性曲面的拉格朗日动力学推导出了准ＤＮＵＲＢＳ摆转曲面的运动方程。举出了一些准ＤＮＵＲＢＳ摆转曲面的应用实例，如曲面倒圆角与调和、曲面拟合及交互式造型等。

This paper represents a concept of simplified dynamic NURBS swung surfaces for physics-based shape design. A dynamic freeform surface model which is useful for representing a broad class of objects with symmetries and topological variability is developed. The new model is based upon swung NURBS surfaces, and it inherits their desirable crosssectional design properties. It melds these geometric features with the demonstrated convenience of surface design within a physics-based framework. The equations of motion for the simplified dynamic NURBS swung surfaces model are derived using the Lagrangian mechanics . Some application examples of simplified Dynamic NURBS Swung Surfaces are showed, which include rounding and blending, scattered data fitting and interactive sculpting.