基于物理的变形曲线曲面造型技术综述

Physics-based Technology of Deformable Curve and Surface Modeling——A Review

现代工业技术的发展对CAD技术提出了越来越高的要求,传统的曲线曲面造型技术属于几何造型方法,已不能完全满足对现代工业产品尤其是柔性件的建模要求,基于物理的曲线曲面造型技术应运而生。该文首先介绍了基于物理的曲线曲面造型技术的产生和研究现状,主要分析了该技术方法的理论基础和实现原理,在此基础上讨论了该方法中求解控制方程的建立,重点比较了两种建模思想:Gossard静态模型和D-NURBS动态模型,并对不同控制方程的求解方法如差分法、有限元法和数学规划法也做了一定的综述。文章最后指出了这一造型技术的优势和存在的问题,探讨了今后发展的方向和思路。

With the development of modern industrial technology, the demands for CAD technology are greatly increasing. Conventional technology of curve and surface modeling, which is pure geometrical modeling method, cannot meet the requirements yet, so a new method - Physics - based Technology of deformable curve and surface modeling is developed. First of all, the paper introduces the development and the nowadays status of the technology. The paper mainly analyzes the theory of the technology, and then discusses the establishment of controlling equations, including two important methods ： Gossard model and D - NURBS model. Several solutions are also compared in the paper, such as Difference,Finite - Element method and Mathematical Programming. Additionally, we point out the advantages of the technology and problems existing in it, and probe into the future development.