随着几何造型工业的快速发展，传统Bézier方法受到了极大的挑战，已难以满足工业产品设计中的各种需求。带参广义Bézier曲线曲面不仅保留了传统Bézier 曲线曲面的优点，而且具有更好的形状可调性，如今已成为CAD 领域研究的一个新热点。本项目基于现有研究成果，重点对带参广义Bézier 曲线曲面的关键技术及其应用进行研究，主要内容包括：构造新的带多形状参数的n 次广义Bézier曲线曲面；提出带参广义Bézier 曲线曲面关于光滑拼接、降阶、形状分析、形状修改、近似合并、分割、延拓、光顺、等距线生成以及加密的关键算法；探讨带参广义Bézier曲线曲面在可展曲面形状优化设计和逆向工程中的应用。研究成果将进一步丰富和发展带参广义Bézier 曲线曲面的相关理论与算法，具有重要的理论和实际应用价值，可广泛应用于各种CAD/ CAM 造型系统中，成为推动CAD/CAM快速发展的重要力量之一。

With the rapid development of geometric modeling industry, the traditional Bézier curves and surfaces are hard to satisfy the various needs of industrial design. The generalized Bézier curves and surfaces with shape parameters is one of the most important extensions of traditional Bézier curves and surfaces. It not only inherit the outstanding properties of traditional Bézier curves and surfaces, but also has a good performance on adjusting their local shapes by changing the shape control parameters. Thus the generalized Bézier curves and surfaces with shape parameters therefore have been a new focus of the investigation. Based on the existing research results, we will mainly do some researches on pivotal technologies of the generalized Bézier curves and surfaces with shape parameters in CAD. In this project, we will construct a novel generalized Bézier curve and surface of degree n with multiple shape parameters, propose some vital algorithms of the generalized Bézier curves and surfaces with shape parameters about subdivision algorithm, connection, degree reduction, approximate merging, shape analysis, shape modification, extension, fairing and so on, and further discuss the application of the generalized Bézier curves and surfaces with shape parameters in reverse engineering and the design of developable surfaces. The achievments of this project will further enrich and develop the theory and algorithm of the generalized Bézier curves and surfaces with shape parameters, which have important values in the theory and the practical application and can be widely applied to various CAD / CAM modeling system, to promote the development of CAD/CAM greatly.