中文摘要：

基于一组带参数的四次广义Bernstein基函数，构造了一种带多形状参数λ、γi的四次广义Bézier曲面，该曲面不仅保留了传统Bézier曲面的性质，而且具有优良的形状可调性，同时还以四次Bézier曲面为其特殊情形；其次，详细分析了该曲面的一些基本性质，以及讨论了该曲面的一些特殊退化曲面的构造；最后，为了解决造型设计中复杂曲面难以用单一曲面表示的问题，进一步研究了该曲面的拼接技术，推导了两相邻四次带参广义Bézier曲面片间G1和G2光滑拼接的几何条件，并给出了具体的拼接步骤与几何造型实例。实例结果表明，所提方法不仅简单有效且易实现，可应用于工程复杂曲面的构造与外形设计中。

英文摘要：

A new geometric model of quartic generalized Bézier surfaces with multiple shape parameters was constructed by using a class of quartic generalized Bernstein basis functions. The proposed quartic generalized Bézier surfaces inherit the outstanding properties of conventional Bézier Surfaces, have a good performance on adjusting their shapes by changing shape control parameters, and have quartic Bézier surfaces as their special cases. Some basic properties of the surfaces were analyzed, and the constructions of some special surfaces degenerated from the generalized surfaces were discussed. With the aim to tackle the problem that the engineering complex surfaces can not be constructed by a single surface, the continuity conditions of quartic generalized Bézier surfaces with shape parameter were investigated. Based on the analysis of the basis functions, the conditions of G1 and G2 continuity between two adjacent quartic generalized Bézier surfaces and the detail process to blend the two surfaces were proposed. In addition, some applications of the quartic generalized Bézier surfaces in geometric modeling were discussed. The modeling examples show that the proposed method is effective and easy to implement and has extensive applications in constructing engineering complex surface.