C-B样条曲线及曲面的光滑拼接与应用

On Continuity Conditions for C-B-Spline Curves and Surfaces

论文在对C-B样条基函数及端点性质分析的基础上,提出了C-B样条曲线间拼接的充要条件;同时给出C-B样条曲面的几何模型,分析了两片C-B样条曲面片拼接的几何条件,并通过合理选取控制参数,简化了拼接条件,给出了相关算法及实例。最后,利用C-B样条分割和拼接技术构造工程曲面,所得结论可应用于CAD/CAM建模系统中。

C-B-spline curves are an extension of cubic B-spline curves. In addition to having many properties that B-spline curves have, they have the adjustable shape parameter , and can represent arcs and surfaces more precisely yet require less memory space in computer. As, to our knowledge, there does not exist any paper in the open literature on the continuity condition of C-B-spline curves and surfaces, we now present such a paper. In this paper, we first present condition of C-B-spline curves based on the analysis of C-B-spline basis functions and terminal properties. Then, the geometric model of C-B-spline surfaces is built and condition for C-B-spline surfaces in u and v directions is derived and simplified by choosing the control parameters properly. The result has its specific geometric significance. As a case in point, condition for C-B-spline surfaces is implemented by assigning check points along their common boundary curve and modifying the adjacent surface to meet the requirements of sharing common tangent plane. Finally, from what has been discussed above, we describe in detail how to construct surfaces of revolution, ellipsoids and sweeping surfaces. Moreover, due to the similar structures between C-B-splines and B-splines, the continuity condition of C-B-spline curves and surfaces can be introduced to the CAD/CAM modeling system.