【摘要】 曲线、曲面是计算机图形学中物体造型技术研究的重要内容,B样条曲线曲面已成为几何造型的核心部分。设计实现了根据4条B样条边界曲线及其跨界导矢,生成过渡CNSBS曲面的方法。首先由B样条曲线曲面的定义,生成4片待拼接的B样条曲面;其次根据待拼接曲面的边界曲线上的型值点,反算求出边界曲线的控制点,生成4条边界曲线,并求出其跨界导矢;运用节点插入法,求出曲面上的控制顶点,分别构造插值于u向和v向曲线及其跨界导矢的2个B样条曲面;根据定理分别求出2个B样条曲面的表达式,将2个曲面合并成一张曲面,求得CNSBS曲面的表达式,该曲面与周边B样条曲面呈C1连续;最后总结了CNSBS曲面拼接方法的特点。更多还原

【Abstract】 Curve and surface are important contents of object modeling technology in computer graphics.B-spline curve and surface has become the core part of geometric modeling.In this paper,we design and implement a method to generate transitional CNSBS surface based on four B-spline boundary curves and their cross boundary derivatives.Firstly,four B-spline surfaces are generated according to the definition of B-spline curves and surfaces.Secondly,according to the type value points on the boundary curves of the surfaces to be spliced,the control points of the boundary curves are calculated reversely;four boundary curves are generated;and their cross boundary derivatives are obtained.By using the node insertion method,the control vertexes on the surfaces are obtained,and the interpolation curves in u direction and v direction and their cross boundary derivatives are constructed respectively.Then,according to the theorem,the expressions of two Bspline surfaces are obtained respectively,and the two surfaces are combined into one surface to obtain the expression of CNSBS surface,which is C1 continuous with the peripheral B-spline surfaces.Finally,this method is summarized.更多还原