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。
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 B-spline 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.
作者
吴丽娟
张心慈
任海清
梁岱立
黄尧
齐维毅
WU Lijuan;ZHANG Xinci;REN Haiqing;LIANG Daili;HUANG Yao;QI Weiyi(College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China)
出处
《沈阳师范大学学报（自然科学版）》
CAS
2021年第2期178-181,共4页
Journal of Shenyang Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(201102205)。
关键词
CNSBS曲面
边界曲线
跨界导矢
曲面拼接
CNSBS surface
boundary curve
cross-border guide vector
surface stitching
