局部构造C^2连续的三次B样条插值曲线和双三次插值曲面  

Local Approach to Construct Cubic B-Spline Interpolation Curve and Surface with C^2 Continuity

作　　者：冯仁忠[1] 查理[1] 

机构地区：[1]北京航空航天大学理学院数学系教育部数学与信息行为重点实验室,北京100083

出　　处：《工程图学学报》2005年第6期110-117,共8页Journal of Engineering Graphics

基　　金：国家自然科学青年基金资助项目(10401021);北京航空航天大学理学院科研创新基金资助项目(0502)

摘　　要：为了避免一般的局部插值算法生成的B样条曲线和曲面在段点处达不到理想的连续性以及出现多重内节点的问题,一种局部构造C2连续的三次B样条插值曲线和双三次插值曲面的方法被介绍。该方法借助节点插入算法逐步地迭代出样条控制顶点,其思想简单、几何直观、算法速度快,在曲线中夹直线段、尖点以及在曲面中夹棱边和平面都能比较容易实现。生成的曲线光滑度高、无重节点。文章最后还利用这种构造方法给出了一种在指定范围内按规定变形曲线的方法。In order to void that B-spline curve and surface created by general local interpolationmethod can＇t attain ideal smooth at joint of two neighbor segments and have multi-fold inner knots, a new for local interpolation curve and surface with C^2 continuity of cubic B-spline is presented. The method determines recursively control vertices by means of knot insertion. Its idea is simple, ntuitive in geometry and its velocity is quick. Inserting a line segment, sharp turn in curve and a sharp edge, local plane on surface is achieved easily. This paper still makes use of the construction idea to give a method of deforming a curve by moving the given data point in a specified curve segment.

关 键 词：计算机应用 C^2连续的三次B样条插值曲线和曲面的构造 局部构造 B样条曲线与曲面 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]