过等参测地线的B样条曲面重构

Reconstruction of B-spline surfaces through isoparametric geodesics

基于一般正则曲面上测地线的几何特征以及B样条乘积和升阶理论,构造了一类B样条曲面插值预先给定的B样条曲线,使这些曲线成为所构造曲面的边界等参测地线.该方法显式地计算了插值曲面上与插值条件相关的控制顶点,并且测地线插值条件中自由参数对曲面形状的影响具有局部性,插值曲面内部的自由控制顶点可作为曲面形状调整一种手段.与传统Coons超限插值方法不同,该方法所构造的插值曲面表示成标准的张量积B样条形式,与当今主流CAD系统的内在要求一致.计算实例表明该方法可行.

Based on the geometric features of geodesic on regular surface and the theory of products and degree raising of B-spline, a B-spline surface interpolating the given space B-spline curves is constructed. The curves are isoparametric boundary geodesics of the constructed surface. The control points associating with interpolation conditions are computed explicitly. The free parameters of the geodesic interpolation conditions only affect the local shape of surface, and the shape of the interpolating surface can be adjusted by its free inner control points. Being different from the traditional Coons interpolation scheme, the constructed surface is presented as standard tensor-product B-spline form, which is compatible with modern CAD systems. The method is illustrated with computational examoles.