Abstract: A bidirectional interpolation modeling algorithm for a B-spline surface is discussed based on Coons-Gordon principle, which makes the final surface interpolates two families of intersected section sample points. Parameters of all samples and knot vector of each section are calculated. The parameter of each section line on the interpolation surface is evaluated. A unified knot vector is deduced according to the knots of section lines in the same family and surface parameters for the section lines in the other family. Three B-spline surfaces are obtained by interpolating the two families of section lines and their common points respectively, the Boolean sum of which is the desired interpolation surface. Examples indicate that the bidirectional interpolation surface has fewer control points and perfect fairness.

Key words: B-spline surfaces, bidirectional interpolation, knots insertion, surface skinning

摘要： 基于Coons-Gordon造型原理，研究了插值两族相交截面线采样点的B样条曲面双向插值造型算法。参数化各采样点并计算每条截面线的节点矢量，估算每条截面线对应的曲面参数，根据每条截面线的节点分布以及另一族截面线对应的曲面参数统一节点矢量。分别插值两族截面线采样点及其公共点得到三张B样条曲面，其布尔和即为插值两族截面线采样点的B样条插值曲面。实例表明，得到的双向插值曲面控制顶点数少，光顺性好。

关键词: B样条曲面, 双向插值, 节点插入, 曲面蒙皮