Expressing Coons-Gordon surfaces as NURBS
The authors combine the techniques of the well-known Boolean-sum approach to Gordon/Coons surfaces with that of the \(B\)-spline representation of curves and surfaces; what comes out is a quite nice method for the \(B\)- spline-representation (linear and to some extend rational) of Gordon/Coons surfaces. To be more precise, here are the three main steps of the method: 1) Apply a \(B\)-spline interpolation scheme to the given boundary curves in order to construct three \(B\)-spline surfaces whose Boolean sum form represents the corresponding Gordon/Coons surface. 2) Make these three surfaces compatible (by using degree elevation and knot insertion methods) so that they have the same degree, control net and knot vector. 3) Turn the Boolean sum of these three surfaces into a (unique) \(B\)- spline surface which is the exact representation of its corresponding Gordon/Coons surface by simply forming the Boolean sum of their control nets. A total of 18 figures illustrates the authors' considerations.
scientific article; zbMATH DE number 530098