ERBS-surface construction on irregular grids

In applications of geometric modeling is surface modeling a key issue. The most important type of surfaces are tensor product spline surfaces. They are in general based on regular gridding, i.e. knot vectors are the same for all "lines" or "columns". Examples are B-spline surfaces, Hermite-spline surfaces and Expo-rational B-spline surfaces. Surfaces based on "irregular grids" has been developed. We find them in for example T-splines and LR-splines. In general, surfaces based on irregular grids can be regarded as a collection of surfaces on regular grids that are connected at the edges and the corners in a smooth, but irregular way. We show that for Expo-rational B-splines (ERBS) the connection can be implemented by using; special blending surfaces between regular patches, and reparametrization to obtain a correct orientation in the parameter plane. We show example of ERBS-surface on irregular grids, indicating practical use in applications.