Surface modelling with an irregular network of curves via sweeping and blending (Q1335426)

The author proposes a method for the generation of surfaces, starting from a given network of curves which are allowed to have rather arbitrary parametric forms and can be defined on an arbitrary topology. The surfaces generated from the network are represented by \(m\)-sided patches, defined on a multivariate coordinate system. Such a patch is generated by blending \(m\) subsurfaces with a transfinite interpolant, where each subsurface is generated by sweeping curves in a network. After reviewing a lot of relevant literature, the author describes in detail several steps of his method; in particular, questions how to treat multiple or \(T\)-connected intersections of curves are investigated. Moreover, it is shown that each patch can be \(G^ n\)-connected with adjacent patches, if all the curves surrounding it are \(C^ n\)- continuous. A total of 8 figures and several colour plates illustrate the results.