Triangular bubble spline surfaces
We present a new method for generating a Gn G n -surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple Gn G n -condition between two neighboring bubble patches, which are used to construct surface patches, connected with Gn G n -continuity. For n?2 n ? 2 , we describe the obtained Gn G n -condition in detail. It can be generalized to anyn?3 n ? 3 . The construction of a single surface patch is based on GordonCoons interpolation for triangles. Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of G0 G 0 , G1 G 1 and G2 G 2 -surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness.
network of compatible surface strips gordoncoons interpolation for triangles gn g n -surface gn g n gn g n g n triangular bubble patch