aG-Spline-Surfaces provide a means to model freeform surfaces. These surfaces consist of polynomial pieces with geometrically smooth transitions, i.e. the normals or curvatures are continuous. One way to construct such G²-surfaces for triangular nets (i.e. quartic box splines) is described in [PU99]. An example is shown below: to the left is the triangular control net of a generalized quartic box spline surface, in the middle the corresponding generalized quartic box spline surface and to the right the resulting G²-surfaces. The goal of this project is to generalize this approach to arbitrary smoothness order while keeping at the same time the number of the required patches to a minimum.

Publications in this project can be found here: [PU06], [PU99].