Localizing the 4-Split Method for G1 Free-Form Surface Fitting

One common technique for modeling closed surfaces of arbitrary topological type is to de ne them by piecewise parametric triangular patches on an irregular mesh. This surface mesh serves as a control mesh which is either interpolated or approximated. A new method for smooth triangular mesh interpolation has been developed. It is based on a regular 4-split of the domain triangles in order to solve the vertex consistency problem. In this paper a generalization of the 4-split domain method is presented in that the method becomes completely local. It will further be shown how normal directions, i.e. tangent planes, can be prescribed at the patch vertices.