Approximation of triangular B-spline surfaces by local geometric fitting algorithm

Surfaces over triangular domain are a powerful and flexible tool for modeling of complex objects with non-rectangular topology. Due to the particular advantages of triangular parametric surfaces, they have wide application and prospect in computer aided design and reverse engineering. The interpolation or approximation problem for reconstructing an arbitrary topological parametric surface from scattered data points or polygonal mesh is one of the significant research areas. This paper deals with the approximation of triangular B-spline surfaces based on a local geometric fitting algorithm and an inverse Loop subdivision scheme. The reconstructed triangular B-spline with the low degree crosses through most of the given data points of an initial triangular mesh. The accuracy of the obtained triangular B-spline surfaces can be carried out by changing the position of control points in the local geometric algorithm as well as a number of the inverse subdivision times. Finally, we demonstrate the effectiveness of the proposed method with some experimental examples.