Abstract
The study of smooth surface reconstruction from a set of 3D range data obtained by a laser scanner has become increasingly important in the area of reverse engineering, animation, and scientific visualization. The most popular representation for fitting such data in geometric modeling is the tensor product B-Spline surfaces. However, it is extremely difficult for tensor product surface to handle surfaces with arbitrary topology, and to maintain continuity conditions near the extraordinary points. New class of surfaces, called subdivision surfaces, which offers an alternative to the tensor product B-Spline has recently received attention in computer graphics and geometric modeling. We present a novel geometric algorithm to construct a smooth subdivision surface that interpolates the n vertices of triangular mesh of arbitrary topological type without solving a linear system. We start our algorithm by assuming that the given triangular mesh is a control net of the Loop subdivision surfaces. The control points are iteratively updated by a simple point-surface distance computation and an offsetting procedure. The complexity of our algorithm is O(mn) where m is number of iterations. Therefore it is very fast compared to the conventional fitting methods, as m>>n.
