Surface approximation of a cloud of 3D points

Presents an implementation of deformable models to approximate a 3-D surface given by a cloud of 3-D points. It is an extension of the authors previous work on “B-snakes” (1990), (1992) which approximates curves and surfaces using B-splines. The user (or the system itself) provides an initial simple surface, such as a closed cylinder, which is subject to internal forces (describing implicit continuity properties such as smoothness) and external forces which attract it toward the data points. The problem is cast in terms of energy minimization. The authors solve this non-convex optimization problem by using the well known Powell algorithm which guarantees convergence and does not require gradient information. Tire variables are the positions of the control points. The number of control points processed by Powell at one time is controlled. This methodology leads to a reasonable complexity, robustness, and good numerical stability