New Method of Numerical Fitting for Overall Smoothing of Closed Convex Polyhedrons

A new method is put forward for holistically smoothing three-dimensional closed convex polyhedron surfaces in connection with the closed surface fitting problems which cannot be solved using aggregate functions in Cartesian coordinate system. In this method, cohesion envelope algorithm is promoted to spatial polar coordinate, area scan fitting is performed for closed convex polyhedrons with the help of mapping technology and interior radius vector sweeping method, and thus the entire smooth closed surface approximating the original convex polyhedron is obtained. The surface is expressed using one fitting function and its fitting accuracy is easy to be controlled. Therefore, such closed surface modeling problems are solved and the effectiveness of this method is proved by examples.