This work describes new approach for the computation of 3D Fourier descriptors, which are used for characterization, classi fication, and recognition of 3D objects. The method starts with polygonization of the object's surface. Next, progressive mesh is constructed from the polyhedron using quadric-based polygonal surface simplification. Then, the same progressive mesh is exploited to efficiently reconstruct the original polyhedron onto the surface of sphere, which is necessary step for the computation of 3D Fourier descriptors. The mapping method is shown to be efficient and fast in projecting an arbitrarily shaped polyhedron onto sphere surface.