Spherical harmonic (SPHARM) description is a powerful Fourier shape modeling method for processing arbitrarily shaped but simply connected 3D objects. As a highly promising method, SPHARM has been widely used in several domains including medical imaging. However, its primary use has been focused on modeling small or moderately-sized surfaces that are relatively smooth, due to challenges related to its applicability, robustness and scalability. This paper presents an enhanced SPHARM framework that addresses these issues and show that the use of SPHARM can expand into broader areas. In particular, we present a simple and efficient Fourier expansion method on the sphere that enables large scale modeling, and propose a new SPHARM registration method that aims to preserve the important homological properties between 3D models. Although SPHARM is a global descriptor, our experimental results show that the proposed SPHARM framework can accurately describe complicated graphics models and highly convoluted 3D surfaces and the proposed registration method allows for effective alignment and registration of these 3D models for further processing or analysis. These methods greatly enable the potential of applying SPHARM to broader areas such as computer graphics, medical imaging, CAD/CAM, bioinformatics, and other related geometric modeling and processing fields.