A method is provided for modeling complex shapes from volumetric data utilizing spherical wave decomposition (SWD) by combining angular-only basis functions of the SPHARM with radial basis functions obtained by asymptotic expansion as a series of sine and cosine Fourier transforms to form the complete 3D basis. The 3D basis is used to expand the volumetric data. The resulting 3D volume representation allows construction of images of both surface and internal structures of the target object.