Recent advancement in 3D digitization techniques have prompted to the need for 3D object retrieval. Our method of comparing 3D objects for retrieval is based on 3D morphing. It computes, for each 3D object, two spatial feature maps that describe the geometry and topology of the surface patches on the object, while preserving the spatial information of the patches in the maps. The feature maps capture the amount of effort required to morph a 3D object into a canonical sphere, without performing explicit 3D morphing. Fourier transforms of the feature maps are used for object comparison so as to achieve invariant retrieval under arbitrary rotation, reflection, and non-uniform scaling of the objects. Experimental results show that our method of retrieving 3D models is very accurate, achieving a precision of above 0.86 even at a recall rate of 1.0.