An analytical approach for the three-dimensional recognition of quadric surfaces for range images is presented. Initially, after describing each of the quadrics in terms of their implicit representations, a new iterative technique is utilized to determine and eliminate the rotation parameters of the surfaces. The main characteristic of this technique is that it converges in a very few iterations. Next, based on the intersections of surfaces with planes of different orientation, a unique set of feature vectors of characteristic curves is determined for each of the quadrics considered. Furthermore, within the same analysis, angular bounds for the orientation of the intersecting planes are evaluated, so that the necessary and sufficient number of planes is determined for characterizing a surface. Experiments conducted on several sets of real data on quadric surfaces indicate that the proposed method is very accurate and computationally inexpensive.