This paper presents a novel approach for fast rigid docking of proteins based on geometric complementarity. After extraction of the 3D molecular surface, a set of local surface patches is generated based on the local surface curvature. The shape complementarity between a pair of patches is calculated using an efficient shape descriptor, the Shape Impact Descriptor. The key property of the Shape Impact Descriptor is its rotation invariance, which obviates the need for taking an exhaustive set of rotations for each pair of patches. Thus, complementarity matching between two patches is reduced to a simple histogram matching. Finally, a condensed set of almost complementary pairs of surface patches is supplied as input to the final scoring step, where each pose is evaluated using a 3D distance grid. The experimental results prove that the proposed method demonstrates superior performance over other well-known geometry-based, rigid-docking approaches.