Abshurct-Th-ihger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a 6nger contact space to the object surface. Conditions are developed to identity the feasible grasping region, F, in the m e r contact space. A "grasping energy hction," E, is introduced that which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to 6nd these critical points. In particular, global optimization techniques are applied to 6nd the "maximal" or "minhal" grasp. Further, modeling techniques are introdud for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces.