This paper presents the use of independent contact and non-graspable regions to generate the grasp space for 2D and 3D discrete objects. The grasp space is constructed via a sampling method, which provides samples of force-closure or non force-closure grasps, used to compute regions of the graspable or non-graspable space, respectively. The method provides a reliable procedure for an efficient generation of the whole grasp space for n-finger grasps on discrete objects; two examples on 2D objects are provided to illustrate its performance. The approach has several applications in manipulation and regrasping of objects, as it provides a large number of force-closure and non force-closure grasps in a short time.