Many object surfaces involve a number of pieces, expressed by different equations. Previous methods of optimal grasp planning can hardly cope with such cases. Ding et al. solve this problem by characterizing the object surface with convex facets and discrete points, then selecting the eligible ones for force-closure, and finally seeking the optimal contact positions on the selected elements. So far, however, no point contact with friction (PCwF) but only frictionless point contacts (FPC) can be used on the facets, while soft finger contacts (SFC) are excluded at all. In this paper, to the above two surface elements we add line segments. Moreover, the limitations on the contact types are completely removed. A general condition and a quantitative criterion of eligibility are presented, followed by a heuristic algorithm and an iterative algorithm for finding the better eligible elements. Three common examples show: the new advances make the formerly tough problems smoothly solvable.