In this work we introduce a novel approach for robot grasp planning. The proposed method combines the benefits of programming by human demonstration for teaching appropriate grasps with those of automatic 3D shape segmentation for object recognition and semantic modeling. The work is motivated by important studies on human manipulation suggesting that when an object is perceived for grasping it is first parsed in its constituent parts. Following these findings we present a manipulation planning system capable of grasping objects by their parts which learns new tasks from human demonstration. The central advantage over previous approaches is the use of a topological method for shape segmentation enabling both object retrieval and part-based grasp planning according to the affordances of an object. Manipulation tasks are demonstrated in a virtual reality environment using a data glove. After the learning phase, each task is planned and executed in a robot environment that is able to generalize to similar, but previously unknown, objects.