In the real world, tools used for manipulation are pivoted with specialized tips for specific functions including grasping and cutting. Manipulating deformable virtual objects with them involves maintaining extended contact, which is difficult due to the variations in applied force. Our method consists in selecting a fixed set of points on the jaws of a pivoted tool, and placing them either equidistant or according to the geometry of the tool. Vertex and triangle proximities are calculated for each of the interacting deformable objects for collision detection. This method was successfully tested in a surgical simulation scenario where a deformable omental fat model was grasped and retracted while maintaining full contact with the pivoted tool tip at all times.