In this paper a method for fast visual grasp of unknown objects with a multi-fingered hand is presented. The algorithm is composed of an object surface reconstruction algorithm and a local grasp planner, evolving in parallel. The former uses an elastic reconstruction surface, whose dimensions are assigned initially by a preshaping process, and which shrinks toward the object until some parts of the surface intercept the object visual hull. The latter moves the fingertips on the current available reconstruction surface towards points which are optimal (in a local sense) with respect to a certain number of indices weighting both the grasp quality and the kinematic configuration of the hand. Experiments are presented, showing the effectiveness...