A method for fast visual grasping of unknown objects with a multifingered robotic hand is presented in this paper. The algorithm is composed of an object surface reconstruction algorithm and a local grasp planner, evolving in parallel. The reconstruction algorithm makes use of images taken by a camera carried by the robot arm. A virtual elastic reconstruction surface is placed around the object. The surface shrinks toward the object until some points intercept the object visual hull. Then, attractive forces with respect to the border of the visual hull are generated so as to compensate for the elastic forces: when an equilibrium between those forces is reached, the surface takes the form of the object shape. Running in parallel to the reconstruction algorithm, the grasp planner moves the fingertips on the current available reconstruction surface, toward points which are optimal (in a local sense) with respect to a number of indices weighting both the grasp quality and the kinematics configuration of the hand. This method, referred to as parallel visual grasp, may represent a valid candidate for applications where online grasp planning is required. A number of experiments are presented, showing the effectiveness of the proposed approach.