Hand redirection is a visuo-haptic illusion offering rich haptic feedback in Virtual Reality while using a limited number of physical objects. This technique relies on a redirection function which determines the virtual hand position depending on the physical hand position. In this paper, we extend the design space of the Handredirection technique by generalizing this redirection function. A user study compares 6 redirection functions. Our results suggest that the redirection function does not deteriorate the illusion offering more flexibility and control to designer over the hand trajectory and avoid collisions.