1. A user interface method, comprising: displaying an object on a display screen; defining an interaction surface containing an interaction region in space, and mapping the interaction surface to the display screen; capturing a sequence of depth maps over time of at least a part of a body of a human subject; processing the depth maps in order to detect a direction and speed of movement of the part of the body and to predict a touch point of the part of the body, responsively to the movement, wherein the touch point indicates a location in the interaction surface where the part of the body penetrates the interaction surface; controlling a computer application so as to change the displayed object on the screen responsively to the mapping and to the predicted touch point; and wherein processing the depth maps comprises identifying, responsively to the detected movement, a collision induced by the movement with a predefined three-dimensional shape in space.