Registration pointer with interchangeable tip and method

A registration pointer for registering points of surfaces of bodily elements in computer-assisted surgery, comprising a handle for being manipulated by a pointer operator. A stem is connected to the handle and has a first and a second tip configurations each having a respective use relating to a registration of points on specified bodily elements. A detectable device is secured to the stem, and is adapted to be tracked in space for position and orientation by a sensing apparatus. A position of the tip configurations with respect to the detectable device is determinable such that a position of the tip configurations is calculable as a function of the position and orientation of the detectable device. The tip configurations are chosen to register points on given bodily elements as a function of the respective use, by recording a position of points of contact between the tip configurations and the given bodily element.