A projected target location of a handheld object is determined based on applying translation factors, scaling factors, and offsets to a location of a reference element of the handheld object detected by a camera on a two-dimensional plane. The translation factors are determined based on a difference between a calibration location on the plane and an initial location of the reference element corresponding to the calibration location, and serve to shift the location of the reference element to generate the projected target location. The scaling factors are determined based on an estimated length of a user's arm holding the handheld object, and serve to scale the location of the reference element to generate the projected target location. The offsets are determined based on polynomial equations, and serve to extend the distance between the projected target location and the calibration location.