Optical projection is sometimes used in reproducing a virtual object on a surface (2D or 3D surface) such as a wall with a projected image so that a painter can paint the wall according to the projected image. In a typical setup for wall painting, an optical projector is connected with a computer and an application running by the computer projects a virtual object in the form of a digital image to the wall via the optical projector. A user goes to the wall with a pencil in hand and uses his eyes to find the digital image. The user can thereby reconstruct the virtual object on the wall with the digital image that he sees and the pencil. With such a system, it is often desired to maintain the exact relative coordinate properties of the virtual object in the reproduction process. For a system for reproducing virtual objects, it is also desired to be able to measure the displacement between a physical object and a virtual object reproduced on the same physical space.