A simple method of finding a visible region for the optimal camera position

There are many applications that use a camera to find, locate, and track a target object, such as spray painting, spot welding, pick-and-place, part insertion, material handling and so on. The most important thing in such a vision task is that the camera should be able to observe the target object at a good position. The more complicated a workspace is, the more difficult it is to find the regions where the camera should be located for observation of the target object. In order to relieve the difficulty to find a visible region in 3D space, we suggest a simple method to find the visible region using object expansion method and projection onto the spherical coordinates.