To obtain visual information of a target object, a camera should be placed within the visibility region. As the visibility region is dependent on the relative position of the target object and the surrounding object, the position change of the surrounding object during a task requires recalculation of the visibility region. For a fast computation of the visibility region so as to modify the camera position to be located within the visibility region, we propose a spherical projection method. After being projected onto the sphere the visibility region is represented in $ heta$-$psi$ spaces of the spherical coordinates. The reduction of calculation space enables a fast modification of the camera location according to the motion of the surrounding objects so that the continuous observation of the target object during the task is possible.