Abstract: This paper transforms the relative displacements of one object with respect to a reference object into image points by a mapping in terms of affine coordinates. The mapping provides a novel mathematical tool that solves interference problems of objects in three-dimensional space. By use of this mapping, the geometrical condition of interference of object is represented by simple inequalities. The inverse mapping provides the means of avoiding interference and can be utilized for articulation of robot arms so as to avoid collision with obstacles.