On translating a set of objects in 2- and 3-dimensional space

Given a collection of geometrical objects, we want to translate them in a given direction, one at a time, without collisions occurring between the objects. We present efficient algorithms to determine whether the translation is possible and to determine in which order the objects can be translated. The paper expands the results of Guidbas and Yao [6] for line segments and convex polygons in the plane to include topologically more complex objects in 2- and 3-dimensional space. The algorithms will be useful in programs developed for graphical applications and robotics.