An analytical formulation for finding the proximity of two arbitrary cylinders in space

This paper presents an analytical formulation for finding the proximity of two cylinders in space. The cylinders are decomposed into four geometric primitives each. It is shown that the original problem is equivalent to finding the shortest distance between five distinct combinations of these primitives. Four of these subproblems are solved in closed form, while the remaining one requires the solution of an eight-degree polynomial equation. The analytical nature of the formulation allows the identification of the degenerate cases, e.g., partial/complete containment of one cylinder inside the other, in a guaranteed manner. The theoretical developments are illustrated with the help of examples depicting various configurations of the cylinders. © 2013 ACM.