Given a polyhedral environment, a technique is presented for hypothesizing a channel volume through the free space containing a class of successful collision-free paths. A set of geometric constructions between obstacle faces is proposed, and we define a mapping from a field of view analysis to a direct local construction of free space. The algorithm has the control structure of a search which propagates construction of a connected channel towards a goal along a frontier of exterior free faces. Thus a channel volume starts out by surrounding the moving object in the initial configuration and "grows" towards the goal. Finally, we show techniques for analyzing the channel decomposition of free space and suggesting a path.