An algorithm for efficient decomposition of interface channels between non-convex polygons in a Computer-Aided Design (CAD) environment is presented. This algorithm forms the computational basis for the solution of several design automation problems. In this paper, the channel decomposition algorithm is presented and applied to the problem of interference detection between non-convex polygons. The resulting interference detection algorithm does not require preprocessing of the data and uses a simple data structure. In a companion paper (Ku and Ravani 1988), the channel decomposition algorithm is applied to the problem of model-based rigid-body guidance in presence of geometric constraints.