Algorithms for Computing Global Accessibility Cones

This paper describes algorithms for computing global accessibility cones for each face (i.e., the set of directions from which faces are accessible) on a polyhedral object. We describe exact mathematical conditions and the associated algorithm for determining the set of directions from which a planar face with triangular boundary is inaccessible due to another face on the object. By utilizing the algorithm to compute the exact inaccessibility region for a face, we present algorithms for computing global accessibility cones for each face on the object. These global accessibility cones are represented as a matrix structure and can be used to support a wide variety of accessibility queries for the object.