A closed-form solution for the reconstruction of a convex polyhedron from its extended Gaussian image

The extended Gaussian image (EGI) of a polyhedron is a compact representation of a polyhedral object and is unique for convex polyhedra. A set of equations is developed, the solution of which reconstructs the polyhedron. The concepts of an augmented EGI, cross-adjacency, and fictitious EGI points are introduced and utilized in the recovery of the adjacency of faces. An example is included to illustrate the use of this technique