Geometric methods for shape recovery from line drawings of polyhedra

Abstract

Using structural geometric arguments, Whiteley showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We here enlarge the class of drawings to which this test applies, including those of polyhedral disks, possibly with perforations. This extension is helpful, as it makes the test applicable to verify and reconstruct drawings from usual scenes with opaque objects. The presented results rely on geometric constructions, thus offering an alternative approach to line drawing interpretation, complementary to the algebraic-combinatorial treatment given in the classic work by Sugihara.