Mathematical structures of line drawings of polyhedral scenes are studied from the viewpoint of scene analysis. First, algebraic structures of line drawings are elucidated, and a necessary and sufficient condition is obtained for a line drawing to represent a polyhedron. Next, combinatorial structures are investigated and the class of pictures that represent nontrivial three-dimensional configurations when vertices are drawn in general position is characterized by incidence structures of polyhedra. The results are furthermore applied to correction of vertex-position errors, discrimination between correct and incorrect line drawings, recognition of unique solvability of some figure-construction problems, classification of line drawings, and other related problems. © 1984.
Sugihara, K. (1984). An algebraic and combinatorial approach to the analysis of line drawings of polyhedra. Discrete Applied Mathematics, 9(1), 77–104. https://doi.org/10.1016/0166-218X(84)90092-1