An algebraic and combinatorial approach to the analysis of line drawings of polyhedra

AbstractMathematical 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