Recognition of polyhedra by a mechanical theorem proving method

Proposes a new application of Wu´s (1978) mechanical theorem proving method for recognition of polyhedra in 3D space from the projection image. First, the authors set up a number of equations which express the vertices on plane segments, line segments, angles in 3D space and those on the image plane, and also the relations between the vertices in 3D space and those on the image plane. Next, they classify all the equations into two parts, a set of hypotheses and a conjecture. Then they obtain a pseudodivided remainder of the conjecture by Wu´s method, which represents a relation of angles or a relation of lengths between the 3D space and its projected image. Also they show that by a stability analysis the remainder can be defined even in the case that vertices on the image plane are in unstable areas of hypotheses whose denumerators approach to zero, so that it cannot be defined by direct manipulations of the hypotheses and conjecture polynomials