RECONSTRUCTION OF POLYHEDRA BY A MECHANICAL THEOREM-PROVING METHOD

In this paper we propose a new application of Wu's mechanical theorem proving method to reconstruct polyhedra in 3-D space from their projec tion image. First we set up three groups of equations. The first group is of the geometric relations expressing that vertices are on a plane segment, on a line segment, and forming angle in 3-D space. The secon d is of those relations on image plane. And the rest is of the relatio ns between the vertices in 3-D space and their correspondence on image plane. Next, we classify all the groups of equations into two sets, a set of hypotheses and a conjecture. We apply this method to seven cas es of models. Then, we apply Wu's method to prove that the hypotheses follow the conjecture and obtain pseudodivided remainders of the conje ctures, which represent relations of angles or lengths between 3-D spa ce and their projected image. By this method we obtained new geometric al relations for seven cases of models. We also show that, in the regi on in image plane where corresponding spatial measures cannot reconstr ucted, leading coefficients of hypotheses polynomials approach to zero . If the vertex of an image angle is in such regions, we cannot calcul ate its spatial angle by direct manipulation of the hypothesis polynom ials and the conjecture polynomial. But we show that by stability anal ysis of the pseudodivided remainder the spatial angles can be calculat ed even in those regions.