Geometric Reasoning in 3d Building Models Using Multivariate Polynomials and Characteristic Sets

In order to generate complex virtual cities, models of buildings have to be defined in advance. A common approach describes individual components of these buildings, which are in turn restricted by geometric constraints such as orthogonality, parallelity or symmetry of building parts. A major challenge is to ensure consistency and avoid redundancy. Tools are needed which support geometric reasoning and thus the modelling of buildings. This leads to the theory of automatic theorem proving. By using this theory it can be shown that a constraint is deducible from a set of axioms that can be realized by using multivariate polynomials. We draw upon Wu’s method and claim that 3D reasoning for building models is feasible.