From theoretical graphic objects to real free-form solids

Formal models can be useful in computer graphics as a conceptual framework supporting representation systems. This allows to formally derive properties and algorithms and proof their correctness and validity. This paper describes a formal model based on a geometric algebra. This algebra has been used to obtain specific representation systems and study their equivalence. The representation systems derived in a natural way from this model are based on simplicial coverings and can be applied to non-manifold solids and to solids with holes. Representations have been developed for polyhedral and free-form solids. Algorithms described and proved include boolean operations and representation conversion.The paper covers the three abstraction levels: theoretical model, representations and derived algorithms. As a practical application an experimental modeller for free-form solid has been developed (ESC-MOD system: “Extended Simplicial Chains MOdeller”).