Topological Method of Construction of Point Surfaces as Physical Models

The shape of architectural objects in general can be treated as an envelope - a two dimensional surface embedded into three dimensional space. We directly perceive only the surface as a synthesis of sequential “photo snaps” - the two dimensional imprints on a retina - a concave screen inside of our eyes. In 15th century Italian architect and theorist L. B. Alberti claimed that the architecture consists in the outlines and the structure (lineamenta et structura in the original Latin text). The visible shape (outlines) exists only because a directly not perceived structure determines it. Like Alberti, the modern mathematical theories of form distinguish the shape as an exterior surface and the form itself as an internal structure. This subtle difference becomes a very important subject in the relationship between a virtual and a physical model in the studies of architectural endoscopy