An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry, in particular of surface theory. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture and numerics.
These talk is about quadrilateral surfaces, i.e. surfaces built from planar quadrilaterals. They can be seen as discrete parametrized surfaces. Discrete curvatures as well as special classes of quadrilateral surfaces, in particular, discrete minimal surfaces are considered. Their relation to discrete integrable systems is clarified. Application in free form architecture will be demonstrated.