The development of digital technologies in the last twenty years has led to an unprecedented formal freedom in design and in the representation in virtual space. Combining non-standard geometry with CAD tools enables a new way of expression and realization of architectural ideas and conceptions. The transformation of a virtual double-curved surface into a buildable physical structure and object is always accompanied by huge costs and big problems like geometric and statical ones. Our structure is a type of shell structure consisting of plane panels. The load bearing system is organized in a way so that the forces are distributed along the edges of the plane elements. A structure with plane elements supports a high stiffness in combination with a relatively small overall weight. This is due to smooth curved shape of the geometry. We show geometric methods how to control the construction of curved surfaces out of planar building elements. The approach is based on the discretization of the surfaces by plane elements derived from tangent planes. The novel process in this work is that we take the surface curvature at local points into account. This solves former problems which occurred when intersecting the planes. The fact that there is an infinite number of possibilities when selecting tangent planes on a surface raises the issue of the way and conditions which make it possible to select specific tangent planes whose intersection would produce a desired three-dimensional shape. In order to satisfy also aesthetical requirements we engage plane geometrical patterns and ornaments and transfer them into spatial shape. So a three-dimensional ornamental shape is deduced from a two-dimensional ornament. Another task which will be showed is how to limit the infinite range of possibilities to generate a preferred spatial ornament and on what conditions surface tessellation would be ornamental in character, i.e. it would generate not only the functional, but also the aesthetic component of a free-form surface.