AbstractAn innovative method of shaping free form buildings composed of many original complete parts roofed with profiled steel sheets transformed effectively into hyperbolic paraboloid strips is proposed in the paper. The method uses tetrahedral compositions of various kinds connected one to another with their relevant faces contained in planes of a spatial network called control structure. The control structures enable: a) controlling structural systems and architectural forms of the complex buildings as well as their morphological systems, b) arranging regularly the roof shells in three-dimensional space, c) integrating the roof and elevation forms as well as their consistent composition into the natural and built environments. The effectiveness of the transformations consists in the fact that displacements of adjacent folds in the sheeting are big, whereas strain is small. The effective transformations affect the fold's shape in such a way that the folds are contracted in the middle on their length and stretched at their crosswise ends depending on supporting conditions produced by curvature and a mutual location of skew directrices. The supporting conditions are diversified along each directrix, so the diversified arrangement of the supporting points of the shell folds to the skew directrices has to be calculated. For this purpose, an innovative computer program was created. Because of the diversified fold shape changes, two individual shell sheeting's cannot be connected one to another with their transversal borders to obtain a smooth shell. However, many shells can be set together with their transversal edges to achieve a compound ribbed roof of medium or large span. Thus, the resultant shell roof has to be characterized by edges disturbing its smoothness.