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This interdisciplinary research project presents a corporation of architects, mathematicians and computer scientists. The team researches new methods for the efficient realization of complex architectural shapes. The present work investigates methods of iterative geometric design inspired by the work of Barnsley. Several iteratively constructed geometric figures will be discussed in order to introduce to the notion of transformation driven geometric design. The design method studied allows interacting with the design forming affine transformations and generates discrete geometries. Further, the handling of specific constraints is discussed. Geometrical and topological constraints aim to facilitate production of architectural free form objects. A surface method based on vector sums is studied. It allows designing free form surfaces that are entirely composed of planar quadrilateral elements. The combination of the proposed surface method and transformation driven iterative design provides new form-finding possibilities while satisfying a certain number of material and construction constraints. Finally, the findings are tested on a series of applications. The studied test scenarios aim to evaluate the advantages of discrete geometric design in terms of efficient integrated production of free form architecture.