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G. Zimmermann, G. Suter:
"A multi-floor topology to geometry transformation procedure based on shape functions";
in: "CIB W78 22nd Conference on Information Technology in Construction", R.J. Scherer, P. Katranuschkov, S. Schapke (ed.); 22nd Conference on Information Technology in Construction, Institute for Construction Informatics, Technical University of Dresden, Dresden, 2005, 393 - 400.

Building Floor plans are often outlined as schematics with zero wall thickness. Using shape functions, wall dimensions and circulation areas can be inserted and more detailed drawings generated. This topology-to-geometry transformation does not solve vertical constraints in multi-floor topologies, as for example the alignment of load bearing walls. The paper shows how dissection based rectangular floor plans can be modified by introducing space area extensions to resolve the vertical constraints. Penalty values can be introduced to control the distribution of area extensions. The algorithm is based on defining constraints between nodes of the dissection tree. In the presence of multiple constraints, several passes through the dissection tree may be necessary. The topology-to-geometry transformation is used in every pass to check if the constraints can be fulfilled. The algorithm is demonstrated with an example.