An Alignment Method and a Dissimilarity Measure for 3D Building Spatial Designs

IEEE Access, vol. 13, pp. 195599–195610

Abstract

We present a unified topology and geometry dissimilarity measure for 3D Building Spatial Designs and a companion visual alignment method that can pinpoint differences between designs. Buildings are represented as prism nets: the building volume is partitioned into non-overlapping right prisms, and discrete color labels merge selected prisms into individual spaces. Dissimilarity between two prism nets combines three normalized terms: Graph-Edit Distance for adjacency changes, minimal Jaccard distance of matched spaces after rigid rotations and mirrors for shape variation, and mean centroid offset scaled by the enclosing cuboid diagonal for positional change. The measure is symmetric, zero for identical designs and is evaluated in milliseconds. The graph-edit step also provides an optimal relabeling, enabling an automatic ’diff’ view that pinpoints where the spatial designs of two buildings diverge. The tests in 31 multi-level prototypes show reliable clustering and diversity-driven subset selection, indicating the utility of the measure for generative design, quality diversity search, and data-driven analysis of complex building layouts.

Authors 6

1. Ksenia Pereverdieva Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

2. Michael Emmerich

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

   Faculty of Information Technology, University of Jyvaskyla, Finland

3. Andre H. Deutz Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

4. Hèrm Hofmeyer

   Eindhoven University of Technology

   Affiliation as printed

   Eindhoven University of Technology, Eindhoven, The Netherlands

5. Tessa Ezendam

   Eindhoven University of Technology

   Affiliation as printed

   Eindhoven University of Technology, Eindhoven, The Netherlands

6. Thomas Bäck Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands