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

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.