Voronoi Grid-Shell Structures

Abstract: We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input surface and we use the resulting tensor field to induce an anisotropic non-Euclidean metric over it. Then we compute a Centroidal Voronoi Tessellation under the same metric. The resulting mesh is hex-dominant and made of cells with a variable density, which depends on the amount of stress, and anisotropic shape, which depends on the direction of maximum stress. This mesh is further optimized taking into account symmetry and regularity of cells to improve aesthetics. We demonstrate that our grid-shells achieve better static performances with respect to quad-based grid shells, while offering an innovative and aesthetically pleasing look.