3D Graphic Statics – Centroidal Voronoi Tessellation

This project explores alternative force diagram generation in 3D Graphic Statics (3DGS) through Voronoi-based spatial subdivision. A 4-sided prism was populated with a set of seed points and subdivided into 3D Voronoi cells, generating an initial force diagram. To achieve a more uniform and optimized cell distribution, Lloyd’s algorithm was applied, producing Centroidal Voronoi Tessellation (CVT). This method ensures a more balanced force network, influencing the resulting form diagram and its structural behavior.

Using PolyFrame and 3D Graphic Statics, the form diagram was planarized and resolved into static equilibrium. The final stage involved geometric rationalization and materialization, converting the polyhedral framework into a structurally legible system. The resulting approach demonstrates potential applications in spatial lattice structures, porous load-bearing elements, and large-scale architectural frameworks.