Curved support structures and meshes with spherical vertex stars

Abstract

The computation and construction of curved beams along freeform skins pose many challenges. We show how to use surfaces of constant mean curvature (CMC) to compute beam networks with beneficial properties, both aesthetically and from a fabrication perspective. To explore variations of such networks we introduce a new discretization of CMC surfaces as quadrilateral meshes with spherical vertex stars and right node angles. The computed non-CMC surface variations can be seen as a path in design space - exploring possible solutions in a neighborhood, or represent an actual erection sequence exploiting elastic material behavior.