Beam meshes.

We present an approach for representing free-form geometry with a set of beams with rectangular cross-section. This requires the edges of the mesh to be free of torsion. We generate such meshes in a two step procedure: first we generate a coarse, low valence mesh approximation using a new variant of anisotropic centroidal Voronoi tessellation. Then we modify the mesh and create beams by incorporating constraints using iterative optimization. For fabrication we provide solutions for designing the joints, generating a cutting place for CNC machines, and suggesting a building sequence. The approach is demonstrated at several virtual and real results. Graphical abstractDisplay Omitted HighlightsNew way to manufacture free-form geometry.Highly relevant for architectural frames.New approach to generate coarse polygonal meshes that approximate a given geometry.Effective procedure to optimize manufacturing constraints on mesh.Includes important details for actually creating the geometry.