How to 3D-print Complex Networks and Graphs

Raymond Aschheim
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 445–448 Short Papers


Artists and scientists have offen the need to get 3D printed models of structures made of nodes and edges, like graphs, networks, skeletons. While 3D printing is now accessible to everyone just by uploading STL files to websites like shapeways or imaterialise, and get an instant validation and quote, the generation of suitable files from graph raw data is still not available through open tools. If the graph has some dozens of edges, it is easy to build the STL with some CSG tool by making the boolean union of cylinders and spheres. But for complex graphs with hundreds of edges, these tools are failing. An elegant solution was presented by George Hart during Bridges 2008 for sculptures with non intersecting struts. We explain here a method suitable when struts are intersecting. We draw in 3D our lines using voxels, then slice it into an image stack, and triangulate it using marching cube algorithm. Optimization steps are needed to minimize the number of faces (under 1M) and the file size.