Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: calculating a radius of incidence for respective pairings of beams of different sizes that converge at a junction in a lattice; determining a maximized radius of incidence for each of the beams based on the radii of incidence for the pairings with that beam; comparing the maximized radii of incidence to find a global radius for the junction; calculating local intersection points and global intersection points, respectively, for each of the beams with a local sphere defined by the maximized radius of incidence for that beam and with a global sphere defined by the global radius for the junction; and generating meshing with sockets for the beams at the junction using the local intersection points and the global intersection points.
