Surfaces with planar curvature lines: Discretization, generation and application to the rationalization of curved architectural envelopes

Motivated by architectural applications, we propose a method to generate circular and conical meshes with planar curvature lines in both directions. The method is based on the discretization of the Gauss map of surfaces with planar curvatures lines. It allows generation of meshes in real-time via two planar guide curves. The resulting meshes can be used as a geometric base to build gridshells with flat panels, torsion free-nodes, node offset and planar arches. A particular technological application is for gridshells built with curved members: those can be built with planar piecewise-circular beams, and identical nodes if beams have circular cross-section.