Robotic hot-blade cutting is a method for carving blocks of polystyrene foam (or other materials) with a heated rod or blade, the ends of which are controlled by a robot. As the shape of the rod can change dynamically during the movement, this allows the fast production of complex geometry for architectural formwork; however a usable theoretical model is required in order to control the result. The shape of the rod is an elastic curve segment, and hence the surface is foliated by elastic curves. Although these curves are well understood, it is difficult to work with them from a computational design point of view.
I will discuss some solutions to this problem, as well as some other related geometric problems.