Circular Arc Snakes and Kinematic Surface Generation. (7th May 2013) - Bartoň, M.; Shi, L.; Kilian, M.; Wallner, J.; Pottmann, H.
Abstract: We discuss the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The discretization of a curve as a smooth sequence of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite‐dimensional shape space. We approach this evolution by a 2‐step process: linearized evolution via optimized velocity fields, followed by optimization in order to exactly fulfill all geometric side conditions. We give applications to freeform architecture, including "rationalization" of a surface by congruent arcs, form finding and, most interestingly, non‐static architecture.