Barton, MichaelShi, LingKilian, MartinWallner, JohannesPottmann, HelmutI. Navazo, P. Poulin2015-02-282015-02-2820131467-8659https://doi.org/10.1111/cgf.12020We 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.Computer Graphics [I.3.5]Computational Geometry and Object Modeling