Circular arc snakes and kinematic surface generation

M. Barton, L. Shi, M. Kilian, J. Wallner, H. Pottmann
EuroGraphics, volume 32, issue 2pt1, pp. 1-10, (2013)

Circular arc snakes and kinematic surface generation


Computational Geometry                


​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.





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