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.Bibtex:
@article{barton-2013-snakes,
AUTHOR = {Barton, M. and Shi, L. and Kilian, M. and Wallner, J.
and Pottmann, H.},
TITLE = {Circular arc snakes and kinematic surface generation},
JOURNAL = {Computer Graphics Forum},
VOLUME = {32}
YEAR = {2013},
}