Circular arc snakes and kinematic surface generation

Michael Barton, Ling Shi, Martin Kilian, Johannes Wallner, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalComputer Graphics Forum
Volume32
Issue number2pt1
DOIs
StatePublished - May 7 2013

ASJC Scopus subject areas

  • Computer Networks and Communications

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