论文信息 - On the flexibility of Kokotsakis meshes

On the flexibility of Kokotsakis meshes

In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any (3 × 3)-mesh made of quadrangles is a Kokotsakis mesh. We express the infinitesimal flexibility condition in terms of Ceva and Menelaus theorems. Further we study semi-algebraic properties of the set of flexible meshes and give equations describing it. For (3 × 3)-meshes we obtain flexibility conditions in terms of face angles.

Oleg Karpenkov | O. Karpenkov

[1] Hellmuth Stachel,et al. A kinematic approach to Kokotsakis meshes , 2010, Comput. Aided Geom. Des..

[2] Tim Hoffmann,et al. On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces , 2008 .

[3] Johannes Wallner,et al. Infinitesimally flexible meshes and discrete minimal surfaces , 2008 .

[4] A. Kokotsakis,et al. Über bewegliche Polyeder , 1933 .

[5] Tomohiro Tachi,et al. Freeform Variations of Origami , 2010 .

[6] Hellmuth Stachel. On the Flexibility of Kokotsakis Meshes , 2010 .

[7] V. Arnold,et al. Ordinary Differential Equations , 1973 .

[8] H. Graf,et al. Über Flächenverbiegung in Analogie zur Verknickung offener Facettenflache , 1931 .

[9] Erik D. Demaine,et al. Geometric folding algorithms - linkages, origami, polyhedra , 2007 .