Freeform Honeycomb Structures

• Published in: Computer graphics forum Vol. 33; no. 5; pp. 185 - 194
• Main Authors: Jiang, Caigui, Wang, Jun, Wallner, Johannes, Pottmann, Helmut
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2014
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Computer graphics; Finite element method; Geometry; Honeycomb; Honeycomb construction; Honeycomb structures; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms; Industrial engineering; Shading; Smoothness; Studies; Topological manifolds; Walls
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12444

Motivated by requirements of freeform architecture, and inspired by the geometry of hexagonal combs in beehives, this paper addresses torsion‐free structures aligned with hexagonal meshes. Since repetitive geometry is a very important contribution to the reduction of production costs, we study in detail “honeycomb structures”, which are defined as torsion‐free structures where the walls of cells meet at 120 degrees. Interestingly, the Gauss‐Bonnet theorem is useful in deriving information on the global distribution of node axes in such honeycombs. This paper discusses the computation and modeling of honeycomb structures as well as applications, e.g. for shading systems, or for quad meshing. We consider this paper as a contribution to the wider topic of freeform patterns, polyhedral or otherwise. Such patterns require new approaches on the technical level, e.g. in the treatment of smoothness, but they also extend our view of what constitutes aesthetic freeform geometry.