Helmut Pottmann, Qixing Huang, Bailin Deng, Alexander Schiftner, Martin Kilian, Leonidas Guibas, and Johannes Wallner. Geodesic Patterns. ACM Trans. Graphics, Vol. 29, Nr.3, 2010 (Siggraph 2010).

Abstract:

Geodesic curves in surfaces are not only minimizers of distance, butthey are also the curves of zero geodesic (sideways) curvature. Itturns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts

Bibtex: 

@article{phdskg-gp-10-2010,
  title = "Geodesic Patterns",
  author = "Helmut Pottmann and Qixing Huang and Bailin Deng and Alexander Schiftner and Martin Kilian and Leonidas Guibas and Johannes Wallner",  
  journal = "ACM Trans. Graphics",
  volume = 29,
  number = 3,
  year = "2010",
  url="http://www.geometrie.tugraz.at/wallner/geopattern.pdf"
  }