Geometric modeling with conical meshes and developable surfaces

Yang Liu*, Helmut Pottmann, Johannes Wallner, Yong Liang Yang, Wenping Wang

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

214 Scopus citations


In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadri-lateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.

Original languageEnglish (US)
Pages (from-to)681-689
Number of pages9
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 1 2006
EventACM SIGGRAPH 2006 - Boston, MA, United States
Duration: Jul 30 2006Aug 3 2006


  • Developable subdivision surface
  • Developable surface
  • Discrete differential geometry
  • Nonlinear subdivision
  • Offset mesh
  • Principal mesh
  • Quad mesh
  • Surfaces in architecture

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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