Geometry of multi-layer freeform structures for architecture

Helmut Pottmann*, Yang Liu, Johannes Wallner, Alexander Bobenko, Wenping Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

101 Scopus citations


The geometric challenges in the architectural design of freeform shapes come mainly from the physical realization of beams and nodes. We approach them via the concept of parallel meshes, and present methods of computation and optimization. We discuss planar faces, beams of controlled height, node geometry, and multilayer constructions. Beams of constant height are achieved with the new type of edge offset meshes. Mesh parallelism is also the main ingredient in a novel discrete theory of curvatures. These methods are applied to the construction of quadrilateral, pentagonal and hexagonal meshes, discrete minimal surfaces, discrete constant mean curvature surfaces, and their geometric transforms. We show how to design geometrically optimal shapes, and how to find a meaningful meshing and beam layout for existing shapes.

Original languageEnglish (US)
Article number1276458
JournalACM transactions on graphics
Issue number3
StatePublished - Jul 29 2007
Externally publishedYes


  • Curvatures
  • Discrete differential geometry
  • Edge offset
  • Hexagonal mesh
  • Koebe polyhedron
  • Multi-layer construction
  • Offset mesh
  • Parallel mesh
  • Support structure
  • Surfaces in architecture

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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