CumInCAD is a Cumulative Index about publications in Computer Aided Architectural Design supported by the sibling associations ACADIA, CAADRIA, eCAADe, SIGraDi, ASCAAD and CAAD futures
Pottmann; Helmut; Brell-Cokcan, Sigrid; Wallner, Johannes
Discrete Surfacesfor Architectural Design
Nashboro Press 2007
Geometric problems originating in architecture can lead to interesting research and results in geometry processing, computer aided geometric design, and discrete diﬀerential geometry. In this ar- ticle we survey this development and consider an important problem of this kind: Discrete surfaces (meshes) which admit a multi-layered geometric support structure. It turns out that such meshes can be el- egantly studied via the concept of parallel mesh. Discrete versions of the network of principal curvature lines turn out to be parallel to ap- proximately spherical meshes. Both circular meshes and the conical meshes considered only recently are instances of this meta-theorem. We dicuss properties and interrelations of circular and conical meshes, and also their connections to meshes in static equilibrium and dis- crete minimal surfaces. We conclude with a list of research problems in geometry which are related to architectural design.