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“CMC” “Constant Mean Curvature”
FROM:
Xavier Tellier (1,2), Laurent Hauswirth (2), Cyril Douthe (1) and Olivier Baverel (1,3)
(1) Laboratoire Navier, Ecole des Ponts, IFSTTAR, CNRS
77455 Champs-sur-Marne, France
(2) Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, France
(3) GSA/ENS Architecture Grenoble, France
“Discrete CMC surfaces for doubly-curved building envelopes”, Advances in Architectural Geometry (AAG2018), Chalmers University of Technology, Gothenburg, Sweden, 22-25 September 2018
ABSTRACT: Constant mean curvature surfaces (CMCs) have many interesting properties for use as a form for doubly curved structural envelopes. The discretization of these surfaces has been a focus of research amongst the discrete differential geometry community. Many of the proposed discretizations have remarkable properties for envelope rationalization purposes. However, little attention has been paid to generation methods intended for designers. This paper proposes an extension to CMCs of the method developed by Bobenko, Hoffmann and Springborn (2006) to generate minimal S-isothermic nets. The method takes as input a CMC (smooth or finely triangulated), remeshes its Gauss map with quadrangular faces, and rebuilds a CMC mesh via a parallel transformation. The resulting mesh is S-CMC, a geometric structure discovered by Hoffmann (2010). This type of mesh have planar quads and offset properties, which are of particular interest in the fabrication of gridshells.
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