Meshes with Spherical Faces

Martin Kilian, Anthony S. Ramos Cisneros, Christian Müller, Helmut Pottmann

Research output: Contribution to journalArticlepeer-review

Abstract

Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory. We therefore systematically describe so called sphere meshes with spherical faces and circular arcs as edges where the Möbius transformation group acts on all of its elements. Driven by aspects important for manufacturing, we provide the means to cluster spherical panels by their radii. We investigate the generation of sphere meshes which allow for a geometric support structure and characterize all such meshes with triangular combinatorics in terms of non-Euclidean geometries. We generate sphere meshes with hexagonal combinatorics by intersecting tangential spheres of a reference surface and let them evolve – guided by the surface curvature – to visually convex hexagons, even in negatively curved areas. Furthermore, we extend meshes with circular faces of all combinatorics to sphere meshes by filling its circles with suitable spherical caps and provide a remeshing scheme to obtain quadrilateral sphere meshes with support structure from given sphere congruences. By broadening polyhedral meshes to sphere meshes we exploit the additional degrees of freedom to minimize intersection angles of neighboring spheres enabling the use of spherical panels that provide a softer perception of the overall surface.

Original languageEnglish (US)
Article number184
JournalACM transactions on graphics
Volume42
Issue number6
DOIs
StatePublished - Dec 4 2023

Bibliographical note

Publisher Copyright:
© 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Keywords

  • architectural geometry
  • computational design
  • discrete differential geometry
  • sphere geometry
  • sphere mesh
  • spherical paneling

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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