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Geodesic patterns

Published: 26 July 2010 Publication History

Abstract

Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 29, Issue 4
July 2010
942 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/1778765
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 26 July 2010
Published in TOG Volume 29, Issue 4

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Author Tags

  1. Jacobi field
  2. architectural geometry
  3. cladding
  4. computational differential geometry
  5. freeform surface
  6. geodesic
  7. geometry of webs
  8. pattern
  9. timber rib shell

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  • (2025)Extracting fiber paths from the optimized lamination parameters of variable-stiffness laminated shells based on physic-informed neural networkComputer-Aided Design10.1016/j.cad.2024.103821179(103821)Online publication date: Feb-2025
  • (2025)Computational design of asymptotic geodesic hybrid gridshells via propagation algorithmsComputer-Aided Design10.1016/j.cad.2024.103800178:COnline publication date: 1-Jan-2025
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  • (2024)Designing Bending-Active Freeform SurfacesProceedings of the 9th ACM Symposium on Computational Fabrication10.1145/3639473.3665793(1-11)Online publication date: 7-Jul-2024
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