期刊
ACM TRANSACTIONS ON GRAPHICS
卷 29, 期 4, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/1778765.1778780
关键词
computational differential geometry; architectural geometry; geometry of webs; timber rib shell; cladding; freeform surface; pattern; geodesic; Jacobi field
资金
- Austrian Science Fund (FWF) [S92-06, S92-09]
- European Community [230520]
- NSF [0808515, 0914833]
- NIH [GM-072970]
- Stanford-KAUST
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [808515] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [0914833] Funding Source: National Science Foundation
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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