2018
DOI: 10.1016/j.autcon.2018.08.007
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Morphogenesis of surfaces with planar lines of curvature and application to architectural design

Abstract: This article presents a methodology to generate surfaces with planar lines of curvature from two or three curves and tailored for architectural design. Meshing with planar quadrilateral facets and optimal offset properties for the structural layout are guaranteed. The methodology relies on the invariance of circular meshes by spherical inversion and discrete Combescure transformations, and uses parametrisation of surfaces with cyclidic patches. The shapes resulting from our methodology are called super-canal s… Show more

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Cited by 22 publications
(11 citation statements)
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“…This strategy brings several potential complications which are not in the scope of this article: since the pentagonal facets are not planar and might thus be harder to manufacture and the assembly sequence of the pentagonal hoop might require a complex assembly kinematic where all the blocks would have to be installed at once. These limitations could be adressed with specific strategies, for example if the quad mesh is aligned with principal curvature directions then the resulting pentagon could easily be planarised [38]: several morphological strategies have been developed in the last decade for that purpose [39,40].…”
Section: Free-edges and Interlocked Structuresmentioning
confidence: 99%
“…This strategy brings several potential complications which are not in the scope of this article: since the pentagonal facets are not planar and might thus be harder to manufacture and the assembly sequence of the pentagonal hoop might require a complex assembly kinematic where all the blocks would have to be installed at once. These limitations could be adressed with specific strategies, for example if the quad mesh is aligned with principal curvature directions then the resulting pentagon could easily be planarised [38]: several morphological strategies have been developed in the last decade for that purpose [39,40].…”
Section: Free-edges and Interlocked Structuresmentioning
confidence: 99%
“…If the target surface has umbilics, the pattern may have discontinuities. It is therefore preferable to use surfaces that do not have umbilics, for example Monge surfaces or surfaces with planar curvature lines in one or two directions (Mesnil et al 2018;.…”
Section: Generationmentioning
confidence: 99%
“…The process constraints as well as performance metrics have been merged in a parametric model, see Figure 6. The curved tessellation has been obtained from the principal curvature lines of a cyclidic net generated thanks to the method described in [9]. Each block has a unique geometry and has been made by robotic hot-wire cutting, see Figure 7.…”
Section: Project Descriptionmentioning
confidence: 99%