Ruled Free Forms

Flöry, Simon; Nagai, Yukie; Isvoranu, Florin; Pottmann, Helmut; Wallner, Johannes

doi:10.1007/978-3-7091-1251-9_4

Cited by 13 publications

(14 citation statements)

References 9 publications

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“…The polyline of rulings is therefore seen as a semidiscrete version of an asymptotic curve on the limit surface. This fact is used by Flöry et al [32][33][34] for the initialization of algorithms for optimization, rationalization and design with smooth surfaces from ruled strips (cf. Fig.…”

Section: Smooth Negatively Curved Surfaces From Ruled Patchesmentioning

confidence: 99%

“…Approximation by ruled surfaces of different kinds: a reference surface (blue) which is an unmodified part of the Cagliari museum project by Zaha Hadid architects is approximated by Flöry et al[33] with a conoidal ruled surface (green) and with a general ruled surface (orange). We show these surfaces superimposed onto each other in order to visualize approximation quality.…”

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confidence: 99%

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Architectural geometry

Pottmann

Eigensatz²,

Vaxman

et al. 2015

Computers & Graphics

Self Cite

233

153

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a b s t r a c tAround 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

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Section: Smooth Negatively Curved Surfaces From Ruled Patchesmentioning

confidence: 99%

mentioning

confidence: 99%

Architectural geometry

Pottmann

Eigensatz²,

Vaxman

et al. 2015

Computers & Graphics

Self Cite

233

153

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“…In the computer aided geometric design literature, quite a few results are devoted to free-form surface approximation by ruled surfaces [7,8,9,10,11,12,13,14,15,16].…”

Section: Previous Workmentioning

confidence: 99%

“…A similar approach that uses asymptotic curve network is proposed in [16]. The segmentation into strips is formulated as a level-set problem, in which discretely sampled points x on the input surface are assigned values f (x) and f is optimized to choose strip boundaries with properties which are desirable, both for the ruled surface fitting and for the overall aesthetic quality of the end-result.…”

Section: Previous Workmentioning

confidence: 99%

Accessibility for Line-Cutting in Freeform Surfaces

Sosin

Bartoň

Elber

2019

Computer-Aided Design

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“…With a focus on physical production, various rationalization algorithms have been proposed for many geometric goals such as: planar mesh optimization [5,6,7,8,9,10,11], multi-layer structures [12], single-curved panels [13], straight panels [14,15], double-curved panels [16,17], ruled panels [18,19], circle and sphere packings [20], circular arc structures [21], point-folding structures [22] and functional webs [23]. These methods typically take a given freeform surface as input, and compute a surface decomposition that relates to a physical layout of panels.…”

Section: Related Workmentioning

confidence: 99%

Interactive design exploration for constrained meshes

Deng

Bouaziz

Deuss

et al. 2015

Computer-Aided Design

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In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm.We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately.Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces.

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Ruled Free Forms

Cited by 13 publications

References 9 publications

Architectural geometry

Architectural geometry

Accessibility for Line-Cutting in Freeform Surfaces

Interactive design exploration for constrained meshes

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