Statics-Sensitive Layout of Planar Quadrilateral Meshes

Schiftner, Alexander; Balzer, Jonathan

doi:10.1007/978-3-7091-0309-8_16

Cited by 27 publications

(24 citation statements)

References 3 publications

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“…The statics-sensitive design of planar quad meshes has been addressed by Schiftner and Balzer [2010] in a decoupled form-finding and PQ-remeshing fashion, which is a method with many limitations. Vouga et al [2012] showed that self-supporting PQ meshes are guided by the coupled curvature of the design surface and the Airy stress surface.…”

Section: Introductionmentioning

confidence: 99%

Form-finding with polyhedral meshes made simple

Tang

Sun

Gomes

et al. 2015

ACM SIGGRAPH 2015 Posters

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We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of userspecified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

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Section: Introductionmentioning

confidence: 99%

Form-finding with polyhedral meshes made simple

Tang

Sun

Gomes

et al. 2015

ACM SIGGRAPH 2015 Posters

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“…Section 2) has been investigated: [86] discuss statics-sensitive quad meshing with planar faces. Equilibrium forces, and the compressive nature of such forces, can however also be incorporated as additional side conditions in the modeling of polyhedral meshes (which is done by [100], see (Section 11)).…”

Section: Further Research Directionsmentioning

confidence: 99%

Architectural geometry

Pottmann

Eigensatz²,

Vaxman

et al. 2015

Computers & Graphics

237

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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“…Schiftner and Balzer [2010] do not simultaneously consider statics and the rationalized geometry. Vouga et al [2012] show how to rationalize any selfsupporting shape by a self-supporting planar quad mesh, but do not directly design it.…”

Section: Prior Workmentioning

confidence: 99%

Interactive Modeling of Architectural Freeform Structures: Combining Geometry with Fabrication and Statics

Jiang

Tang

Tomičí³

et al. 2014

Advances in Architectural Geometry 2014

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Abstract. This paper builds on recent progress in computing with geometric constraints, which is particularly relevant to architectural geometry. Not only do various kinds of meshes with additional properties (like planar faces, or with equilibrium forces in their edges) become available for interactive geometric modeling, but so do other arrangements of geometric primitives, like honeycomb structures. The latter constitute an important class of geometric objects, with relations to "Lobel" meshes, and to freeform polyhedral patterns. Such patterns are particularly interesting and pose research problems which go beyond what is known for meshes, e.g. with regard to their computing, their flexibility, and the assessment of their fairness.

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Statics-Sensitive Layout of Planar Quadrilateral Meshes

Cited by 27 publications

References 3 publications

Form-finding with polyhedral meshes made simple

Form-finding with polyhedral meshes made simple

Architectural geometry

Interactive Modeling of Architectural Freeform Structures: Combining Geometry with Fabrication and Statics

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