ArchitecturalChallenges-Hambleton

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Study o Panelization Techniques to InormFreeorm ArchitectureDaniel Hambleton, Crispin Howes, Jonathan Hendricks, John KooymansHalcrow Yolles Partnership Inc.207 Queens Quay West, Suite 550Toronto, Ontario, Canada M5J 1A7

Keywords

1=Freeorm geometry 2=Planar quadrilateral meshes 3=Panelization 4=Discretization

Abstract

The authors give a qualitative analysiso past and present techniques or thepanelization o reeorm architecture.These techniques are comparedby economy, constructability, andadherence to the original designintent. From this analysis the authorsconclude that the industry is currently

transitioning rom a state o Canwe build this?, to a state o Shouldwe build this?. A discussion outure trends and open problems opanelization theory is given.

Introduction

Over the past two decades, thearchitecture and design industry hasundergone a digital revolution. CAD,3D modeling, and script driven designprograms are commonly used in mostmajor architecture oces aroundthe world. Modeling technology is

now so advanced that it is possible toproduce extremely complex geometricalorms rom minimal design input.As a consequence, the prominenceo reeorm geometry in the builtenvironment has grown rapidly duringthis time. Although there is no doubtthat this new ound reedom has givenrise to some incredible and beautiulorms, it has also widened the gapbetween the original design intent oa project and what can reasonably beconstructed. This tension is especiallyapparent in the structural glass industry,since it has been the medium o choice

in a wide variety o projects involvingreeorm geometry.In order to investigate this situation,

we have created a study projectenvironment in which we bring areeorm surace rom initial sketchto a ully coherent design solutionin a number o dierent ways.The techniques we have chosenprogress rom past to present andinclude triangulation, rationalizationby primitive objects and rotationalsuraces, discretization via conjugatecurve networks, and developable stripmodeling. Each o the resulting design

solutions is then evaluated on nodesimplicity, structural transparency,adherence to original design intent, andmaterial wastage.

From this investigation we concludethat presently the industry is at a crucialpoint. Until now, we have been trying to

answer the question: Can we build this?It is our belie that in the context oglass panelization o reeorm geometry,this question has been answered inthe armative. We can now begin toinvestigate the question: Should webuild this? A question that is especiallyimportant given the current nancialtrends.

Objectives

All architecture projects begin withan initial sketch or model illustratingthe main design concept. We assumethat the orm is presented as a smooth

surace modeled with a commerciallyavailable modeling package, in our case,Rhinoceros3D. Our task is to produce adesign solution that panels the suracein such a way that node simplicity,structural transparency, adherence tooriginal design intent, and materialwastage are optimally balanced. Wewill use the term optimal in both aqualitative and quantitative way, andwill clearly indicate which one is meant.In addition, our design solution will begiven as layout with which one coulddesign the physical nodes, and althoughwe will give an example o how thismight be done, we will not completethe design in general.

The panelization techniques will begiven a number between 1 and 5 in

each o the mentioned categories. Weuse the convention that 1 implies poorperormance and 5 implies excellent

perormance. Node simplicity will beevaluated on the ease o connectionand the torsion o the structuralelements at each node. Structuraltransparency will be evaluated on thecomplexity o the details necessary tonish the design and number o edgesthat meet at a typical node. Adherenceto original design intent will be theamount that the panelization schemedeviates rom the original surace.Material wastage is the percentage othe bounding box that a standard paneloccupies.

Initial SurfaceAlthough reeorm geometry doesnot have an ocial denition, it cangenerally be recognized by its smooth,fowing lines, unique and varyingshape, and lack o inherent symmetries.Our study surace, although notwildly bizarre, is a reeorm surace,and is complex enough to make thepanelization process dicult (Figure 1).

Triangulation

The rst panelization technique weconsider is that o triangulation.

Approximating a smooth surace withtriangular elements is the oldest andstill most popular way o panelization(Figure 2). It is particularly well-suitedor panelization with glass, since it

Figure 1:

Design intent for a free-form surface

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is always possible to construct a fatelement through three points. However,a discretization into triangular elementshas a number o serious drawbacks.Such schemes have the highest panelcount o any scheme, resulting in thehighest number o overall cuts. Atriangular scheme also means that sixedges meet at a typical node, whichimplies high node complexity and lowstructural transparency.

Despite their fexibility, there arecertain geometrical conditions thathave considerable infuence on theappearance o triangular meshes. Theseconditions are well-known in the worldo dierential geometry, and relate tothe curvature o the underlying surace.Thus, there is an inseparable linkbetween the panelization scheme andthe geometry o the smooth surace. Inorder to ully understand and controlthis link, we must introduce some newterminology.

A mesh is a set o points that areconnected in some predetermined way.Pairs o connected vertices are callededges and groups o three or moreconnected vertices are called the aceso the mesh. Knowing which verticesare contained in a given edge or aceis called knowing the combinatoricso a mesh. Meshes are the discreteanalogues o smooth suraces andwill give the basis or the panelizationscheme. However, the geometricaltheory behind meshes is signicantlydierent rom that o smooth suraces.This dierence is oten the cause omany o the issues that arise whenpaneling reeorm suraces. For instance,

given two smooth suraces, the distancebetween them is measured by thedistance between corresponding points.Given two meshes, there are threedierent ways o measuring the distancebetween them: the distance betweenvertices, edges, and aces (Figure 3) ([3]).

In act, a undamental result opanelization theory is that the meshesmost suited or structural glass panelsare those or which a second meshexists that can maintain a constantdistance rom the original one in atleast one o the three ways ([2]). Suchmeshes are called oset meshes and are

currently being developed by memberso the Geometric Modeling andIndustrial Geometry group at TU Vienna,and the Discrete Dierential Geometryand Kinematics in Architectural Designgroup at TU Berlin.

Planar Quadrilateral Meshes:Primitive Approximation

A planar quadrilateral (PQ) meshis a mesh whose aces consist oour, coplanar, vertices ([2]). Planarquadrilaterals t their bounding boxmore eciently than triangles andreduce node complexity. PQ mesheshave many desirable properties, butsince our random points almost neverlie on a plane, they are quite dicult toapply to an arbitrary surace.

Figure 2:

A triangulation of thesurface with structural ele-ments

DesignSolution 1

Node SimplicityStructural

TransparencyDesign Intent Material Eciency

TriangulatedSurace

1 1 3.5 2.5

Table 1: Our analysis of a panelization scheme based on triangles

Figure 3: The three different ways of measure the distance between meshes

Figure 4:

Approximation by conesegments

DesignSolution 2



PrimitiveApproximation

1.5 3 2 3.5

Table 2: Our results for panelization by primitive approximation


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I, however, the surace is notarbitrary, but part o a special classo suraces that is already wellunderstood, then creating PQ meshesis straight orward. Figure 4 shows ourapproximation o the original suraceby primitive objects, in this case, conesegments.

Planar Quadrilateral Meshes:Fitted Rotational Surfaces

Translational and rotational suracesare suraces that are generated bytranslating or revolving one curvearound another. By doing this, we canapproximate a reeorm surace whilemaintaining a standard underlyingstructure ([1]). Although there are somevery sophisticated techniques or ttingtranslational suraces to reeorm ones,unless the original surace is designedwith this process in mind, most o theoriginal intent will be lost (Figure 5).

Planar Quadrilateral Meshes:Principal Curvature Meshes

In the years 2005-2007, techniquesor adapting PQ meshes to reeormsuraces were developed ([2], [3]).These techniques require the underlyingsurace to be parameterized alongcertain classes o curve networks,called conjugate curve networks. Sinceconjugate curve networks are thesmooth analogue to planar quadrilateralmeshes, taking the intersection points oa well spaced conjugate curve networkas vertices o our mesh will producepanels that are close to fat. Using theoptimization procedure proposed in

([2]), we can minimally perturb thevertices so that the panels becomecompletely fat (Figure 6).

I, in addition, we use the networko principal curvature lines as theconjugate curve network, then theresulting mesh will be a ace oset mesh([2]). This means that each o the acescan be oset a constant distance alongits normal direction. Adjacent planeswill intersect in a point, and these pointswill be the vertices o a new ace osetmesh at a constant distance rom theoriginal one, resulting in torsion reeand prismatic structural elements ([3]).

Face oset meshes are ideal or themultilayer nature o a structural glasspanel (Figure 7).

Developable Strip Model:

As a urther renement o the planarquadrilateral model, developablesuraces can be used to interpolatebetween adjacent lines o one amily oparameter lines ([4]). Since developablesuraces are curved in one direction,the resulting scheme will approximatethe design intent more closely thanfat panels. However, because otheir curvature, panels cut out o adevelopable surace are more expensivethan fat panels, but not nearly asexpensive as doubly curved panels. It isalso possible to use a small number o

Figure 5:

A rotational surface withPQ panels compared withoriginal surface

DesignSolution 3


TransparencyDesign Intent Materia l Eciency

Fitted RotationalSurace

4 3.5 2 3.5

Table 3: Our results for panelization by rotational surfaces

Figure 6:

A face offset mesh withstructure and the under-lying curve network

DesignSolution 4


TransparencyDesign Intent Materia l Eciency

Principal CurvatureMesh

4 4 4 3.5

Table 4: Our results for panelization by principal curvature lines

Figure 7: Multilayer design of structural glass panel


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oversized moulds to reduce abricationcosts ([4]).

There is no question that conicalmeshes solve most o the traditionalproblems associated with panelingsmooth suraces with glass panels.However, they also raise a number onew issues. For instance, since aceoset meshes depend heavily onthe principal curvature lines o thesurace, some suraces will produce aace oset mesh that is not suitableor construction. Singularities andimpossible panel sizes can occur oneven very simple suraces. This is aresult o the surace having complicateddierential geometry characteristics,despite being simple in appearance.

Results

We summarize the results o ourqualitative survey o dierentpanelization techniques in the ollowingmatrix (Table 6). The results show thatthe principal curvature mesh providesa constructible panelization scheme or

our study surace.

Standardization

The study o dierent panelizationtechniques shows how powerulstandardization o certain elementsin the construction o reeormgeometry can be. Standardization canbe interpreted as avoiding specializedunits, such as doubly curved panels, orit can be interpreted as the repetition ocertain elements throughout the project.A particularly powerul example othis would be to standardize the beam

depth or a give reeorm shape. Suchmeshes are called edge oset meshesand can be applied to certain kinds oshapes. It is still unknown i they can beapplied to an arbitrary surace ([3]).

Standardization can also be achievedby having some degree o repeatabilityin the types o panels that are used.This would achieve economies o scaleand acilitate abrication. However, inorder to be eective, there has to bea very small number o dierent kindso panels relative to the overall panel

DesignSolution 5



Developable StripModel

3 4 4.5 2.5

Table 5: Our results for panelization by developable strips

Figure 8:

Approximation with de-velopable strips

Design SolutionComparison Node Simplicity

StructuralTransparency Design Intent Mater ial Eciency

TriangulatedSurace

1 1 3.5 2.5

PrimitiveApproximation

1.5 3 2 3.5

Fitted RotationalSurace

4 3.5 2 3.5

PrincipalCurvature Mesh

4 4 4 3.5

Developable StripModel

3 4 4.5 2.5

Table 6: The table of results

Figure 9: Alternate panelization schemes

Figure 10: A panelization scheme that maximizes sun exposure at a giventime

Figure 11: Application of directed panels


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count. This ratio can generally not beachieved with a basic error correctingdetail in the structural support. For fatsuraces the theory o periodic andaperiodic tiling is well understood, butor smooth suraces it is not so welldocumented. Figures 9 - 11 show somealternate paneling schemes that explorepossible avenues o investigation.

Conclusion

The results o our study show thatthe panelization scheme given by thetheory o oset meshes perorms best inbalancing structural transparency, nodesimplicity, design intent, and materialeconomy. However, the true impact ooset meshes goes deeper than that.We can now view reeorm geometryas we would any simpler surace.Oset meshes provide a benchmarkagainst which we can compare anarray o panelization techniques.Schemes that urther simpliy andrationalize panel layout can be viewedas reducing costs, and schemes that

add complexity to the panel layoutcan be viewed as added premiums.We believe that incorporating adetailed study o dierent panelizationtechniques into the dialogue betweenarchitect, engineer, and contractorwill dramatically increase our ability toresponsibly and economically realizethe visions o the worlds most dynamicdesigners.

References

[1] J. Glymph, D. Sheldon, Cristiano Ceccato,J. Mussel, H. Shober, A Parametric Strategyor Freeorm Glass Structures using Planar

Quadrilateral Facets, Automation inConstruction 13 (2004) 187 202

[2] Y. Liu, H. Pottmann, J. Wallner, Y. Yang, W.Wang, Geometric Modeling with ConicalMeshes and Developable Suraces. ACM Trans.Graphics 25, 3, 681-689.

[3] H. Pottmann, Y. Liu, J. Wallner, A. I. Bobenko,and W. Wang, Geometry o multi-layerreeorm structures or architecture, ACMTrans. Graphics 26 (2007), no. 3, #65, 11 pp.

[4] H. Pottmann, A. Schitner, P. Bo, H.Schmiedhoer, W. Wang, N. Baldassini, and J.Wallner, Freeorm Suraces rom Single CurvedPanels. ACM Trans. Graphics, 27/3, Proc.SIGGRAPH (2008).


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