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Eunjoo LEE, Yoshitaka IDA, Sungho WOO and Tsuyoshi SASADA

Environmental Design using Fractals in ComputerGraphics

Introduction

Fractals have been used to describe spatial patternsin many landscape-level applications. One suchapplication has been used to measure the geometriccomplexity of landscape features. Moreover, fractalsin computer graphics offers not only a way to createscenes which are startlingly life like, but also a way tocreate scenes filled with infinite detail. The statisticalself-similarity of fractal shapes is inherent in the naturalworld and may be exploited to create a newenvironment, which is harmony with existinglandscape.

But when we build real world by fractals, we havesome problems considering economic efficiency andconstructive difficulty. How can we build real world?This is a polygon-reduction problem. In the virtual

Computer graphics have developed efficient techniques for visualisation of the realworld. Many of the algorithms have a physical basis, such as computational modelsfor the light and the shadow, models of real objects (buildings, mountains, roadsand so on) and the simulation of natural phenomenon. Now computer graphicstechniques provide the virtual world with a perception of three dimensions. Theconcept of the virtual world and its technology have been expanding and intensifyingin recent years. Almost everything in the real world has been simulated in virtualworld.When it comes to a terrain model, what we need is labour and time. But now it ispossible to simulate terrain like the real world using fractals in computer graphicswith a very small program and small data set. This study aims to show how to builda real world impression in the virtual world. In this paper the authors suggest alandscape design method and show the results of its application.

Keywords: fractals, polygon-reduction, computer graphics, virtual world andcollaboration

world that we simulate it is a big problem to deal withlarger 3D models in real time.

Nowadays polygon reduction tools are solving thisproblem. Those tools optimise the models by reducingthe number of polygons while preserving all modelfeatures, such as textures, materials, colours, object/scene, hierarchy and volume. In real world we areliving it’s also possible to apply polygon reduction todesign concept considering the relationship betweendistance and landscape.

In this paper, the authors have examined theapplicability of landscape design utilising fractals andpolygon reduction. Consequently, the design ofcoastal facilities is produced by this supportingmethod. And, it is shown that this landscape designconsidering fractals and polygon reduction can be oneof reasonable design methods to reflect the

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naturalness of coastal zone and make real worldthrough virtual world. To design coastal facilities usingnew kind of approach, we adopt the coexistence ofharmony and contrast. In other words design objectseems to be harmony with landscape from a distance.But it seems to be contrast with landscape as we comenearer. In this case it’s possible to realise the designidea based on fractal theory and polygon- reductionprinciple.

Project W

The Local government of W in Japan wanted to securebuilding site on the sea considering growing needs ofcommercial area. But the area surrounding the siteis famous for beautiful scenery involving islands, andthe residents did not want to harm the scene formaking landfill. Therefore local government wantedto make man-made island which looks like a naturalisland. But the problem was how to make a man-madeisland looks like a natural island.

Modelling

Before designing the shape of man-made island weneed to review the view from famous viewpoints. Thedistance between viewpoints and the site is more than700 meters. First of all we need to make topologicalmodel of man-made island and it was never attemptedbefore. Because we always made a model of topologyfrom map which contained contour line. There is noreference to make it. No map, no picture. Thereforewe copied peripheral topology to the site, anddescribed rough shape of the island by trial and error.For processing that kind of process we found somecharacteristics on topology in that area. If we designman-made island looks like a natural island, it musthave same characteristics as peripheral topology. Sowe began to study how to make a model with same

features, and learned that fractals could help us tovisualise it in virtual world. We measured fractaldimension of this area and applied it to maketopological model. Finally we succeeded to make avirtual model of man-made island using fractals andit looked like a natural island because they had samefractal dimension as surrounding area (figure 1). Butcan we call it the design?

Inspiration

When we were making the topological model, thedesigner got inspiration from the wire-flame of themodel (figure 2). We use models to describe a naturalscene in virtual world but we don’t try to use thesemodels to realise it in real world. He mentioned thisconcept as “Demodeling.” (the term “Demodeling” wasused for the first time in the keynote paper ofCAADRIA’99 and defined by Tsuyoshi Sasada in hiskeynote speech in 1999).

From long experience of modelling and rendering,people who know about CAAD understand the ideaof an object on a 2D grid like a pixel and 3D grid likea solid. The idea came from that kind of thinking. Afterwe got the idea, we designed the shape of man-madeisland and began to doubt the possibility ofconstruction. To make it realise we built up designteam.

Collaboration

Th design team was composed of an architect,harbour professional and artificial professional. Wealways suggested CG for their understanding andother professionals added their view by speech ordrawings. Then we refined the design through iterateddesign meetings.

The First Design Meeting

We made a CG still image based on the idea of

Figure 1 (left). Man-madeIsland using Fractals

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designer and showed it to other professionals forchecking doubt the possibility of construction (figure3). The answer was yes.

The Second Design Meeting

Harbour professional suggested the plan as figure 4.If the cubes were placed on seaside they would makea weak the power of wave and there was no need toput the tetrapod in front of man-made island.

The Third Design Meeting

Finally the design was refined by the collaboration ofthe design team and some still images were producedfor activity on the site as follows (figure 5).

Observations

FractalsMandelbrot’s fractal geometry provides a way ofmeasuring many natural shapes. Researchers haveapplied fractals to describe special patterns in naturalscene or landscape. Most of this work used fractalsto characterise the features in landscape. In other workthe fractal dimension of individual landscape featureswas measured as an index of classification. Some ofthem analysed the fractal dimension of Japanesegarden. Lam (1990) used fractals to discuss the spatialcomplexity of three land types. Milne (1990) appliedfractals to estimate the probability of locating alandscape patch shape; in most cases, a single fractalvalue was determined for the entire landscape forselected cover types or for all cover types (Turner,1990). But fractals is used for not only describingnature but also making nature.

Process

Considering the kind of characteristics of fractal, thisis a perfect concept for making new land on sea.When we make a terrain model we need to scan themap of topography and then drew every contour line.It need many working hours and labours. More wecan say topological model is the largest part of thevirtual world and most time-consuming work. But

Figure 2 (top right). Sketch bythe designer

Figure 3 (middle right).Perspective view of the idea

Figure 4 (bottom right). Planby harbour professional

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Figure 5 (left). Activity

owing to fractals it’s very easy to generate hugetopological model from small data. Sometimes we canmake a non-existing model like a man-made islandby simple program. In Hollywood they make planet-like virtual world using fractals. But we can use it forreal world.

The process of making man-made island is asfollows.

• Analyse fractal dimension of surrounding areaof the site

• Copy the representative model of the area tothe site

• Drew the contour line in interval of 16m

• Make a terrain model using modeller like aFormZ

• Save as DXF format• Convert to fractal terrain model using

transformation tool• Get fractal terrain model as dense as you want

Sasada Laboratory developed this transformationtool early in 1991 and it was often used for makingmodel of rocks on the beach. It needs the fractaldimension and iteration number. After we got thefractal terrain model of man-made island, we made aphotomontage to review it from famous viewpoints. Itlooked like a natural island as local government wants

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and there are two kind of methods to build it. One isto use artificial rocks on concrete wall and the otheris to build a small mountain in front of the site for hidingit from famous viewpoints. The simplest way to satisfythe client and residents is to use artificial rocksbecause it is easy to get it in the market and tocombine it considering construction on sea. Thereforewe considered the detailed model of man-made islandfrom all angles. The distance between the site andviewpoints is more than 700 meters and there is noneed to build it as fractals showed. We made someCG still images using Polygon-reduction tool andcompared it with each other considering therelationship between the landscape and the distance.

Polygon-reduction

When we make a CG for environmental design, weneed huge data set for example, mountains, mainbuilding and its peripheral buildings, trees, roads andso on. For fast rendering, sometimes we replaceddetailed model to simplified model. But the quality ofCG is inversely proportional to the speed of rendering.Therefore we need to make two kinds of models i.e.simplified model and detailed model for fast renderingand high quality. And when we make CG animationwe replace it each other according to viewpoint andits range. In VRML it used LOD (Level of Detail)according to scene for saving time to display onbrowser.

For solving those problems, nowadays somepolygon-reduction software is used. The softwaresimplifies polygons while preserving whole feature ofthe original shape.

Process

We tried to make a simplified man-made island formaking artificial rock panel. Because the panel is needto make a model of it. We applied polygon-reductionsoftware to make a simplified man-made island. Theresults are as follows (Figure 6). If you look at thosemapped models from remote viewpoints, you can’tfigure out the difference between them.

New method

Through those process we realised that using artificialrocks seems to be engineer not designer. We needanother method to realise man-made island. At thatmoment, designer got an inspiration from thosesimplified models (Figure 2).

Therefore we decided to divine man-made islandinto green and cliffs. The model of green came outfrom fractals and cliffs came out from polygon-reduction.

Process

• Get fractal terrain model as dense as you want• Divide its area into green and cliffs• Replace concrete blocks to cliffs using

transformation tool• Combine green and concrete blocks

When we replace concrete blocks to cliffs, weadded each height of concrete blocks referenced fromfractal terrain model.

Conclusion

Project W show that it is possible to get an idea ofdesigner from computer graphics technology. The ideais quite original, but wisdom of collaborators is added.In this project we attempted a new design method

Figure 6 (right). Polygon-reduction of a man-madeisland

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based on fractal and polygon-reduction (figure 7). Wewould summarise our view as follows.

• CG is a design tool and also it can be aninspiration tool.

• The visualised idea stimulates creativedesign.

References

Eunjoo Lee, A Study on the Application of ComputerGraphics Technology to Landscape Design ofCoastal Areas, Ph.D. Thesis, Department ofEnvironmental Engineering, Osaka University,1999.

Lam, N. S., Description and Measurement of LandsatTM Images Using Fractals, PhotogrammetricEngineering a Remote Sensing, (1990) 187-195.

Milad Saad and Mary Lou Maher, Sharedunderstanding in computer-supportedcollaborative design, Computer-Aided Design,Vol. 28, No.3 (1996) 183-192.

Milne, B. T., Lessons from Applying Fractal Models toLandscape Patterns, Quantitative Methods inLandscape Ecology, (M.G.Turner andR.H.Gardner, 1990)

Tsuyoshi Sasada, Computer Graphics and Design,in: Proc. CAADRIA’99, (Gu Jingwen and WeiZhaoji, Shanghai, 1999) 21-29.

Tsuyoshi Sasada, Open Design Environment andCollaborative Design, in: Proc. ECAADE’94, (TomMaver and Jelena Petric, Glasgow, 1994) 3-6.

Turner, M.G., Spatial and Temporal Analysis ofLandscape Patterns, Landscape Ecology, (1990)21-30.

Web References

[A] CUMINCAD home page,http://www.fagg.uni-lj.si/cumincad/cumincad.cgi/Home

Figure 7 (left). Perspectiveview of final design

Eunjoo LEE (1), Yoshitaka IDA (2), SunghoWOO (3) andTsuyoshi SASADA (2)(1) Department of Architecture and Building ScienceUniversity of Strathclyde, UK(2) Department of Environmental EngineeringOsaka University, JAPAN(3) Department of ArchitectureUniversity of California at Berkeley, USA