Housing Layout Design using Fractals:

Transcription

1 Housing Layout Design using Fractals: Computer Tool and its Practical Use Yoshihiro Kobayashi, Ph.D. Subhadha Battina Arizona State University School of Architecture and Landscape Architecture

2 Contents 1. Introduction CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 2

3 Phoenix is a capital city of Arizona State. 5 th Population in US: 1,400,000 (Metropolitan Area has 3,500,000) Bigger than 7 States : 1088km 2 CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 3

4 Housing Layout Design is to develop a town with hundreds of houses and their layout pattern. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 4

5 This paper introduces a computer-based tool for three dimensional (3D) simulations of housing layout design using the concepts of fractals as an Iterative Function System (IFS). CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 5

6 In the current CAD/CG systems, it is a Tedious process for designing housing layouts to 1. model elements 2. copy them 3. move them to some positions and 4. paste it. 5. Evaluate the output and save each case as a different file if it looks fine. 6. Edit the elements and try to design others. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 6

7 Need a tool To easily arrange identical/similar elements on a site. To generate and enumerate design alternatives quickly for comparing and evaluating. To visualize 3D scene for viewing and understanding the design CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 7

8 As a generative system 1. Based on Probability -Generates new models using attributes extracted from existing models. (Kato, et al, 1999) - The value of each attribute is calculated probabilistically. - Good for game developers to generate different towns from a seed one. - Poor at generating new and different design and controlling the outputs. 2. Rule-based approaches such as Shape Grammar - Generates new models editing rules. (The original rules should be prepared) - Good for generating new and different design. - Need professional knowledge to control the rules. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 8

9 We use the idea of Fractals, because 1. it can generate numerous alternatives including similar and completely different ones. 2. each rule can be parameterized easily. Probability based approach cannot. 3. each element can be replaced easily. Rule based approach cannot be. Only a few elements should be replaced. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 9

10 Fractal is the study of mathematical shapes that display a cascade of never-ending, Selfsimilar, meandering detail as one observes them more closely. Media art Architectural Analysis Urban Patterns CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 10

11 Especially, most CG applications make use of fractals for creating nature objects such as marble stones, clouds, trees, etc. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 11

12 Methodology Our approach is based on Sierpinsky Gasket. - the Parent Unit or the main stage in the IFS is subdivided into 3 smaller child units each consisting of similar transformations, creating a fractal. Geometrical Rule A Geometrical Rule A Geometric Parent Parent 2 nd Iteration 3 Children 3 rd Ite Parent 1 st Iteration 3 Children CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 12

13 We expand the Sierpinsky Gasket as 1. Any number of child-unit can be defined. 2. Rotated Child-unit is allowed. 3. Any shape of rectangle is OK as well as square. 4. Each child has two options for stop-condition. Since the two vectors defining its parent-unit, Up & Vp are independent of Uc&Uv, which are for child-unit, any transformation including overlapping, over-sizing, etc. can be represented with Up&Vp. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 13

14 Minimum length Stop Condition in SG If the length of unit is less than predefined length, the iteration shops and each unit generate a marker. All 3 Children Stop at the same time. Marker In our approach, 1) Put Predefined Objects using reference point and UV directions. (STATIC) 2) Rescale it using UV lengths. (SCALABLE) Minimum length Only one child stops. Static OR Scalable Predefined 3D/2D Object CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 14

15 Since the geometrical transformation rule is simple, it is easy to save the rule as a file with simple data structure such as XML. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 15

16 Step1: Open.dxf file from GIS or CAD STEP 2: A: Define the parent and child-units manually, OR B: Import XML file. Step2: Define Parent and Child-units Step2: Load saved XML file Step3: 1. Analyze 2D Pattern using Scalable units 2. Design each unit by assigning components Step4: Generate 3D Model and Evaluate Design CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 16

17 STEP 2: A: Define the parent and child-units manually, OR B: Import XML file. Step1: Open.dxf file from GIS or CAD Zoom Fit CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 17

18 Step2: Define Parent and Child-units 1. Click here 2. Click here Activate Rectangle Tool 1. Type x, y, and z values of one corner OR 2. Type x, y, and z values of the opposite corner CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 18

19 Step2: Define Parent and Child-units Click a point of the rectangle. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 19

20 Step2: Define Parent and Child-units 1. Click the reference point Move the child-unit, the end point of UV. Erase the Child-unit or components on the unit. Create a Child-unit. Rotate the Child-unit. Change the position of reference point and UV directions. (Reference point has 4 possibilities and 2 choices for UV and VU direction) 2. Drag and release the moues. Zoom in and out the screen. Pan the screen. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 20

21 Step2-3: Define Parent and Child-units 1. Generate 2D Image 2. Check the output 3. Change the unit and repeat the process. (User can save any number of outputs.) CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 21

22 Step3: 1. Analyze 2D Pattern using Scalable units 2. Design each unit by assigning components Static Components House1 House2 CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals Tree1 22

23 Step4: Generate 3D Model and Evaluate Design CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 23

24 Step4: Generate 3D Model and Evaluate Design Import 3DS file from other applications such as SketchUp and 3DS Max. Move the camera position using mouse. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 24

25 As Web designers use Color-Index books when they need to find the color combinations, we need some categories to use this application because the outputs are beyond our imaginations. Basic Active Quiet Progressive Rich Muted Culture Natural Accent Basic Scale Overlap Extend Dense Poor CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 25

26 Basic: Square child-units. Three child-units. Useful to understand basic symmetric functions. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 26

27 Scale: Rectangle child-units with different length of U and V. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 27

28 Overlap: Some units overlap each other. Useful to create interesting patterns. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 28

29 Extend: Some units extend the parent-unit. Useful for growth patterns. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 29

30 Dense: More than 4 units with overlapping makes dense patterns. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 30

31 Poor: No useful patterns. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 31

32 Conclusion Unlike many other probabilistic or rule based systems, using fractal concept is one effective method for housing layout design. We demonstrated to generate a variety of alternative designs quickly and easily with simple one GUI without expert knowledge. 1. representing simple geometrical rules between parent and child-units 2. replacing the components in the unit. Future Work Find the solution to generate houses on the site where the streets pre-exist. Find the application for the more practical stage such as a decision-making system for residential house developers. (Modify each unit corresponding to the constrained rules using automated planning approach such as PDDL.) Educational use such as 3DS Max plug-in. CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 32

33 REFERENCES Batty, Michael, and Paul Longley Fractal cities: a geometry of form and function, London; San Diego: Academic Press. Bovill, Carl Fractal geometry in architecture and design. Boston: Birkhäuser Kato, N., A. Okano, H. Kanoh, and S. Nishihara Building Layout Using a Genetic Algorithm for Virtual Cities, The proceedings of System and Information, vol. J82-D-II No. 10: Tokyo: The Institute of Electronics, Information and Communication Engineers. Kobayashi, Yoshihiro and Subhadha Battina Generating Housing Layout Designs: Fractals as a Framework. The Proceedings of Sigradi 2004: Brazil Kurause, Jim Color Index: Over 1100 Color Combinations, CMYK and RGB Formulas, for Point and Web Media, Ohio, HOW Design Books. Mitchell, William. J The Logic of Architecture: Design, Computation, and Cognition, Massachusetts, MIT Press. Peitgen, Heinz Otto, Hartmut Jürgen, and Dietmar Saupe Chaos and Fractals: New Frontiers of Science. New York, Springer. Stiny, George and William J. Mitchell The grammar of paradise: on the generation of Mughul gardens. Environment and Planning B, 7: IMAGES in this presentation Russel, James, 2005, Las Vegas Gambles on Growth, Architectural Record , , New York, Mcgraw-hill CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 33

34 The project files (source code, paper, and presentation) are downloadable from Thanks CAAD Future 2005, Vienna, 6/20/2005 Housing Layout Design using Fractals 34