[ARCH 689] Parametric Modeling in Design
Instructor - Dr. Wei Yan
Final Project - Algorithms and Scripting for Parametric Design
Melbourne Recital Centre
1. Introduction - Voronoi Algorithm
Voronoi algorithm was defined by Gerogy F. Voronoyi when he studied the general n-dimensional case in 1908. Voronoi algorithm is a method to divide space into a number of reference points also known as seeds, sites, or generators. Voronoi cells generate from each seed to each corresponding region as shown in Figure 1. [1]
Voronoi algorithm was defined by Gerogy F. Voronoyi when he studied the general n-dimensional case in 1908. Voronoi algorithm is a method to divide space into a number of reference points also known as seeds, sites, or generators. Voronoi cells generate from each seed to each corresponding region as shown in Figure 1. [1]
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| Fig. 1. Demonstration of Voronoi Cell Generation [2] |
2. Project Description
The Voronoi algorithm is picked up by me for a parametric facade design. However, the Voronoi algorithm generates in a certain boundary such as a square, a circle, or a sphere. Therefore, the original facade design is changed from a unique boundary to a square boundary for a parametric as shown in Figure 2.
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| Fig. 2. Boundary Change |
Each reference point will be placed in the square boundary randomly through the 'Populate 2D' node as shown in Figure 3. Plus, the number of seeds will be controlled by the number slider for seeds.
Fig. 3. Populate 2D Node
3. Voronoi Algorithm for Parametric Design
1) Design for Parametric Voronoi 2D
The Voronoi 2D algorithm needs the reference points to generate the Voronoi cell. However, reference points are picked up by the user manually. If the user wants to show the different Voronoi designs, the user needs to pick up another reference points again and again until the expectation that the user makes a decision. However, this is a time-consuming work and difficult to satisfy with the many opinions of participants at the same time. But the Voronoi 2D node can provide the various design options when it goes with the Populate 2D node to generate the random facade designs as shown in Figure 4.
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| Fig. 4. Parametric Voronoi 2D Algorithm with Random Generated Reference Points [3] |
2) Count Variable for Reference Points
The number of Voronoi cell is changed by the count slider. The parametric design will give the various design options to determine the best fit of a facade design as shown in Figure 5.
Fig. 5. Parametric Design with a Count Variable
3) Seed Variable for Reference Points
The reference points are located randomly by the seed slider as shown in Figure 6. The design options are diversified by the seed slider as a parametric variable when this variable is combine with a count variable.
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| Fig. 6. Parametric Design with a Seed Variable |
4) Voronoi Facade Thickness
The thickness of Voronoi cell can be changed by the Z - dimensional factor slider. It helps to figure out the proper thickness of facade. One of possible final designs is shown in Figure 7.
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| Fig. 7. Final Facade Design |
5) Design for Parametric Voronoi 3D
The Voronoi 3D algorithm can provide another perspective for the design options through the algorithm as shown in Figure 8. The Populate 3D node used to generate the reference points in the 3D-space.
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| Fig. 8. Parametric Voronoi 3D Algorithm with Random Generated Reference Points [3] |
The reference points are located up and down by the number slider in the 3-dimensional space. Random generated random points are in the 3D space with the wall contained Voronoi cells as shown in Figure 9. This Voronoi 3D node can be the another parametric design option because this Voronoi 3D node dose not contain the Voronoi cell thickness. This is almost portrays the original facade design of Melbourne Recital Centre.
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| Fig. 9. Parametric Design with Voronoi 3D Node |
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