Classification of 2D, 3D and Centroidal Voronoi Diagram.
Voronoi Geometry generated in plugin.
Voronoi Geometry drafted manually.
original point set as base for construction of Voronoi.
Delaunay triangulation on the original point set.
Voronoi diagram built from Delaunay triangulation.
ANALYSING VORONOI:
Boundary-based approach
Domain-based approach
Network-based approach
In order to understand the output of Voronoi tessellations in design, these are some defined design variables that are taken into consideration.
•Materialising information.
•Material Optimization.
•Structural Performance.
•Variety Production.
These variables are interrelated but if individually taken as an initial operator in a design process, application of Voronoi algorithm can be a solution.
Developing an understanding between Voronoi algorithm (diagrammatic representation) and the defined variables.
Based on the output of Voronoi algorithm as networks it can be categorized into boundary and domain. If we analyse it further on the basis of its output, it can also be defined as a tangible output and an intangible output. Both holds an equal value in terms of output and can help in understanding the relation with design variables and Voronoi algorithm.
Understanding first defined variable, which is Materializing Information
For materializing information, the output matters in terms of the volumes achieved. So the boundaries, which can be the tangible output behaves as a by-product.
Boundaries are considered as a by-product because if this step in a design process is not the final step which will not lead to any tangible output than for such consideration (design variable) the volumes or domains are important in terms of an output.
Thus Design Variable of materialising information has been categorized under as
A domain based approach.
Understanding second defined variable, which is Material Optimisation.
To partition six random points inside a square of 50 x 50 mm with minimum length of lines.
For this output Voronoi algorithm for random points is applied, the original point set is not changed.
The total length of all partition lines (i.e., the red lines) is : 153.1721 mm.
For this output Centroidal Voronoi algorithm for random points is applied, the original point set is changed for all points to become the centre of mass of their respective cells.
The total length of all partition lines (i.e., the red lines) is : 147.9051 mm.
From the study of dragonfly wing and soap bubbles, in which both deals with material optimization and structural performance it appears quite difficult to categorize material optimization as a variable, resultant of a boundary based approach.
But for a diagrammatic understanding of Voronoi networks and the sequential or step wise approach of algorithms, material optimization can be categorised as
A boundary based approach.
The output of such a variable is always measured with respect to material, thus it has to be a tangible output which directly puts it into a category of boundary in such analysis.
Understanding third defined variable, which is Structural Performance.
Frame A
Frame B
As the volume of the frames is same, when we convert them into any material their respective weights will be same.
For this exercise, aluminium 1050-O is selected as a material. Thus the weight of both the frames will be same.
Now in order to understand structural performance with respect to network based approach, pressure of 0.004 MPa is applied as a variable on both the frames in this manner.
The shorter faces are held as restrain faces and the pressure is applied on the top of both the frames.
Simulation results from frame A
Results from frame A
Simulation results from frame B
Results from frame B
While understanding and performing this exercise, the approach was compulsorily a network based approach. It is not logical to proceed when any of the one component i.e. either boundaries or domains are considered an individual entity.
Thus, while understanding structural performance as a design variable the structure has to be realised as a network, in which the boundary and the domain both are equally respondent. None of them can be taken into consideration separately because of its responsive character.
It is
A Network-based approach
UNDERSTANDING DESIGN TO ANALYSE VORONOI :
Design Program.
Concept.
Context.
Design Programme.
For the purpose of understanding Voronoi, here design programme is understood as a relationship of activities. Design programme can be definitive as well as generative.
A definitive design programme:
A generative design programme:
Design Programme is always a combination of both, a definitive as well as a generative approach is taken into consideration according to design scope and requirement.
Such categorization is done here to have an understanding for the application of this tool (2D Voronoi).
Concept.
An initiator approach – In such approach the design concept or idea acts as a guiding factor throughout the design process.
A problem solver - Such approach is defined as a specific task oriented problem.
Context.
For any design process, context acts as an element that gives an identity to the design.
Context provides with a varied set of tangible and intangible parameters which can be used as a guiding factor in design process.
Design Programme and Voronoi
Application for Voronoi Algorithm in any design is a very straight forward approach reflecting the design programme requirements. Reflection of programme can be understood in two different ways.
First when the output is conceived beforehand in terms of form, Voronoi algorithms help as this tool is easily flexible and adaptable.
Second way is that when design programme is generative or experimental. Under such conditions Voronoi algorithms makes it easy to link the variables and conceive form accordingly. In such case the output is purely a resultant of variables and the model is always open for modifications and iterations.
Concept and Voronoi:
In understanding Voronoi algorithm as an initiator of design process or a big idea, its acceptance or application is purely based on designer’s sensitivity and contextual responses.
Voronoi algorithm can also be a very helpful approach in terms of bio understanding.
These algorithms can give a very experimental take on logical ideas and such process can be easily controlled and modified at any step.
As a problem solver the application is adaptable but it also is a lot controlled by the factor of scale. Its application can get limited at some situations where its scale will not give a satisfying result.
Context and Voronoi:
Voronoi algorithms have a very direct relation with the context. When the context for any design is providing a scope of its translation into variables, this algorithms works directly onto it to give a result. The translation of context when done in a logical method the resultant network can directly link them.
ANALYTICAL FRAMEWORK:
The analytical framework deals with two aspects:
First is through these categories in which case studies are understood.
•Design Metaphor
•Strategy
•Material Behaviour
•Structural Performance
•Installation Methodology
Second aspect is based on the analysis of looking at application of Voronoi algorithm based on an approach, i.e.
•Network-based approach
•Domain-based approach
•Boundary-based approach
APPLICATION OF 3D VORONOI
(WEAIRE-PHELAN STRUCTURE)
IN WATER CUBE PAVILION
Based on two 12-sided and six 14-sided polyhedrons, the cells are packed together in three-dimensional space to infinity. This repeating unit tiled in space is then rotated and cut along prescribed axes along the exterior to form the exterior geometry of a box, and then the interior cells are sliced to form the large interior spaces for the swimming facilities, etc. The polyhedron surfaces were then replaced with the building membrane and the edges became structural steel tubes. Where the steel members meet one another they are welded to large spherical steel nodes to form solid moment connections.
In spite of its complete regularity, when it is viewed at an arbitrary angle it appears totally random and organic.
Based on the study of Water cube pavilion, in this project Voronoi algorithm is applied as a design metaphor, but except that it also helps in material optimization.
Type of Voronoi Algorithm used – Centroidal Voronoi Algorithm.
Application – 3 dimensional.
Maximum affected category:
Strategy.
Material Optimization.
Defined Approach based on analysis:
A Boundary based approach.
In Water Cube Pavilion the application of Weaire-Phelan structure was initially for the purpose of achieving a particular design metaphor, but it not only helped the project to achieve a desired look but it also affected the overall strategy of the project.
Eventually it resulted into structural performance of strength for the skin.
It optimized the material that was used for the outer structure, though not desired initially but this variable can be seen as the most affected due to the application of Voronoi algorithm.
Thus in this project the boundary based approach is very evident.
CONCLUSION :
Describing an approach to apply algorithms in design through computation.
DRAGONFLY INSTALLATION.
WATERCUBE PAVILLION.
C_WALL.
SMART CLOUD
VESSEL CHAIR
PARADISE PAVILLION.
Chart explaining the effect of Voronoi Algorithm for all defined Categories.
Voronoi algorithms can be looked upon as a final solution or as an intermediary step in any design process.
When and why to use Voronoi should be purely based on the need and scope.
Forcing such an approach on design can lead to various forms but the sensitivity and contextual relevance can go missing.
Thus Computational approach does not end just with an output of form, but can help a lot more when dealt logically and in right place