Surface tessellation_Hexagon Planarization
After trying to simulate beehive flashing diffusion pattern both in computer and physical prototype, Hive is somehow telling that it needs to be expanded in its size, form and other parameters.
We are now ready to develop the project; however, we need to consider so many parameters in order to design the final hive. We need to tessellate freeform surfaces by hexagons and they need to be planar so we can use planar material (Plywood) and laser cut the pedals patterns. We also have a limited budget, so the prototype needs to be affordable. Therefore, we need a tool to see mentioned information about the model when we change parameters.
According to Affordable, Performative and Responsive “In order to create affordable responsive architecture, the early design stage should be simple and practical. From the time and cost point of view, results will vary according to the size, complexity and geometric definition of each prototype.” (M.Kamil Sharaidin and Flora Salim, 2011)
I am thinking about creating a collection of generative free-form surface (Hive) and then compare them in every aspect and finally choose one for the final prototype. In this method, I am able to see multiple different results and choose the item I think is most appropriate.
Due to the problems I experienced during designing and making prototypes, now those obstacles need to be considered as parameters and tried to be solved via our tool.
Hexagon Packing (Relaxation & Planarization)
Based on the need of generating planar hexagons on NURBS surfaces, The first step is to make sure that we can do the simulation in software. There are several related articles in this area. Two articles used Kangaroo 2 in grasshopper environment which is a physic engine and tries to solve and make a balance between its input (Goals) through a set of iterations. There are different solvers which we specifically used bouncy solver.
Some parts of the method they used for defining anchors did not work for my surface, so I changed the definition and wrote my own script:
There are lots of components (Goals) related to line. Due to the importance of keeping hexagons edges equal to each other, Since our pedal is already designed and its edges are equal, the component ‘Clamp Length’ were replaced by ‘Length’ and ‘Equal length’ to minimise the deviation of edges as much as possible. Since they are both line-goals, they cannot be used simultaneously and therefore there was a need to test them individually.
Based on articles, deformation of hexagons in positive surfaces are more than the surfaces having negative curvature. Here are first tests:
Not all of surfaces need anchors in order to planarize hexagons on them. In some cases, if you use anchor, it will deform the pedals therefore every surface must be tested with different factors in order to receive the best result. Below are tests with different components and various factors on the same base surface.
One of the questions was: is ‘length’ component really able to keep lines lengths as it claims? I wrote a simple code to calculate minimum and maximum length. The numbers before and after relaxation are wonderfully equal and it means kangaroo can calculate data accurately and precisely.
Another method for planarization is just planarizing panels on their locations without using kangaroo. There are several components for this purpose. In this definition, ‘planarize’ component in ‘Heteroptera’ add-on was used. It has both advantage and disadvantage. The first one is that it doesn’t deform hexagons like kangaroo. The latter one is that it gives deviation (no connection) between edges of hexagons. Although, Due to the space we need between pedals, this deviation is not obvious to the viewer. So, it can be a solution for planarizing of pedals.
Although, choosing the method of planarization depends on the surface. So the next step will be designing hive surface.
M.Kamil Sharaidin and Flora Salim. 2011. AFFORDABLE, PERFORMATIVE, AND RESPONSIVE. [Online]. Available from: http://papers.cumincad.org/data/works/att/caadria2011_011.content.pdf
Marinella CONTESTABILE and Ornella IUORIO. A digital design process for shell structures. [Online]. Available from: http://eprints.whiterose.ac.uk/153362/1/Contestabile_Iuorio_x%20sympl.pdf
Ornella IUORIO, Emil KORKIS and Marinella CONTESTABILE. Digital Tessellation and Fabrication of the ECHO shell. [Online]. Available from: http://eprints.whiterose.ac.uk/153345/1/Iuorio_Korkis_Contestabile_x_sympl.pdf