The voronoi diagram is a method of partitioning space. It has numerous applications in biology, chemistry, geography, astronomy, 3d visualization, and more. Any field where spatial analysis is useful one can find the voronoi diagram. I will choose not go into the peculiarities of its construction as this has been done better
elsewhere but, I would like to expound on it's architectural significance.
The voronoi diagram can be seen in various phenomena including cell structure, protein structure, and astral organization. Essentially, each point in a voronoi diagram is encapsulated inside a region where its distance from any surrounding point is divided by a voronoi edge. Due to this, if each point is represented as a region of particular strength, the voronoi edge is the optimal path of stress through a material. This is why the voronoi diagram is an optimal method by which shattered glass can be simulated. Thus, were a structure created in order to counter this phonomena, it is hypothesized that its optimal structure would be the voronoi diagram.
In order to investigate this hypothesis a construction was planned. The voronoi diagram would be used as the generative method for a half-arch, a bridge. Essentially, this would be a test of the individual voronoi region as a compressive element and the entire structure as a stress distributing mechanism.
I thank my lucky stars daily for David Rutten's Pointset Reconstruction Tools for Rhino for the scale of this project would be impossible were it not for its existence. Before this, a method using qhull to compute the 3d voronoi regions and piping this information to rhino was devised; a terribly inefficient plan. Thank you, Mr. Rutten.
The pointset is really what determines the form of a voronoi region. The form of a voronoi region is determined by the location of its center and the location of at least 4 neighbor points. One can observe the points used in this project in the first, second, and third pictures in this section.
The point set was determined in relation to the installation space, the fourth floor western stair well of the Bayard Ewing Building at the Rhode Island School of Design. The span of the bridge is 6.5 ft and the height is 10 ft.
Material
It was not acceptable financially nor idealogically to use a vast quantity of
PVC or similar plastic. 20 x 4 ft. of 1/32" thick post-consumer recycled plastic was obtained from
Recycling for Rhode Island Education for $1.60.
Cutting
To cut the individual pieces, laser cutting was unacceptable as it would yellow my transparent plastic and would put control too far away from myself. This became quite important near the end of the project. Thus the choice was natural (and extremely laborious), each piece would be individually cut out of the material using razor blades.
Joining
Because each edge and joint in the construction is unique (and the fact that the whole project would be completed in a week) it was obvious that some sort of universal joiner was necessary. Although several methods were attempted (rubber bands, zip ties), it eventually came down to
Scotch Transparent Tape.
Problems
There were two key problems in this process. The first is that it became obvious that the very thin (1/32") thick plastic was not strong enough in sizeable voronoi regions under significant compression force. It buckled easily along long edges that were not sufficiently triangulated. Thus, a material transition to chipboard (1/16" thick) had to take place that coinsided with the increased region size near the bottom of the half-arch.
The second problem is that this process is highly labor intensive. The material limitations made it necessary to cut the material in this way. Thus, I send out much, much gratitude to (in no particular order) Henry, Joe, Katie, Natalia, Jessie, and Caricia for helping me.
The construction was completed in about 3 days. It weighed 12 lbs in total. The installation was removed almost immediately due to the fact that the school year was over but, it stood for about 8 hours and seemed ready to stand for ages.
Regrets
Due to the overall complexity of the object, the tape is hardly noticeable. However, were there more time, a more elegant method of joining the regions could have been devised. Zip ties and/or rubber bands held promise, but were terribly slow and clumsy compared to tape. Also, the moment at which the object joined with the stairwell was not executed as precisely as desired. This was designed for, but the material was not sufficient for the high compression and tension at this point. In order to do a similar installation in the future, it is necessary to improve on this moment. It was probably the weakest point in the structure.
