A voronoi diagram is a way of decomposition or subdivision of space based on an initial set of objects or points (for more information http://en.wikipedia.org/wiki/Voronoi). Voronoi diagrams have countless applications from statistics to biology and urban planning. Lately they are becoming ‘popular’ also in architectural design. There is indeed a number of reasons making voronoi diagrams useful in architectural design:
a. Their structural properties, both in 2d and 3d.
b. As a way to subdivide/organize space, based on proximity/closest neighbor.
c. The fact that they can describe many natural formations, like soap bubbles, sponges or bone cells.

There are two problems arising though. The first is a method to construct them. It looks that the most reliable solution until know is Qhull (http://www.qhull.org/) , in relation to rhino or generative components. Rhino script could be another option.

What is more interesting though is the problem of defining the initial set of points. Of course there can be several different solutions, for example program requirements. Although, it would be far more interesting to use voronoi diagrams in relation to a growing process, for example cellular automata or l-systems. That could produce dynamic voronoi diagrams, and at the same time would be closer to their mathematical/algorithmic nature, by defining a specific simple set of rules for the generation of the initial set of points, in a similar way that the points are defining the voronoi diagram.

Readings:

-Aranda, B., Lasch, C. Tooling New York: Princeton Architectural Press, 2006.
-Bollobas, B., Riordan, O. Percolation Cambridge: Cambridge University Press, 2006.
-Kim, M.S., Shimada, K., (eds.) Geometric Modeling and Processing – GMP 2006 Berlin: Springer, 2006.
-Klein, R. Concrete and Abstract Voronoi Diagrams Berlin: Springer-Verlag, 1987.

-Okabe, A., Boots, B., Sugihara, K., Chiu, S.N. Spatial Tessellations, Concepts and Applications of Voronoi Diagrams West Sussex: John Wiley & Sons Ltd, 2000 (f.e. 1992).

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