To make it work, you need to download qhull. Get it here: http://qhull.org/. After you install it, double click the scripting component and edit the path to your qhull folder (line 101). If things do not work, take care to unblock (right click and fiddle with the permissions) the qhull execs (sometimes window$ blocks them).

Nevertheless, please take your time and read this or/and this article as an exercise in self-critique (especially the first one). Maybe you’ll change your final presentation discourse a bit.

A symbolically critical pamphlet

For the hip architectural public, there surely isn’t any need of introducing the (in)famous Voronoi diagram. If there is, then you probably shouldn’t be reading this text and you’re better off doing something else.  Nevertheless, I find myself under increasing pressure to express my thoughts regarding what I find to be a shallow, often completely mis-interpreted and un-justified use of what started out to be a mathematical “toy”. The practical applications of the Voronoi diagram are quite numerous highly fascinating. However, they are beyond the scope of this article – I want to focus mainly on the (mis)use of the aforementioned algorithm in architecture and urbanism.

I think it is quite safe to state that voronoi diagrams have now probably become the “golden mean” of computational architecture. However, I am quite surprised that it took this long for people to notice this – and, what’s even more surprising, there seems to be a severe lack of constructive criticism regarding this quite common and recurrent space-partitioning algorithm. Before moving forward, I would like to clarify the fact that I am not against using voronoi in architecture or urbanism whatsoever – there are clearly numerous meaningful uses, both in generating actual geometry and, probably more, in analyzing and visualizing data on an urban scale. What I am trying to criticize and draw attention to is the mental lock that this catchy algorithm has imposed, and, even worse, the common and frequent misconceptions induced by its strong affiliation with natural phenomena.

There are many reasons for the constant abuse of Voronoi cells (be they two-dimensional or three-dimensional) in architectural and urbanistic projects (the majority of which, by a lucky turn of events, are yet to be built). Crucial to this point is the association of voronoi patterns with organic structures found throughout Nature (living and non-living as well). The unmistakable silhouette can be found in numerous instances: you can see it under a microscope in almost any compact tissue like skin, you can see it in the way cells are distributed in a tree trunk, you can see it in the wings of a dragonfly; the list can carry on for quite a bit more. Taking into account the respective system’s constraints, voronoi cells can provide the most efficient structure or spatial routing paths for matter to organize itself into. This frequent recurrence in nature elevated the voronoi algorithm to the same status as that of the Fibonacci series and the golden mean  was enjoying before. On top of this, its organic and apparently random appearance made it the perfect candidate for a wide range of good-looking geometric experiments. Furthermore, its close ties with nature somehow transcend the barriers of reason and magically attach organic, eco-friendly, pro-environment qualities to any product designed by using this technique.

For example, one common misconception is the fact that generating structure via a three dimensional voronoi diagram would automatically create a super-efficient, really optimized and, on top of this, organic looking structural system. This quite big confusion is probably caused by the numerous natural structures that resemble the output of a voronoi algorithm. There is however a quite obvious missing link in the association which should pop up instantly to any attentive observer. The structures generated by the voronoi algorithm are to be found at microscopic scales, starting off from somewhere near 1*10^-5 m and continuing to decrease. Let’s say, for the sake of argument, that architecture begins somewhere around 10¹ m. There’s quite a big difference in scale, and due to symmetry breaking, physical laws (which, as any scientist worth his pay would tell you, are not universal truths, but the best approximations humankind has found for the way things work) rarely transcend through big scale jumps[1]. In the present case it’s quite obvious – the predominant force in a living tissue at 10^-5 m is a uniform pressure exerted on a cell by surrounding cells – and nature’s elegant response is a complex three dimensional voronoi structure which can be said is roughly indifferent to the main constraint which has shaped structural systems in architecture – namely Gravity. If you do a simple FEA analysis on a voronoi cell grid, you will see you’ll probably need more steel than a simple orthogonal grid to support the same loads, you will double production and building costs[2], besides getting less flexibility in terms of interior organization (spaces restricted to unique, bulky but flexible-looking cells). On the other hand, when used in straight-forward metaphorical approaches, and when this status is recognized and clearly expressed and not masked by a multitude of seemingly objective attributes, the approach can be considered to be “fair use”[3].

Another type of misuse of the Voronoi algorithm can be found throughout large scale urban projects – masterplans, local developments, etc. Cities are not composed of living “cells” in the literal sense – that’s where voronoi works. Cities are living organisms, but the rules behind the dynamics of city growth and crystallization are something completely different from a two-dimensional petri dish[4]. You can use the voronoi diagram to compute the shortest possible paths around a set of point-like obstacles, but this argument is insufficient for justifying its direct transformation in a street network[5]. Actually, street networks never had anything to do with the forces found generating voronoi cells. What you can often see is actually the same dangerous attitude and way of thinking behind modern urbanism clothed and presented as the exact opposite – naturally grown, organic urban lattices etc. – while in the end, if you start to rationally question and compare both approaches you can find dangerous similarities: both are lacking the same links with reality and are somehow strictly imposing their vision. This discrepancy noted here is actually, I believe, part of a bigger and much more comprehensive issue relating to digital and computational architecture[6].

What I find most distressing is the fact that there is a lot of cover-up work being done – voronoi diagrams, be they in three dimensions or two, always stand for some deep underlying natural phenomena whose efficiency and environmental-friendly qualities are automatically transferred to the respective project through a few rhetorical loops empowered by sophisticated jargon. The Voronoi algorithm does generate beautiful patterns and structures – which, when carefully used in the right places, are completely justifiable, sometimes even by aesthetic principles only. To conclude, I strongly believe that a certain level of sincerity should be (self)enforced when employing voronoi diagrams in architecture. While the manner in which this article is written might seem to some to be a bit too vehement, I am deeply concerned about the ease and nonchalance with which the voronoi algorithm is used – in the manner of an architectural recipe which can be applied anytime and anywhere, regardless of any other considerations. That’s why I have tried to raise awareness about the creative abuse taking place and its philosophical idiosyncrasies which, on a broader scale, do not restrict themselves to just this algorithm.

Dimitrie Stefanescu, 28 Oct 2010, Delft

Notes:

[1] The most straightforward example of this is probably the duality of gravity and quantum forces. While at a large enough scale, space is dominated by gravitational fields. The smaller the space gets, gravity loses influence in the favor of electrostatic forces, in the end becoming a negligible factor. The analogy is quite relevant – voronoi-like patterns are found mainly at microscopic scales, whilst architecture operates on a completely different level which can be said to be under the strong influence of gravity.

[2] I am acutely aware of the advances in fabrication technologies and related sciences which might render this argument useless in the possible future. I am trying to argue that, given the sensible ecological context of our current world, we should look for more sensible uses and applications for the tools and techniques that science makes available.

[3] As any ego-centric person would do, I can’t help not to throw in a reference to one of my early projects: http://dimitrie.wordpress.com/2007/12/03/77/

[4] For more in-depth knowledge of this, I strongly recommend both Manuel DeLanda’s much praised  A Thousand Years of Non-Linear History, as well as his interview with Neil Leach in the Digital Cities issue of AD (June 2009, p.50).

[5] I am not afraid to admit that I know this from personal, first-hand experience of the mentioned trap: http://improved.ro/blog/2010/01/urban-developement-proposal/

[6] To be more specific, an overall observed trend is that of employing computational geometry algorithms, often with spectacular visual results followed up by an active effort of fitting architectural qualities in the resultant shapes which usually ends in projects which are, for lack of a better word, fake.

Deprecated. Here’s the new version.

More as a scripting experiment, when i was mucking about trying to make the delaunay triangulation work in grasshopper i somehow found the wonderfully complex qhull library which i promptly set to push and pull to get it to work with grasshopper. As advised on their website, the best way to do it is to call it as an external program, which is exactly what i’ve done:  no files are written or read, no dos windows pop up, everything’s smooth.

Given that you don’t have many complex operations in grasshopper after the solution is generated, you’ll be able to handle quite an impressive amount of points (say 200 on my three-year old toplap) in real time. If you add the simple planarSrf operation, then say 60-70 and it gets sloppy.

What you’ll need to do to get things rolling:

0. Download the 3dvqhull definition and example file, and remember not to use it for commercial purposes, share-alike whatever you do with it and take the time to give the proper credits: 

1. Download qhull, and unzip it in a folder of your choice.

2. Get going and search for “System.dll”. What you’re interested in is the 2.0 version which you’ll usually find in here: “C:\WINDOWS\Microsoft.NET\Framework\v2.0.5[...]\”. If you can’t find it, I’m amazed grasshopper works for you. Anyway, you can find and install it from here.

3. Add the newly found System.dll version 2.o as a referenced assembly of the qhull component in the definition file.

If it turns orange, it’s cool.

4. Write in the panel that is linked to the “path” input the full path to the qhull program qvoronoi. You don’t need to add the .exe extension, but you can do it if you feel confortable.

5. There’s just one more thing you should know: facets that contain the infinite vertex are omitted altogether, without remorse. So as to have as little facets tending towards infinitum, I always add the corners of the points bounding box to the input sites.

You can scale the bounding box in respect with its center, or you can just call the whole thing off – it’s your choice.

I think this just about covers everything. Take care and have fun.

didi out.

PS: Qhull does more than voronoi. So if you have the time to explore and test, please do – the package is very powerfull and it can be used for more than this.

How about 60 points for real-time 3d voronoi manipulation in grasshopper?

Here’s a screenshot:

This isn’t a scam. Stay tuned for more free voronoi PrOn (and other qhull-enabled goodies.)

Out of popular demand, I have compiled a nice file detailing the possible uses of the Voronoi node, complete with the accompanying rhino file.

Download. (60 kb .zip)

For those who really like to play with voronoi regions and stuff, here’s the final grasshopper definition file (right click, save target as – else you’ll get a ~250kb of useless xml in your browser window).

The vcell component outputs now individual cells as closed polylines and closed nurbs curves. This is useful if you are using this for some urban project like i am i would have liked to, mostly due to easy offsetting and area calculation possiblities – included in the definition file – or height extrusion – included as well. You can even go further and color (using shaders) each cell coresponding with its mass/area/height etc.

Download the definition.

(right click and save target as)

Some nice people over in Spain (Laboratorio de Arquitectura y Computación) have made a nifty video detailing on how to use the thing:

[youtube=http://www.youtube.com/watch?v=iEynRywJIb4&hl=en&fs=1&rel=0]

Source code of the Vornoi2D node.

Have fun, and drop a line if something isn’t working the way it should (take care to select the boundary points in order – clockwise or trigonometric – doesn’t really matter).

The project’s challenge was to transpose the notion of perfume in an architectural form. Wikipedia suggests many trails. Chevalier’s Dictionary of Symbols suggests some more. Balzac: “Tout parfum est une combinaison d’air et de lumiere.”; Hugo: “Le parfum est de la lumiere.”. Floral motifs, blobitecture, incense and religion, drugs – it was up to you to decide on how to visually speculate perfume.

I was fed up of the meanings and interpretations of perfume. Perfume nowadays is synthetic. Leave me be. Smell chemistry. You can’t contradict that.

I broke the visual representations of the chemical components of a standard perfume (chemical representations have very strict geometric rules – 120 deg angles, pentagons and hexagons) and got voronoi regions.

Ahhh, sweet metaphor of computational architecture. Isn’t it beautiful? Elegant? Yet it has nothing to do with architecture. Form is detached from function and we are approaching a similar crisis of that of modernism, when the exact opposite happened. People don’t find themselves included in such designs. Computation that strictly refers to form/ellegance alienates architecture from its goals. I don’t trust the starchitect theory as being the solution; it won’t last or it will split us into sculptors and engineers. 

(Please do read that article. It’s a must. It shows past (as in blobitecture and zaha), present(not the “so last year” deconstructivism or – worse even – post-modernism) and pushes through to the question posed by the future.)

Enough theoretical blabber. I’m giving all this computational business some thought. Code in architecture is nice, as long as it serves the people, not just ellegance. (Please do notice I didn’t use the term “function”. I prefer the much more accurate and revelatory word “people” = complex emergent system.)

Here are some pics of the model:

Programmed in Rhino. Finished in Sketchup. Model made in ManualManufacturyCAD(hand glued). Laser cutting here.