d the voronoi diagram
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7/23/2015 (the teeming void): Uniform Diversity: SpaceFilling and the Voronoi diagram
http://teemingvoid.blogspot.in/2010/08/uniformdiversityspacefillingand.html 1/6
friday, august 13, 2010
UNIFORM DIVERSITY: SPACEFILLINGAND THE VORONOI DIAGRAMThis post is a short excerpt from a paper recently published inArchitectural Theory Review 15(2) a special issue on architecture andgeometry with lots of good (Australian) stuff. My paper (pdf) is a criticallook at spacefilling geometry in generative design. It touches on severalthings already blogged the Water Cube and ideal foams, and somegenerative projects that use selflimiting growth. This excerpt looks at theVoronoi diagram as a spacefilling process.
The Voronoi diagram has become a ubiquitous motif in recent generativearchitecture and design. It, too, can be usefully read as a spacefillingmodel. In formal terms, a Voronoi diagram is a way of dividing up spaceinto regions so that, for a given set of sites within that space, each regioncontains all points in the space that are closer to one site than any other.The result is also foamlike, but as a model the Voronoi diagram hasattributes quite different to the ideal Kelvin or Weaire Phelan foams.
Firstly, while the formal model is again based on a strict set of conditions(in this case proximity) it works with an arbitrary input — the given sites —rather than defining a regular structure. The Voronoi is thus a procedural
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7/23/2015 (the teeming void): Uniform Diversity: SpaceFilling and the Voronoi diagram
http://teemingvoid.blogspot.in/2010/08/uniformdiversityspacefillingand.html 2/6
geometric structure in a way that the ideal foams are not: its structureemerges through the application of a specific process or algorithm to agiven set of inputs. In this way, the specific spatial relations betweenneighbouring cells depend on, and emerge locally from, the given spatialrelations of the specified sites. This trait also gives the Voronoi model a kindof malleability; sites can be added, removed, or moved, and the spatialstructure readily adapts
Again we can read off the attributes of the Voronoi as a model in this way. Itis multiplicitous, but in a different way to the gridlike uniformity of thefoam models. In this case, the multiplicity can, in fact, be irregular: the sitescan be positioned anywhere within a given space. However, this does notamount to much, in terms of heterogeneity: while the sites can bepositioned arbitrarily, the procedure, and the relation between sites that itencodes, is entirely uniform. Each site, taken as a formal entity, is identicalto every other; this is a kind of uniform diversity. Like the foam models, theVoronoi diagram treats space as indefinite and extensive: it can go onforever; its only practical limit being the computational resources requiredto calculate the diagram. The model itself has no way of defining an edge orbound. Finally, the variability of the Voronoi can be phrased another way,as arbitrariness; in other words, that there is no inherent reason for a givensite to be where it is. There is nothing internal to the model that cangenerate that differentiation.
In Marc Newson's Voronoi Shelf, for example (above), we see acharacteristically organic variety: a range of cell sizes and shapes, different
wall thicknesses, all in an agreeable state of harmony. The form gives an
impression of inherent logic. It is as if the harmony of the relationships
between the cell sites assures us that there must be a reason for them to be
as they are. This is unsurprising, given our familiarity with, and aesthetic
attunement to, naturally occurring structures that resemble these cells. The
visual signature carries an association of organic logic: but in formal fact
the cell sites are arbitrary, that is to say, designed. There is no necessary
relation of one to another, only (we can but assume) a designer's choice,
SPACE SPECIFICITY SYMBIOSISSYNAESTHESIA SYNCHRESIS
SYSTEMS ART THEORYTRANSMATERIALITY URBAN VIDEO
VIRTUOSITY VISUALISATIONVORONOI
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7/23/2015 (the teeming void): Uniform Diversity: SpaceFilling and the Voronoi diagram
http://teemingvoid.blogspot.in/2010/08/uniformdiversityspacefillingand.html 3/6
which is concealed by an appearance, much as the surface of the Water
Cube conceals the regularity of its foam model.
Conversely, some designers directly address the arbitrary input to the
Voronoi diagram, treating it as an opportunity and exploiting the
malleability of the model. As Dimitris Gourdoukis writes, "the problem of
deciding on the initial set of points is, I think, one of the most interesting in
relation to voronoi diagrams." In Gourdoukis' Algorithmic Body project(above), the locations of the Voronoi sites are specified by a second
generative system, a cellular automaton; here the Voronoi acts as a
geometric filter, interpreting and interpolating one set of spatial data into
another. In Marc Fornes' POLYTOP, the designer proposes a masscustomised product in which customers can design the point cloud that
drives the Voronoi geometry; here a problem of arbitrary choice is turned
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7/23/2015 (the teeming void): Uniform Diversity: SpaceFilling and the Voronoi diagram
http://teemingvoid.blogspot.in/2010/08/uniformdiversityspacefillingand.html 4/6
LABELS: ARCHITECTURE, CRITIQUE, GENERATIVE DESIGN, MODELS, SPACE,VORONOI
1 COMMENT:
adam said...
I love Voronoi diagrams. I while back I was playing around with them to try andcompress an image into a set of points and colours using only a genetic algorithm.I never got very far with it but had some fun and sent a patch to the maintainer ofMath::Geometry::Voronoi which got applied. I forgot to patch the docs though soI'm not listed as an author. This mostly came about after I saw the hill climbmethod applied to a bunch of translucent triangles to generate an approximationof the Mona Lisa.
I should dig my code out again and see if I can make it do something interesting.
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