Jan '05 - Mar '06
A presentation by Michael Silver this afternoon on new fabrication technologies got me musing about the mathematical problems involved with the use of two computer-controlled machines he showed: a hot-wire foam cutter and a bandsaw. 
With both machines, you're bound by the limits of only being able to cut with a straight line through a volume of material, so each cut creates a ruled surface (or more specifically, one of a limited subset of ruled surfaces--no Moebius strips or Pluecker's Conoids allowed).
What volumes can be formed from a combination of such cuttable surfaces? It seems fairly intuitive that because of the cutter's limitations, the shapes must be continuous, non-self-intersecting, and holeless. There is also some sort of convexity requirement, thought I'm not sure exactly how to phrase it--I don't know a mathematically strict definition of concavity and curvature that would categorize all the shapes you can cut--hypars, hyperboloids, etc--together. I'm pretty sure the answer is in here somewhere, if only I could read it.
Also, doubly-curved surfaces--a sphere, for example--meet all of the above criteria, but you still don't want to cut them with one of these devices because they can only be approximated, and then only inefficiently (too many cuts).
At any rate, it seems that this whittles the set of available shapes down a little more than I'd like, in terms of architectural potential. That means chopping up multiple bits of foam and sticking them together into more complex shapes.
So the next question becomes: what shapes can be subdivided into multiple cuttable volumes whose interfaces are cuttable surfaces?
Paul Haeberli's Lamina is basically solving a related problem in 2d surfaces, instead of solid volumes.
There's got to be someone working to develop efficient algorithms for breaking down arbitrary 3d volumes into the most efficient set of cuttable volumes. It's way over my head at this point, but a super-interesting problem...
11 Comments
derek- if we wait long enough google will do it for us.
silver = no good.... ive seen what that foam machine can make..... a freakin mess
nice post - though the real question (no offense) is since when do we build buildings out of foam?
my suspicion with the CNC fetish milling around grad school these days is not to do with the somewhat overindulgent new geometric and algebraic auto-computations, but more with the fact that we still build the same way we did 100 years ago and building materials – although expanding rapidly in terms of selection – remain somewhat typical. If less time were spent trying to justify gratuitous forms as an excuse to use new machinery in our post-Gehry euphoria, and more time spent trying to see what the materials alone can do with current construction and pre-fabrication methods. After having worked in both Europe and America, it is really amazing how different the priorities are in terms of architecture. Here, in the US, architecture is turning its back on buildings (probably because we don’t get hired for those anymore) in favor of interiors, installations, and product design. And the grad schools perpetuate this. Just a thought, really.
No wonder archinect has a bad reputation: such a bunch of haters.
It's called research.
Thanks for your thoughts, lifeform. You bring up some very good points about the applicability and use of fabrication technologies. Can you give some examples of the differences between European and American priorities? I'm curious about your observations.
I'm in agreement about the limitations of pursuing gratuitous form (though a little every now and then is nice :). I was glad to see that that panel discussion that Silver was involved in yesterday also mentioned benefits in cost, scale, time and safety brought on by new fabrication tools, and didn't just focus on formal potential.
I'm not sure I get your point about using current materials and methods, though. The last 100 years has seen an enormous amount of material and technical innovation in building construction, which has been invariably followed shortly by new formal trajectories, as well as new developments based on cost, etc. For example, new concrete types (high-strength, lightweight, fiber-reinforced, foamcrete, etc) led to Nervi's and Hadid's amazing surfaces, as well as the proliferation of freeways and shopping malls. But why stop with current techniques, instead of pursuing new ones?
Even something like Shigeru Ban's Hannover Pavilion--which is surprisingly primitive in materials and construction (bolt sticks of bamboo together, bend, cover with paper)--could never have been constructed without advanced computational techniques for the complex structural problems it creates.
I'm interested in new materials and fabrication methods as 'enabling technologies'--if you can solve the 3d foam-cutting problem above, and build, say, a concrete-casting infrastructure around it, it's a step towards a number of possible innovations: crazy new shapes; cheap and fast standardized precast panels; lightweight, mass-customized formwork; etc. It's about putting something new out into the world and seeing what people do with it. I trust that architects will use it for good and not evil.
ps post-gehry? last I checked, Frank's still alive and practicing :)
Derek brings up the important point that some of the advanced fabrication techniques are more suited for supporting the fabrication of building (e.. formwork) rather than actually being the elements buildings are fabricated with. Lifeform pinpoints another important issue which is the fact that architecture in the US seems to have turned its back on, you know, actual buildings. Interesting that you pair this with the question "what buildings are made foam" because I believe that some of the things happening in the rapidly expanding suburbs are taking advantage of foam and other not-typically-architectural materials. I know of foam being used as an internal insulator for cast concrete structures and a kind of plaster substrate. These companies are also (kind of) delivering on the current architectural dream of pre-fab construction-- firms like Ryland Homes build houses from a small set of plans which are mostly assembled in a factory before being shipped to the site for tilt-up. It doesn't produce anything interesting from an aesthetic point of view, but architects may benefit from an investigation into the materials and techniques actually being deployed by builders.
Homes like Ryland's are typically built using SIPs (notorious for durability issues, now banned, I believe, in a few states...), which are basically foam sandwiched between layers of particle board or OSB.
At the other end of the spectrum of foam architecture, there's William Massie's Evans house, which is in fact polyurea foam sprayed over a PVC framework (see the playa urbana project for what the framework looks like). The foam isn't machined, but the steel structure supporting it is. I don't know how durable it is, but it's a great experiment.
Also take a look at the big sky house, whose concrete walls were cast using CNC-machined styrofoam panels as forms, IIRC.
bryan - calling something "research" does not vaidate it against criticisms of method and content. that is my beef. and if archinect isnt about an open discussion about method that i am missing the point of these (very useful) blogs.
derek - i am in no way suggesting that we should not pursue new methods of construction. in fact, that is something i am seriously dedicated to. what i am saying is that too often the emphasis is on the geometry and the algebra (read: form) and less on the application and material (read: construction). That is my beef with foam. The use of foam renders construction and material issues null. They appear as secondary concerns to the more seductive possibilities of wolfram mathland contortions. Which, i know, becasue i have sat on them, critiques and reviews tend to center around.
Thanks for your point about materiality. And I am glad to see that you , for one, have an understanding of the architecture realted possibilites of the technology. I think there is interest in new materialism in North America through ventures like transmaterial, gsd mori research, and what iwamoto is doing out at berkley. But, arguably, as a whole, top grad schools and the pedagogues preaching at them seem to favor the geometric over the constructive and material.
Generally what i am seeing is a shift from architecture to interior and product design; which leaves the buildings to whom?
this book will give you a good sense on emerging differerences in application of technology between north america and europe/asia. My beef is more with application; in europe/asia they use it to build; in the us they use it to make shop interior shelves for high-profile commercial clients.
anyway, i am just saying that i am suspicious of the hype. sometimes, i think rural studios are pushing the envelope of construction far more than the greg lynns.
(oh, sorry, and by "post-gehry" i just mean post-bilbao, or after the proliferation of catia and other software to make buildable complex geometries.)
lifeform- my comment was directed at 438NNwhatever. Apparently you hit the send button just before I did.
One has to accept research as a work in progress. How long has Testa been talking about a carbon fiber tower... but everyone knows it's still just a proposition.
Ah, I understand your point now, and I think we're basically on the same page. I like your distinction about form and construction, although I'm not sure I'd draw the line in the same place as you.
It's at the intersection of materiality, fabrication, assembly/construction and form that a lot of the potential in architecture lies, and I think it's counterproductive to try to posit a working model where an architect can make 'Mayannaise' (as a critic once referred to undifferentiated Maya-based blobbiness) and then click 'print' and have some machine spit out a building. Which, as far as I can tell, is what some people (certainly including some at columbia) dream of.
The use of foam I envision is as a formwork, mold, positive for casting, or some other basis for construction from elements--not a finished building.
My descent into mathiness that seems to have scared you arises from two things: first, a conviction that for this kind of fabrication to work, the math problems like those I state above have to be worked out and incorporated into digital tools, and are therefore fundamental the discussion of fabrication, and second, spending too much time this week on Eric Demaine's site. :)
l/g,
why it it not possible to achieve complex curvature with a wire cutter and band saw?
just curious,
b
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