Are you talking about curves with three varying tangents (curves in three dimensions) or surfaces with a Gaussian curvature not equal to zero (double-curved surfaces)?

The definition of double-curved surfaces goes something like "surfaces where in each point a plane tangential to the surface will have curvatures in two directions". This means that both a sphere and a hyperbolic paraboloid are double-curved surfaces, although they have different geometrical properties. The problem with double-curved surfaces as such, is that they are often built by deforming existing flat panels, like glass or steel. Since transforming something from flat to double-curved means (geometrically speaking) that the surface will contract along some parts of the surface, and expand along others, it is very difficult to achieve a panel that has even thickness, and therefore doesn't crack. Compare for example bending a paper into a cylinder (easy) with twisting its two sides in opposite directions to form a hyperbolic paraboloid (difficult, since the paper isn't very elastic).

But that's only the problem with your facade skin. Since a double-curved surface also has normals that vary with three parameters (x,y,z), you have to design some clever, tight joint between skin and structure. Why? Because the structure is often of rectilinear geometry, with static normals, just because it's easier and cheaper (it is handy to be able to fix points in a rectilinear coordinate system by just using weights, strings and rulers). This is where geometrically complex projects often disappoint - they simply fail to be 100% double-curved, instead favouring a fat wall where geometrical differences between structure and skin, interior and exterior, are resolved.

Can't recommend any particular texts on the subject, but some basic differential geometry and logical thinking is a good starting point. I'm planning to translate my own writing to English someday, but it will take some time.

Oh, well there's "Twist & Build" by Karel Vollers (010 Publishers) but it's not that well-written...

the sailmaking (and to a lesser degree hull making) industry has some pretty cool technology for dealing with this by using carbon fibers laid up over an infinitley flexible forming bed to achieve whatever curvature is necessary. i suppose that they're leading the way for what may in the future be building panel skins.

Spanish Glass company Cricursa (www.cricursa.com) are experts when it comes to glass/curves. They did the Herzog & de Meuron St Jakob Stadium facade.

please look at a project by Eric Owen Moss I am unable to remember the name of it however it employs this type of glass construction and I have read about the difficulty they had in doing this work specifically designing the clips that tied the glass back to structure, also you will find the glass used in the cafeteria project of the Conde Nast building in New york city by FOG as well incorporates these techniques, also the bubble BMW exhibit by Bernhard Franken and ABB Architekten at the IAA '99 Auto Show in Frankfurt, Germany


also, have you ever been to a glass manufacturing plant, float glass

you should really make it a point to take a tour of your local glass plant and see what it is like to make float glass, also, how to curve glass in one axis (vault) it will provide you the insight you will need to understand these principles of glass deformation and the problems, structural and cost associated with it

the REAL question is why, not how, to curve it in the first place...
anyway, they have been doing it in car windshields for more than 40 years.

it aint like e. owen moss invented double curved glass.

no eric owen moss did not invent curved glass, or double curved glass for that matter,

architects rarely invent anything, but those who have conceptualized and actuated the use of it in their projects have the undertanding of the impacts of it on a project

so what do you mean by the real question being why to use it?

like the projects I mentioned, why?, because that is the method of choice to achieve the desired outcome,

do you mean why, costwise, ethically, structurally, can you desribe exactly what you mean by WHY?

Hi

I find a-f 's post best describing the real problems in the real world.
As here is a language problem you must do with my 500 english words, but even you form a pipe mesh and have triangled sheets cut, you will find that the expenses will make most double curved surfaces unreal, they simply ask to much thought just to be made to leave any thought about the other practical problems, they promise a lot but unless you want to compromise it is nothing but expensive special fittings and an army of skilled craftmen. Beside projecting you must ensure that each face can expand or move as any stress will deform the intire structure. Now you all know my ansver about forming the exact same forms but in a way that make a better promise about manufactoring whatever form, then who say that we are stuck with the zero thickness surface that must be the origine for the tread, the zero thickness AutoCAD mesh that made so much trouble so many promises and so many compromises.
Now this is a question about cost, as surely you can order cast glass and produce a small structure but you will only have the surface no real structure unless you exploded the mesh and offset the surface frames and still you willbe left with problems that ask innovation as how will you ensure a tight fit along the glass panels and how to have the cross members produced. Now unfolding seem not to be the solution, producing a double curved surface is just part of an even more complicated task that most often ask a compromise, there simply seem not to be a production technike that support the visions the double curved mesh entities unless you accept that when done, the skilled craftmen let go the measures to make it fit.
Still possible it is you can even draw a lapstrake hull in AutoCAD with it's zig-zag overlaps even the program will fight you to make it smooth surfaced --- but then you will not get the craft the form you projected, you will not have the boat with the ability you asked, still steel and glass is much more demanding in terms of crafts so even you can form beautifull boats this don't mean that you can produce structures that anyone can pay.

http://home20.inet.tele.dk/h-3d/stv-1.jpg

As I said before there are a solution ,one that make any form and make you develob even more exiting expressions .

Per,

That sounds very interesting what is this solution you speak of, do you have any more information?

As J3 says, I would recomend you to talk to Cricursa (www.cricursa.com) whenever you have any question regarding difficult curved glass. I think they really can manufacture architectural glasses with very strange shapes.

They've made the folded glasses for the Greenwich St. building and the double curved glasses of Publicis, that you can see in the Venice Biennale article (biennale article).
They also made the bubbled glasses of the Prada Tokyo by Herzog & de Meuron.
And I think they were the first ones to manufacture spherical glasses in 1992 (the dome Imax in La Defense - Paris).
They like developing new shapes and innovating with glass. In their booth in a tradeshow in Paris they displayed glasses following the internal surface of a toroydal shape (the hole of a doughnut) curved with two oposite radious.

the cricursa web site is really annoying

Hi
Punkt , --- I think it is very important to know the basic limitations and realise where the real trouble is. Glass is made any shape any color and can be formed, but glass have weight and ask a frame most often ,anyway there are limits, even you proberly find glass studio's that will be able to make whatever, still cost proberly is an issue .
I se glass as an option for sheet material aswell as steel or plywood, why do you still think you must bend somthing. To form a curve ,it is not nessery as you can form anything within a sheet framework as long as you can't se the obvious ansver doing it round in flat sheets it's called 3D-HoneyComb,like forming a framework ,You Romans are so antious to bend somthing , you don't need to ;))
Try find a wise argument for bricks.
I suggest one way to make sheetmaterials do that without having somone to form the actural detail form, it's digital from CAD drawing to the exact building part, replacing beams and profiles knees and nuts, what do sheet glass cost, what is the cost having it processed cut full of holes and shapes .There you have the framework in glass sheets without bending and with frames if this is what you want ,it's not my point to prove the cost ,only to do the job this time at a third the cost four times as strong

try emagine hardened glass being the framework as a simple assembly plain glass sheets 3D-H structure, cut with N.C. water cutter .
If you only will make bend pieces by acturly forcing the material instead of just making the framework ,and realise that any form can be projected with just sheet material. glass is sheet material and acturly bring the individual building part in real N.C. Codes to produce the actural framework for the structure still you are bound in just bending the actural detail, then I just question the limits using such heavy material
Guess you got my point.

Punkt:

For more information on Per's 3D-H, check out the discussion named "Hi all you fancy graphic lovers". If you can cut through the various personalities shining through (including Per) the various arguements against Per's system are pretty clearly established. Unfortunately Per has yet to directly address them.

Per:

Can we not turn this into another 3D-H thread? I know this project is "your pony" as you've stated plenty of times, but lets stay somewhat on topic. The issue of bending glass was brought up for a reason, and I don't think its very productive to dismiss it as old-fashion and then start plugging your system.

Hi

Pixelhore you are quite right, my point rather is that to often we think we need to bend and fiddle, where it is possible to shape round without the members being forced or made in detail follow the round form, then I guess I am also talking about having a bigger choice.

per you are incorrigible, tell me what is the bigger choice I really want to know

anyway,

I went down to the Greenwich St. building yesterday and of the enitre facade the curved panels really look bad, almost as if they are having a really hard time getting them in, I dont know if it was poor installation or what, does anyone live in NYC that has any insight as to what the heck happened there, its really a shame because the entire facade looks great except that one spot

Hi

aseid I can\t respond on that topic as I didn't se that building, what I can say is that if you project glass panels as computer meshes ,you will face some problems that others been fighting . Reson I ended up with a different aproach is not that I didn\t solve these, but that I realised other limitations such as being able to provide a frame to hold the panels ,one that can acturly be manufactored .
With a Dome there are no problems with double curved panels but as soon you try to shape organic shapes others than the Dome or Doughnout the tradisional shapes, then the double curve in this technike can only be provided by individualy forming each plane or make it into two triangles ------ Now flat materials are the cheapest forming ask exact manufactoring of each panel .
What I say is very very different, as in my application you _must not_ try curve anything everything must be plane as cut.

This is what I talk about and this is what I point to in the graphics . Not my lame designs but a way to build round without bending one single piece, but at the same time change focus from the manufactoring of then being difficult individual pieces ,to a simple way to cut standard flat materials, forming actural curved structures any shape, square or curved same cost.
Now tha't new isn't it.

Per you just show a sructure but not a shell. How are you going to solve this problem? In other words, how are you going to fill the holes left by your concept?

Hi

The structure fill out any Solid you form in fact you can use a mesh for that --- then you have two things the mesh and the exact structure that will support this. The holes as you refere is not the absent of pressant but exact defined spaces with nothing , but isn't this how a building usealy perform except you have a hell of trouble interconnecting horisontal with vertical members ,acturly most common structures is rather like card houses.
Then think it this way, that the weak points in the WTC seemed to be the be just those connections --- now with 3D-HoneyComb there are no such connection they are replaced with somthing quite different, so no floor can ever fall for the same reson.

Hi

Maby I shuld add that from the start it's your choice what form to make structure for, that mean that doing it for a Dome make sure the panels is flat, chose any other of the forms that make this you shuld be able to use only flat panels, if you need frames for that do it in mesh ,explode the mesh find the corners for each panel in the mesh use that for a bit math to calculate a bit smaller panel and the frame.
As easy as that.

Sorry I realy mix things up, automating an assembly framework that count several different floors walls and stair foundations, will turn into an assebmly sheet structure at some point, but then more walls are made from the frame., --- still you build round and flat sheets cut to frames that form the most wonderfull places, now also please note, that I didn't bend anything if I made an offset of each plane in a stupid Dome . You can even calculate the frame, have a mashin do it Eifel fasion but at what cost. Now I could free form it in styrofoam, but realy ,don't you think sheet material is a much more relevant way a new Dimention right ?
Bilbao you shaped from a wire mesh digital model so they said back then, that is points from my best knowleage, I find Design much more important and designing a round form even with floors and stairway ,a honeycomb structure is ideal .

I still talk about choice of material and cutting the shapes with water cutter as this is the obvious choice I don't know why, but the form of each panel if it exist 3D in a drawing, is no different from real world. Ofcaurse you could make a program that roll out the exact framework for cut panels also flat but proberly triangled, but it will not be from me ,as you can build round, with flat sheets you just do it in 3D-H.