This page in french ... and a note for english speaking fellowsfeel free to improve this rough translation from french to globish in order to reach true english :) :)
surfaces in practice
Les Grands Ateliers de l'Isle d'Abeau [GAIA]
the project
The « Grands Ateliers de l'Isle d'Abeau » give the opportunity to carry out forms and complex structures on a large scale. We propose to carry out a voute in the form of rather large free form surface (3 to 4 meters height on about fifteen meters in plan). We need it simple enough for a fast realization with little material and "rich" enough so that the study of the curves is profitable. We eliminate the sphere, the cylinder, the cone, the torus and it would be desirable that surface presents zones at positive, negative and null curvature. We will thus go beyond the pH. The approach by the "forms pascaliennes" or "pFormes" will provide the basic language.
a tool, the pS33
The simplest pSurface answering the preceding schedule of conditions is the pS33which can even define portions of sphere, cylinder and torus, while working with points in R4; but this is another history.... It is entirely defined by the data of 9 points, which can be seen like points of control (or poles) of 3 parabolas.
The algorithm of de Casteljau is used in two times :
- the control points of the couples : starting from the 3 initial parabolas one builds the parabola medium, then the parabolas at 1/4 and at /4, and so on until obtaining the number of desired couples; one can consider that 9 couples give a good resolution,
- the points of each couple : for each parabola_couple, one builds the point medium, then the points at 1/4 and at 3/4, and so on until obtaining the number of desired points; one can consider that 9 points give a good resolution. There are now at this stage 9x9 = 81 points defining surface as 8x8x2 = 128 triangular facets.
putting 81 points in space
We have now to put in position in space these 81 points.
- First idea: direct construction of the sections in situ
- the last visible image of this first group shows a possible actually, the figure is false! Could you tell me where I was mistaken? for a couple: one traces on the ground the 3 points of control of the parabola, then the 6 other points are built. An assembly of 5 boards and 4 stems is enough "to memorize" the positions and the unit is raised and put in position,
- One needs two of them to position two successive couples (18 points) which will be connected by triangular facets (whose nature is to be defined, thick paperboard, laminated...). Problem: a scaffolding is needed!
- Second idea : construction of the sections on the floor
- the first couple is traced on the ground and the second upon it; we place "chairs" at the right height and tight cords on which the points will be marked, no more boards; the chairs can be pyramids made up of 6 tubes connected by sliding collars
- the 18 points are thus easily accessible without scaffolding and the triangular facets are built directly. The whole then is raised and put in position. No scaffolding is needed !
assembling 128 facets
... to be defined : simple skin, double skin, ...
curvature analysis
One wishes to study the curve of surface in each point, his effects on the structural properties and perception of the form.
In each point of a surface one considers the tangent plan and the normal to this plan at this point. A plan containing this normal intersects surface according to a curve which one will study the curvature (i.e. the radius of the osculatory circle at this point). It is thus a question of plotting this curve and of studying its variations while making turn the plan around the normal; one will be able to thus determine the directions of maximum and minimum curvature (positive or negative) and the directions of null curvature, the geodetic directions and the asymptotic directions. One considers two methods to plot these curves.
- the first method consists in positioning a source of light on the normal on the surface in this point and a plate tangent in this point and provided with a slit; the luminous curve plotted on surface is the line of sought curve; it will be enough to memorize by a mark this luminous curve then to make swivel the slit to pass to following
- the second method is an approximation which consists in tracing the immersed segments (within the meaning of the approach by the pFormes), by using the squaring defined by the triangular facets. It will be interesting to compare the two traces.
One will be able to also trace small triangles (curvilinear) and to compare the sum of the angles with the value of 180° which one obtains in the plan, lower than 180° for the zones with negative curvature and higher for the zones with positive curvature.
Other analyses possible... to come.
a basic shape
One proposes to work on a surface made up of two concatenated pS33, the first with positive curvature, the second with negative curvature. Dimensions are based on the yard modulus 90. While exploiting the position of the poles it is possible to generate many forms...
application
A first example of application is based on the concatenation of several elementary surfaces (in the simplest version) leading to a long hull which one can pose on two large blocks (servant spaces); one thinks of the Japan Pavilion built by Shigeru Ban in Hanover in 2000. Contrary to the building of Shigeru Ban, surface is corrugated in opposition in plan and rise, the idea being to preserve the length of the couples as well as possible, horizontally to simulate the deformation without stretching of a rubber pinch plate on the two longitudinal edges.
Other examples to come...
next
A whole family of dissymmetrical surfaces can be approached while acting on the points of control of the pS33. Beyond that, it is possible to complexifie surfaces:
- by increasing the number of points of control (cf pS55),
- or by assembling them and while working on the curves intersections (cf Sagrada Familia based exclusively on pH and HR)
... keeping in mind these two principles:
- " Less is More " Mies Van der Rohe
- " Moore is More " Charles Moore
the shell to build
We chose the simplest one to have a chance to go to the end.
the built shell
... to be translated in english (don't forget the comments of the pictures ...)
Et voilà ! Le Workshop vient de se cloturer... On a passé une super semaine, et malgré quelques charettes (jeudi jusqu'à 5 heures du mat), on a (quasiment) réussi le pari de construire une free form courbe avec des segments de droites et des plans triangulés.
Défi relevé, à quand le prochain ???