layout and panelization
how to split up an irregular surface into similar bits
the method that i have actually applied takes ideas from both
concepts described above.
to project longitudes of a sphere on a free-form shape is a charming idea: the longitudes are geodesic lines and what we are really looking for is a way to find geodesic lines on the free form. i have already mentioned the technique of finding the nearest neighbour point to a known point, when the new point must be on a curve that is part of the surface. for the kunsthaus shell we had a sucession of closed curves, each located in a plane that was parallel to its neighbour (=the ribs). by starting from one point on a curve you find the nearest point on its neighbour curve and then the nearest from the new point to the next neighbour curve and so on. (mind that the process is not reversible, you do not get the same result from left to right or opposite, but for us the difference was not important)
|the whole process is much the same than to roll a strip of scotch tape over an uneven surface. the result is a non-planar curve, but the scotch tape is still straight. the way the scotch tape runs is only influenced by the initial direction you choose (in my example: this is the alignment of each rib in its planar surface). now we know how to place lines on the surface - but how about the width of each longitudinal plexiglas strip? i have already mentioned the simple technique of dividing an arch into equal segments before. the problem is that there is no privileged arch that asks for division. but what you want to get is strips that are as wide as possible. the limit is the available width of a regular plexiglas panel (about 1.95 meters) so you have to find the areas where the strips have the tendency to get very wide.||my approach: the strips have a main direction (orthogonal to the base planes of the arches) the arches are strictly convex and therefore i know that a strip gets wider when it runs along an arch that goes further outside than its neighbour. as a consequence, the line that shows the furthermost outline is the silhouette of the shape as seen normal to the main plane. next thing is to transfer the silhouette into a flat plane and measure its length in order to subdivide this curve into equal segments of a desired maximum dimension. now you have a chain of points that will be transferred back to the surface. these are your starting points for the geodesic lines that will establish an order on your free-formed shell.||what you get is a large number of nearly rectangular fields. the technique is useful for shapes that are gently curved. they should roughly follow a longitudinal axis (that does not have to be straight, a slightly curved longitudinal axis may be possible). endcaps are an extra problem (or all surfaces that are nearly parallel to the main planes). you can overcome this by carefully selecting other main planes, since they do not need to be parallel. we used parallel arches because we did not want the layout to be overly complicated and establish an orthogonal system that allows others (e.g. external planners) to understand the structure.||
the whole method is not really scientific, but it helped us to reduce
the amount of excess plexiglas and to find a good way of subdividing
the structure into a number of similar elements.
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