Hi All,
I have another Forum looking at this and it was suggested to cross post to you people. So.
Hi All,
There are two other forum posts sort of related to this post, but they are not quite what I need, so here goes.
I am designing a Sculpture that incorporates a geodesic sphere. Geodesic spheres are created by projecting either a tetra-hedron, octa-hedron or iscosa-hedron onto a sphere. These are the only regular polygon shapes that are constructed of regular triangles only. The more triangles involved in the projection, the more spherical the ultimate figure. 3V refers to the original triangle shapes being split into three triangles on each side. There are tools in AutoCAD that will do this, but the problem is that they end up not being quite accurate enough and give many different strut lengths. A 3V sphere should be able to be constructed of only 3 different strut lengths that consists of 12 pentagonal shapes and 80 hexagonal shapes. In the Sculpture this will consist of the 92 machined connectors and the 270 A,B and C struts. The great thing about the design is that it can be scaled naturally to ANY size by multiplying the Strut ratios by a Constant. Simply - if you want a bigger sphere then multiply the strut ratios by the same constant, as long as the struts still fit the connectors then it will work.
The connectors are fairly straight forward to design and are identical, the problem is drawing the finished dome accurately so that it can also be scaled. I know all of the angles, but manually calculating angles for each strut will be a nightmare.
Example.
For a 2m diameter sphere, the struts will be, A = 348.6 mm (60 required), B = 403.5mm (90 required) and C = 412.4 mm (120 required)
The connectors will be based on a Pentagon made of A and B struts, and Hexagons made of B and C struts. The Pentagon angles will be 54 degrees around the edges, 72 degrees in the middle with a rise from the edge to the centre of 10.135 degrees. The Hexagon will be 60 degrees around the edge and at the centre and a rise of 11.992 degrees. Assembly will look like this:
This graphic is from the Desert Domes website: http://www.desertdomes.com
I don't know how they generated this graphic, probably with a computer calculating and building the image. What I want is to do the same thing in AutoCAD without having to manually work it out. Then being able to extract the co-ordinates of each connector and list them.
My thoughts run along the lines of this:
Drawing the Hexagonal and Pentagonal shapes and locking them into a Block shouldn't be too hard, but I still need to work out the angle of the plane to paste each Block (92 of them). The angles will be constant and the edge of the Hex or Pent will be a mirror plane for the adjacent shape. The thing that bollocks it all up is the 12 Pents will be in regular positions but scattered around.
There must be some kind of script that can calculate this (all be it unwritten so far) but I cannot get my head around how to write it myself. Simply splitting the faces of an icosahedon into three triangles each side them projecting it onto a sphere will give struts of irregular length. There must be a way of fixing the length and angle then recursively (?) building the sphere.
Ideally the script would take the strut lengths as parameters so that a sphere of any size could be generated.
Any help would be appreciated but I am thinking this might be a Guru who likes a Challenge solution somehow.
Cheers
Andrew
