SPECIAL GEODESIC!!

[geod...@gmail.com]

In the last days I have been trying to get the geometry of this specific geodesic dome in SketchUp unsuccessfully. Is someone up for the challenge? Or any pointers towards info on this geometry?

The pictures on SketchUp below are my attempts and the other 2 are the real ones.

Source: http://domeofvisions.dk/the-architecture/dome-3-0/

DoV 3:

[Moty Marcos Dorfman]

I think the photo shows a plastic sheet with triangles painted on it, streched over a round sphere

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[geod...@gmail.com]

Robert, I have seen all the pictures and understand that it is made by equilateral triangles projected onto a sphere. But how is this geodesic dome composed? It is not icosahedron based so how would you realize it in a 3d software? What solid is it based on?

On Saturday, December 30, 2017 at 11:15:04 PM UTC+1, Robert Clark wrote:

Dome of Visions 3.0.  Here's an image that might help you understand how they created the geometry.

[Ashok Mathur]

If you use Google Translate to convert the web site from Dutch, you will find that the web site contains links to earlier versions i.e. 1 and 2.

Both versions contain many details of the architecture.

Its a double layered dome with one layer of laminated wood and an outer layer of rhombic transparent material.

The domes are a collaboration between two architects
Kristoffer Tejlgaard
Benny Jepsen

Regards

Ashok

Regards

Ashok

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[Ashok Mathur]

Dear Robert,

The first version of the project says that it is based on Bucky Fullerene C60.

That is nothing but a the standard hex-pent obtained by truncating an icosahedron.

"Dome of Visions 1.0 is a 10.5m high and 21m wide dome with a land area of ​​350 square meters. The domain consists of two overlapping geometries. The outer layer consists of 256 thin polycarbonate slabs cut into nine different five and six sides that overlap each other in a disc-stable 850 m2 pattern. The inner layer is made up of 250 kertobells of 3400 mm, which are assembled in a lattice-stable pattern with 91 hubs in steel. The grid grid is a model of a carbon molecule (C60), one of nature's strongest building blocks. Geometry makes the dome stable, and the polycarbonate boards achieve high carrying capacity by tensioning in a curved shape. The plate, the so-called hat, on top of the judgment can handle a load of one and a half tons."

Regards

Ashok

Regards

Ashok

On Sun, Dec 31, 2017 at 9:04 AM, Robert Clark <clark.rob...@gmail.com> wrote:

You're right.  This is not based on a icosahedron, there are no pentagons.  It is a grid pattern of equilateral triangles distorted over the surface of a hemisphere.

I'm not a very experienced SketchUp user, so I would instead be modeling it in SolidWorks.

I would create a sketch of the triangular grid pattern.

Then, I would choose a singular point above the plane that would be in the location of the point source light as seen in the previous image we were discussing.

Next, I would extrude triangular pyramids up to the singular point.  All pyramid apexes would meet at that same point.

Finally, I would use a Boolean cut feature to create a hemispherical shape that would reveal a similar strut pattern as on the Dome of Visions 3.0.

Hope this helps.

best regards

Robert

[Geodo Mode]

This is a video of my attempt: https://vimeo.com/249220109 but I run into problems in the corners of the dome, how would I fix this?? As Robert stated, you have to distort the equilateral triangles but not quite sure on how to do it. If the equilateral triangles are not distorted you get my corner problem.

[Geodo Mode]

Thanks Ashok!

Though I'm interested on the 3rd version of the dome and on the dome itself, not the different materials.

On Sunday, December 31, 2017 at 6:50:32 AM UTC+1, Ashok Mathur wrote:

Dear Robert,

The first version of the project says that it is based on Bucky Fullerene C60.

That is nothing but a the standard hex-pent obtained by truncating an icosahedron.

"Dome of Visions 1.0 is a 10.5m high and 21m wide dome with a land area of ​​350 square meters. The domain consists of two overlapping geometries. The outer layer consists of 256 thin polycarbonate slabs cut into nine different five and six sides that overlap each other in a disc-stable 850 m2 pattern. The inner layer is made up of 250 kertobells of 3400 mm, which are assembled in a lattice-stable pattern with 91 hubs in steel. The grid grid is a model of a carbon molecule (C60), one of nature's strongest building blocks. Geometry makes the dome stable, and the polycarbonate boards achieve high carrying capacity by tensioning in a curved shape. The plate, the so-called hat, on top of the judgment can handle a load of one and a half tons."

Regards

Ashok

Regards

Ashok

On Sun, Dec 31, 2017 at 9:04 AM, Robert Clark <clark.rob...@gmail.com> wrote:

You're right.  This is not based on a icosahedron, there are no pentagons.  It is a grid pattern of equilateral triangles distorted over the surface of a hemisphere.

I'm not a very experienced SketchUp user, so I would instead be modeling it in SolidWorks.

I would create a sketch of the triangular grid pattern.

Then, I would choose a singular point above the plane that would be in the location of the point source light as seen in the previous image we were discussing.

Next, I would extrude triangular pyramids up to the singular point.  All pyramid apexes would meet at that same point.

Finally, I would use a Boolean cut feature to create a hemispherical shape that would reveal a similar strut pattern as on the Dome of Visions 3.0.

Hope this helps.

best regards

Robert

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[Bryan]

Hi,

your attempt looks close enough to correct. The difference between your B image and their C image is that they have truncated the hemisphere so that the height is less than the radius. You can also see it if you look at the pic on their website that shows the dome from a distance (above the hub pic).
The geometry on the bottom layer is horrible, and truncating is probably the only way to get a reasonable result...

[Bryan]

Here is my attempt. I have inserted hidden edges to create visible planes in otherwise non-planar sections...

[Geodo Mode]

That was my initial though but as you can see in the image it is not true. The triangles form the corner are way more elongated.

[Geodo Mode]

Ohh that's useful info :) !! I tried doing the same method from below the dome but got the same results (obviously), don't really know how to make them curve outward, will keep trying!  Thanks a lot. Here is the skp file if somebody wants to take a look at it. 

On Sunday, December 31, 2017 at 3:51:28 PM UTC+1, Robert Clark wrote:

Looking at your video, I can see where you are having trouble.  Your convergence point is on the wrong side of the hemisphere.  See attached images:

[Geodo Mode]

This was my other attempt using a 6 sided pyramid but was unsuccessful too. Don't really understand how an equilateral triangle geodesic sphere can be achieved. A bit confused.

On Saturday, December 30, 2017 at 9:02:02 PM UTC+1, Geodo Mode wrote:

[Bryan]

The way I did it was, drew my grid plane on the hemisphere. Then used trig to calculate the height of a projected vertex from the grid plane vertex. A bit time consuming but only needed to do 1/6 of the surface and copy / rotate for the rest... Reason why, sketchup is not good at precisely representing arcs / spherical surfaces. So intersecting rays with the spherical surface wouldn't be too exact.

[Geodo Mode]

"So intersecting rays with the spherical surface wouldn't be too exact." Exactly!! I understand what you did but not how you made the calculations, do you have any literature I can read to do what you did? What formulas did you use?

[Geodo Mode]

Understood it fully! Thanks so much, I am sincerely thankful for your help Robert & Bryan :)

On Sunday, December 31, 2017 at 5:24:52 PM UTC+1, Robert Clark wrote:

Map projections are similar to what you are trying to do, except instead of projecting from a curved globe onto a flat sheet, you are doing the reverse and projecting from a flat sheet onto a curved globe.

All points on the flat sheet (a triangular grid pattern) are projected upwards towards a common singular point.  Then, you insert a spherically curved surface somewhere between the flat plane and the singular point.

Intersections of projected lines on the surface of the hemisphere mark your geodesic pattern.

Robert

[Bryan]

Hi,

First off I was wrong about truncation of my (parallel?) projection as their method. Robert is correct and it does look like they used a converging point projection. Attached is a model with 30 degrees from the point to the edge of the hemisphere. I guess you would say 60 degrees field of view??? It really reduces the stretched effect. I think I have one or two more rows...

I succeeded in that by projecting a row of lines in one go. Sketchup creates planes in between each projection and I was able to use the sketchup "intersect faces" function (between the planes and the sphere surface) to get arcs on the surface of the sphere with their end points. Otherwise it can be hit and miss trying to find the intersections. *** Was just playing with it and got the ray intersection every time...

To answer your question about calculating a vertical ray height - assuming unit radius, Cos(ArcSin(distance from origin to vertex)), or Cos(ArcSin(distance from origin to vertex / radius)) * radius.