Geodesic domes

[livelonger]

I am looking for a program that calculates oval domes rather than
round domes. I have used the desertdome calculator for the round
domes and it works very well. But I canot find a similar calcluator
for oval ones. Any help out there>

[Dick Fischbeck]

What kind of dome do you need?

Can't help with the calculator question.

[TaffGoch]

Usually, more-specialized programming is required, however, SketchUp can "stretch" a spherical dome into an ellipsoid.

 

I use SketchUp's "scale" tool to increase the size of a dome along one axis only. The attached image shows example results. (I've also attached an example SketchUp model file. I increased the scale along the green axis only, by 1.333)

 

I'm sure there must be some program available online (somewhere?) but I use SketchUp because of it's ease-of-use and immediate visual results. (Sort of like a word processor or spreadsheet - you can do a lot of "what if" editing.)

 

Taff

[Adrian Rossiter]

Hi

Carmen Laski asked about this on the geodesic list last year.
She might be worth getting in touch with. Here is her web page

http://www.laski.com/html/carmen_laski.htm

I have included the reply I sent below.

After scaling the spherical dome into an ellipsoid there
is quite a variation in strut length so an extra step to
equalise strut lengths on the ellipsoid might be useful.

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

Hi Carmen

On Thu, 2 Oct 2008, Carmen Laski wrote:
> 360 triangles each. I would like to build an oval dome but cannot find
> the geodesic formulas to build the triangles. I saw these formulas
> about 2 years ago on the net but cannt find them anywhere. Any help
> out there with this?

You could calculate the lengths and angles with the Antiprism
programs.

http://www.antiprism.com/

Here is an example showing how you would do it.

Generate an F3 icosahedral geodesic sphere and scale it by 2
along the x-axis to make an oval base

geodesic 3 | off_trans -S 2,1,1 > oval_dome.off

You need to see the vertex numbers so open it in Antiprism's
antiview program like this

antiview -n v oval_dome.off

Alternatively make a VRML model to show the vertex numbers

off2vrml -n oval_dome.off > oval_dome.wrl

Here is the model of the geodesic ellipsoid with numbered
vertices

http://www.antiprism.com/misc/oval_dome.wrl

A base triangle runs between vertices 81, 80, and 12. Get the
strut lengths like this

off_query -e 81,80,80,12,12,81 Evl oval_dome.off

The output is

E0,81 80,1.4272883590923595
E1,80 12,0.7384708168734635
E2,12 81,0.73847081687346305

To find the mitre angles you first need to add a point
at the centre of the model. The joint "axes" will pass
through this point.

echo "0,0,0" | off_util > centre_point.off
off_util -o oval_dome.off oval_dome.off centre_point.off

Find how many vertices are in the model

off_report oval_dome.off

One less than this is the index of the centre point, in this
case 92.

To work out the angles of strut 20,12 at the end 12. First
find the joint axis angle at 12 (along 20,12,92)

To work out the angles of strut 20,12 at the end 12. First
find the joint axis angle at 12 (along 20,12,92)

off_query -f 20,12,92 Fa oval_dome.off

This gives the angles of the triangle 20,12,92 and the
angle at 12 is the second value, around 83 degrees

E0,58.553885026443339 82.925065091715098 38.521049881841577

It should be possible to find the mitre angles to cut at each
side of the joint axis by querying for the two dihedral angles
each side of the plane through the strut and joint axis, like
this

off_query -f 80,12,92 -f 0,12,92 -e 12,92 Ea oval_dome.off

Unfortunately, this doesn't work! There is a bug relating
to the reporting of dihedral angles when extra elements are
added using -e or -f. I will fix this.

However, if you think you would like to calculate your dome
like this I could write a short program that would produce
a list of the joint axis angles and the mitre angles at
each vertex of the dome. I think will write some code to do
this anyway as I imagine it may be of more general interest.

If you wanted extra vertices for the base, for example
between vertices 12 and 13 to split the wide triangle
12,81,80, you would have to add them by hand to the
off file produced by 'geodesic'. Then project onto
a sphere with 'off_util -S', and then scale as before
e.g 'off_trans -S 2,1,1'

[TaffGoch]

On Sat, Sep 5, 2009 at 5:37 AM, Adrian Rossiter <adr...@antiprism.com> wrote:

After scaling the spherical dome into an ellipsoid there
is quite a variation in strut length so an extra step to
equalise strut lengths on the ellipsoid might be useful.

That's the one thing I dislike about axis-scaling.

 

Does antiprism provide any capability for such equalizing on the surface of an ellipsoid.

(I use java applets for equalizing on a sphere, but haven't one for ellipsoids.)

 

I'd love to equalize on the surface of superellipsoids, too, but that's pretty specialized (I'd think.)

 

Taff

[Adrian Rossiter]

Hi Taff

Antiprism currently only supports equalising on a sphere (or
edges in free space.)

The method I use is very basic. I just move a vertex towards
(or away from) its neighbour in a straight line, and then
project back onto the sphere surface along a straight line
with the origin.

However, this also easily works with an ellipsoid or
superellipsoid so I have added this in to the minmax program.
It will be available next time I make a snapshot release.
The program option takes four floating point numbers, the
first three for the axis lengths and the last one is the power.

Here is a test Class III 4,3 octahedron on a 2x1x1 power 3
superellipsoid

http://www.antiprism.com/misc/sup_ellipse_o34.jpg
http://www.antiprism.com/misc/sup_ellipse_o34.wrl

You can see that the edges are an improvement on a
simple projection, but with four triangles around a square
there is only so much that can be done to equalise on a
single edge length. Also, the octahedron vertices have
wandered.

[TaffGoch]

I certainly didn't anticipate you editing the feature set, based simply on my earlier comment.

 

Nice enhancement! 

 

Looking forward to the snapshot release. 

 

[Adrian Rossiter]

Hi Taff

On Sun, 6 Sep 2009, TaffGoch wrote:
> I certainly didn't anticipate you editing the feature set, based simply on
> my earlier comment.

I was going to add in ellipsoids, but superellipsoid don't really
require any extra code (just a couple of lines for reading in the
final power argument) so I thought I might as well add them in
too.

Adrian

[Gerry in Quebec]

Dear livelonger,
CADRE Geo 6.0 will generate images and data tables for all kinds of
ellipsoids. This includes not only oblate and prolate spheroids
(squashed or elongated figures with a circular base), but also
ellipsoids in which both the dome's profile and its footprint are
elliptical. The only problem with such "double ellipsoids" (I don't
know the technical term), is that just about every strut in the dome
has a different length. I think the producer of this software, CADRE
Analytic, has a demo version you can download free. Here's the site:
www.cadreanalytic.com.
Good luck.
Gerry in Quebec