Generating a 2D irregular polygon for a geodesic floor plan


#1

I am building a geodesic dome which has a 2D floor plan of a 15 sided irregular polygon. All of the sides are chords or segments whose end points lie on a circle with a radius of 17’ 7/34". Five of the chords are 6’ 11 3/16", and 10 of the chords are 7’ 7 3/4". I can generate a polygon with the correct radius, but not an irregular polygon. Do I need to construct it piecemeal moving and rotating each chord into place (I’ve done this and it is neither pretty nor elegant) or is there a function somewhere to generate the shape?

And is there a plugin available to generate a geodesic sphere?

Thanks.


#2

Is there any required sequence? May the two lengths be segregated? May they be intermingled?

I don’t know of any geodesic plugins, but you can’t go another day without perusing the models of TaffGoch. Take a look and become geodesicated.

-Gully


#3

Yes, the sequence is 2 long, 1 short, 2 long, 1 short, etc.

I am a little familiar with the TaffGoch models, but will continue exploring them.

Thank you.


#4

Given you know the length of all three sides of the two triangles; Didier Bur’s [Trilateration Plugin][1] will draw the two necessary triangles.

A radial array of the triangles in the sequence you described should produce the 15-sided polygon.
Unfortunately the dimensions you provided don’t quite work.
As shown in the attached model, the sum of the angles is ~363.5°
15-Sided Irregular Polygon.skp (55.8 KB)
[1]: http://sketchucation.com/pluginstore?pln=trilateration


#5

Build a pentagon with sides equal to 6’ 11 3/16", (83.1875)

the radius would be = side / sin(arc) /2
=83.1875 / sin (36) /2
=70.76351412

then consider rectangles perpendicular to sides of the hexagon, they are @ 72 degs, divide equal at the point of the hexagon. 36 degs,
we can form a triangle with angles 36, 62, 82, by forming the shapes within a larger circle which in includes the added rectangles. As the known side of the polygon is 7’ 7 3/4" (91.75)

using the sine rule: then 91.75/sin(36)=x/sin(82) there x = 154.5753231 which is the required size of the rectangles
Draw a circle to enclose the rectangles, divide and should be able to produce the other sides

(edit previous assumption in regards to radius was incorrect)


#6

Realize made mistakes in this discourse, although the 72 degs, is true the complement angles to 36 vary so need to gives this some more thinking


#7

How did you develop the dimensions you’re working with?
Were you provided a formula or the angles? Sharing that would help us help you.
Working in four-place decimal inches vs. feet, inches & fractions will improve the accuracy of those calculations.


#8

Hi,
I needed to satisfy my perceived challenge in figuring this out, so I built a dynamic component (a way of creating many variances with auto-drawing) So thus you can change the variables as you desire to achieve the best out come.

Options for the dynamic can be accessed either by the toolbar if you have it shown or right clicking the object (context menu) choose Dynamic, then options.

you can enter feet, inches with fractions, however the user- form changes it to decimal. There are two variables, the length of the first polygon side, then you can adjust the length of the inserted second side to achieve the required divided edge.

poly_maker.skp (105.7 KB)

I must admit I am interested in following up on geodesic domes
cheers
Philip


#9

Yes I find it very interesting too!
I really need to learn making DC’s. !!

Maybe somebody will have a go making DC with this approach:
Can be varied after whatever number of sections and so on.

You just need radius and one side to make the rest.


And you can work the otherway around starting with L1
Cheers


#10

Hi K,

Solution in DC as per your method

poly_maker_Radius.skp (59.6 KB)


#11

I went back to my original info and noticed that the radius is given as 17’
7 13/16".
There is a 1/16" inch difference from what I originally posted.

Geo, to answer your question, I am constructing a dome supplied by Natural
Spaces Domes http://www.naturalspacesdomes.com/ out of MN.

Since I am using this info to make a floor plan, I suppose I don’t need to
carry it out to 4 decimals, although I can certainly see why that is
important to the construction of the struts. But that will be done for
me. Geodesic construction is more exacting and less forgiving than
standard box framing, which typically can be pretty sloppy. I did make a
dome back in the early 70s with parts I cut myself. I took on faith that
the info I got from The Dome Book was accurate, and when I began putting it
together I was nervous that it might be wrong. Fortunately, it fit
together nicely and was very sturdy.


#12

Correcting the .0625” error didn’t do much in terms of fixing the problem.
The dimensions you’ve given still don’t work.
As shown again in the attached model, the sum of the angles remains ~363.5°

15-Sided Irregular Polygon Redux.skp (71.1 KB)


#13

A thousand pardons. I read the small print by dim light. Try this: 17" 9
3/4"

I’ll bet that makes a difference.


#14

I constructed the two triangles using that new radius.
A radial array of the triangles in the sequence you described gets closer to creating a full circle…
…but not quite.


#15

And if the radius is changed to* 17’ 9 13/16"*? I sent this figure last
night, but it came back to me because the email was too short.


#16

Attempting to construct the polygon from fractional dimensions found on an ordinary red plastic ruler doesn’t foster accuracy or confidence.
I wouldn’t know offhand how to calculate the length of all the parts of a geodesic dome.
Nonetheless, I’m quite certain the lengths of all the parts are inexorably interrelated.
Obviously, if one dimension is changed, then all the others must change as well.

Let’s guess and say this radius you’re not quite certain of is the controlling dimension from which all others are derived. How do you intend to develop the length of all the other parts?
In the absence of the math behind the dome, you simply cannot draw a truly accurate footprint.


Here’s the result of your latest dimensions.
The given dimensions still fail to to describe triangles that when arrayed complete a 360° circle.

15-Sided Irregular Polygon Using Given Fractional Values.skp (68.0 KB)


Here’s a guess based upon the given radius while allowing the cord lengths to float.
Click … Window > Model Info > Units
If you change the Units to Architectural with 1/16" precision it agrees with the lengths you provided.
Understand, those are approximations, rounded to the 1/16"

The true lengths of the geometry are not the decimal equivalents of the given fractions.
Thus the Architectural dimensions with 1/16" precision are misleading.
One might call call them fools dimensions.

15-Sided Irregular Polygon Guesswork.skp (66.1 KB)


Perhaps one of these will help:
Dome CalculatorsDomerama.com


#17

There was a free plugin that made simple geodesics or Archimedian solids, I can’t remember which. I had it installed 5 years ago, but never used it. I took it out, and I can’t remember the maker or exact name.

You can google Archimedian solid angles (all side lengths will be equal) and construct a sphere, but it’s tough to locate the points in 3d space. Especially when it gets to breaking down the original solid to a second or third order structure, where everything gets kerflooey as you adjust strut lengths to maintain the optimally strong spherical placement of the vertices.

Sketchup itself will do you no favors here. It doesn’t draw circles, it draws polygons, and you’ll be working with polygons that are very irregular and difficult to predict, depending on where you slice the dome. You can’t scribe two arcs to locate a point on a plane, or make three spheres to locate a point in space accurately. To work around this, you’ll first have to draw a line at the proper 3d angle from origin, then go out the proper distance from each line. Why? Because you’ll never know if your two circles intersect at a vertex (farther) or midpoint (closer) of a side until you draw them. Spherically, it’s even tougher, and I"m not even sure it’s possible to get accuracy by intersecting SU’s “spheres”.

Everything you draw will be limited by the accuracy of your original angles, and they won’t be easy whole numbers, or particularly easy to figure out. And in 3d space, there are two of them for every point. It’s a lot of cumbersome, in other words.

I’m sure there is a workaround, but you have to get pretty deep into it to figure it out. Maybe go into pure math to generate the points, then draw them in SU.


#18

See the topic titled Domebook 2 at TaffGoch’s Geodesic Help Group

Taff’s Geodesic Collection — 3D Warehouse


#19

Hi @pcmoor, Thanks a lot for your example!

Will study.
Cheers