Breaking a surface of a Sphere in to Triangles? 1

[penguin221]

Does anyone know how I can take the surface of a sphere and make it into triangles? An example would be the Spaceship Earth Globe at Disney's EPCOT.



Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[penguin221]

Creigbm,

Nope it is never too late to get involved. Just go to the site and Register for a login. It is free. Then just log in in and join the Forum discussions. We are in the early phase of getting started. Read all the posts to get up to speed a little and join in.

We would be glad to have your help and anyone else that is interested.

Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[CorBlimeyLimey]

NHPilot
No, your model was fully constrained & had no problems. I was referring to the fact that you did not/could not use edge coincident mates all around (which you should be able to) & had to resort to a parallel one in one instance. As you mentioned before, you get an over-constrained situation if you do use edge mates all around.

It might well be a video glitch on this machine ... I will check tonight on my home computer ... but if you zoom in really REALLY close on a vertex you will/may see that the edges of the Hexagons & Pentagons do not exactly align. It is probably way less than .00000000" but nevertheless is a mismatch & may be enough to stop the final coincident mate.

from (the City of) Barrie, Ontario.

If you choke a smurf, what color does it turn?

 

[SBaugh]

I know I don't have the file to look at, but from what I read...

I was referring to the fact that you did not/could not use edge coincident mates all around (which you should be able to) & had to resort to a parallel one in one instance. As you mentioned before, you get an over-constrained situation if you do use edge mates all around.

Why don't you use the (under the mate property manager) in the "Options" Property of the mate, Click "Use for Positioning Only". This will put the part parallel, but will not put an actual Mate in.

Regards,

Scott Baugh, CSWP

http://www.3dvisiontech.com

http://www.scottjbaugh.com

faq731-376

 

[CorBlimeyLimey]

Thanks Scott, I will try that to see what happens. The way NHPilot had mated the facets worked fine, but me being me, tried experimenting to see if it could be done my way, so that I could understand it better ... but it didn't work my way!!! (I still think it should though). If you have time, & if NHPilot does not mind, I will send you the model to look at. Is that OK with both of you?

from (the City of) Barrie, Ontario.

If you choke a smurf, what color does it turn?

 

[NHPilot]

I'm fine with that.

 

[SBaugh]

That's fine with me too.

Regards,

Scott Baugh, CSWP

http://www.3dvisiontech.com

http://www.scottjbaugh.com

faq731-376

 

[penguin221]

Ok I have a question. I am getting close to figuring this out, but I am making an assumtion that may or may not be correct.

On a geosphere or any other geometric sphere, would all of the nodes lie on the suface of the sphere and be equal distant form the center ( equal to the radius of the sphere)?

Do you understand what I am asking or did I just confuse everyone?

Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[NHPilot]

Penguin221,
You are correct.

 

[penguin221]

Ok. I beleive I finally figured out at least one way to do this. I say that because once you figure out how to do something, the alternate solutions and simplifications usually come easy.

However, I have one piece of information I need to find so I can finish and post the results.

I hope someone can help or I can find what I am looking for.

Here is what I need.

12 pentagons make up a sphere. Now take one of those pentagons out of the sphere and brake it up in to 5 triangles. What I need is the calculation to determinr the arc length of the one leg of the triangle that runs from the center of the pentagon to one of its nodes.

The triangle would not be flat but a portion of the sphere curve. That is why I need the arc length, or anything that I can use to determine the size of the triangle.

Did I confuse everyone?

Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[penguin221]

Yippiddy diggidy dog. I do beleive I've got it. I have figured it out. I have one minor flaw that needs to be fixed, but the principal and design is done. I know of a couple other ways to do the same thing, but in principle it is done. Now I will spend my time refining and simplifing.
If anyone would like the SW files I would be gald to email them.

Check here for a quick rendering.

http://img6.photobucket.com/albums/v16/penguin/monorail/geosphere.jpg

Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[ctopher]

Very nice. Yes I would like a copy, please.
Just curious, the actual sphere at Epcot, doesn't it have the triangles projecting as pyramids? If they do, re you going to try to model them?

 

[CorBlimeyLimey]

Sure, we've come this far with you ... might as well see the end result. Address is in my profile. Thanks.

from (the City of) Barrie, Ontario.

If you choke a smurf, what color does it turn?

 

[penguin221]

ctopher,

Yes it does and yes I am. I figured that once I got the base done I could figure out and implement the pyramids.

I will eventually have a replica.

Stephen Getsy
Product Development Engineer
Silgan Plastics

http://www.silganplastics.com

 

[CorBlimeyLimey]

SBaugh
I have tried to send you the file but it keeps being returned as "Undeliverable".
I am using the "credence@" address ... is that still valid?
If you send an email to my address, I will do a "reply" & attach the file to it.

from (the City of) Barrie, Ontario.

If you choke a smurf, what color does it turn?

 

[Istre]

I've recently undertaken the geodesic sphere just to keep up with my SolidWorks skills. I did a geodesic based off of an icosohedron (20 sided regular solid made of equilateral triangles). Each of the 20 triangles is further subdivided by drawing lines parallel to the sides so that there are 9 smaller equilateral triangles spanning each side of the 20 larger triangles. This translates into 1620 base triangles just to mesh the icosohedron.

Now, you construct the geodesic by drawing the circumscribed sphere of the icosohedron, then shooting lines from the center of the sphere, through each intersection in the icosohedron, ending on the sphere. The points where the shot lines intersect the sphere are connected to construct the actual triangles used to build the geodesic, and are definitely NOT similar. The one I built required 26 different triangles to get the geometry right. If you want to facet the geodesic, you will be looking at 4 times the triangles to construct the pyramid features, so on my model, I have about 8100 total triangles between the base solid and the final geodesic.

Since the geodesic is based off of a repeating pattern built on the faces of a solid, the easiest way I've found to accomplish this is to construct the required base triangles of the geodesic, use those to build one section of the geodesic corresponding to one face of the icosohedron, then save as an assembly and build a second assembly out of the 20 repeating patterns to complete the sphere.

I did this today and it took me about 6 hours to get through it all. Of course, I practiced on a 5 frequency geodesic last week before tackling the 9 frequency. Also, expect your machine to cry. The mates alone brought my machine to a crawl, and I'm running a dual hyperthreaded Xeon workstation at 3.2 GHz, 2 GB RAM, and a FireGL X1 AGP Pro display adapter. This model is a monster, but it's pretty cool to look at when you finish.

 

[cpretty]

Hi guys,

I have managed to acheive it using the icosohedron method. I modelled a single triangle of the icosohedron as a part, then assembled these to form the actual icosohedron.

I then did a bit of surfacing to create a spherecal surface, and checked that this translated into the assembly OK. Well I got a perfect sphere.

I then divided the triangle into multiple equally sized smaller triangles. This is where things get repetitive.

Using an axis through the centre of radius, and each point, I was able to 'project' each vertex of the triangle onto the surface. Each set of 3 points then defined a plane, in which a sketch could be created of the triangle to define the surface. These surfaces then can be knitted with side surfaces and the bottom triangle to form a solid.

The model I have created is quite compact actually (1.7 second rebuild on segment on P4 1500). The part and assembly totals 1.5Mb. The assembly itself doesn't slow down the machine at all.

I also created the pyramids on the surface, by using the same sketches as for the surfaces, qhich were then extruded with large draft (70 deg). I don't think I have enough surfaces, but as I don't particularly care about an exact model, but the method for doing it, I am happy.

I have emailed the files to penguin221 as I don't have a facility at present to post on the internet, or send them out to large numbers of people.

Cheers for the Challenge
Craig