Breaking a surface of a Sphere in to Triangles?
Breaking a surface of a Sphere in to Triangles?
(OP)
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
www.silganplastics.com






RE: Breaking a surface of a Sphere in to Triangles?
(Not sure if you can bring it back in to SW without another program to convert to parasolid or IGES.)
Jeff Mowry
Industrial Designhaus, LLC
http://www.industrialdesignhaus.com
RE: Breaking a surface of a Sphere in to Triangles?
Exporting as an STL will break the surface into triangular facets, though you won't have much control over the shape of the facets.
One possibility is to use an FEA mesher, perhaps from COSMOSWorks. You could at least get node positions and triangular elements. I'm not sure how to translate a mesh back into geometry, though.
http://www.EsoxRepublic.com
RE: Breaking a surface of a Sphere in to Triangles?
STL will not work for this application.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
Don't try to do the whole sphere. Do a sector of the sphere, perhaps 10°-15° of longitude in width. Also, perhaps separate that sector so that you can mesh the triangular tip separately, as well as other "rectangular" sectins in the middle.
http://www.EsoxRepublic.com
RE: Breaking a surface of a Sphere in to Triangles?
Regards,
Scott Baugh, CSWP

http://www.3dvisiontech.com
http://www.scottjbaugh.com
FAQ731-376
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
To add to that - Then once the assembly is made, you can save the assembly as a part and be back where you started... kind of.
Regards,
Scott Baugh, CSWP

http://www.3dvisiontech.com
http://www.scottjbaugh.com
FAQ731-376
RE: Breaking a surface of a Sphere in to Triangles?
Don't think I want to create 11,520 cuts or assemble 11,520 parts.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
If these triangular elements are the same then you'd need only one part. Make a subassembly with an appropriate pattern of these elements. This doesn't have to create the whole "sphere" in one fell swoop. You can then make an assembly of this subassembly. It might go a lot faster than you think, especially if you locate the part and the subassemblies using patterns instead of mates.
- - -Dennyd
RE: Breaking a surface of a Sphere in to Triangles?
Now how the heck do you pattern a feature or part that is a triangle and get a sphere or part of a sphere?
I guess that is my dilema. I can't get trianlges to pattern well because there really is no symmetry to the final product. All the edges of the triangles create odd angles. I don't believe you can create a section of the sphere either, you will have to do it all at once.
I guess I am just lost and need to work at it some more.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
There were a few examples of this in an issue of solid digital digest, maybe last year?
You could also use just pentagons and make a dodecahedron. There are actually many ways to divide up a sphere.
Do a google search for geodesic.
RE: Breaking a surface of a Sphere in to Triangles?
What I am actually going for is to model the Spaceship Earth Sphere from Disney's EPCOT. I am modeling EPCOT in SW as a hobby and training.
I finished the monorail and now I am stuck on this geosphere. I am still searching for ideas. If anyone has any other ideas please let me know. It would be appreciated.
Thanks for everyone's help and input.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
Do you have your models posted anywhere on the web? I would like to see your work.
RE: Breaking a surface of a Sphere in to Triangles?
Check here
http://img6.photobucket.com/albums/v16/penguin/monorail/monorail2.jpg
http://img6.photobucket.com/albums/v16/penguin/monorail/monorail1.jpg
Let me know what you think.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
1 - imagine a sphere surface with center C and radius R
2 - imagine 3 lines L1, L2 and L3 intersecting in C
3 - each line define a point when intersecting the surface, that is all lines have length R from a given point C
4 - the angle between L1 and L2 should be equal to the angle between L2 and L3 and between L1 and L3
5 - the angle should be such that (360/angle)=integer
6 - the 3 points in the end of the lines define a planar triangular surface, which is a "segment" of a sphere
7 - do circular patherns of this surface around C
Can this work? I will give it a try!
Good Luck
RE: Breaking a surface of a Sphere in to Triangles?
http://www.grunch.net/synergetics/domes/domegeo.html
RE: Breaking a surface of a Sphere in to Triangles?
I haven't quite understood your line of thought yet, but will try to figure it out and see if it works.
Thanks
swcadman
I have been to that site. The problem I am hving the most trouble with is creating what I need in SW. I think I pretty much have the whole understanding of how a geosphere is designed and works, I just can't figure out how to create it in SW.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
Thats pretty cool, I wish I had some time to play around with that. Keep us posted!!
RE: Breaking a surface of a Sphere in to Triangles?
I will keep you posted, although right now I just got involved in a new project.
Check this out www.deepwaterstudios.com and click on the Epcot model.
We are going to model Ecpot and turn it into a virtual reality walkthrough.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
We have actually created the sphere in a few different pieces of software. I am just on a mission to try and do it in SW for my own little home project.
I beleive Jason did all those models in the Pic in Maya.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
If you do a google search you will find a site that gives formulae to calculate the sizes for goedomes. (Been there a couple of years back but can't remember the ULR - it's mostly "fascinating" trivia by some guy with a geodome fetish. However I noticed that he is not a millionare yet.) Anyway it gives the lengths for the side members of the patches based on the sphere diameter and number of faces or some such. I am sure you could convert it to what you want. I used it to essentially do the same thing, but I was not as adventurous as you are (many times less patches). Also bear in mind he is making domes, not spheres, so he ends up with odd partial patches at the hemispherical edge that you will not need.
Also, if you look carefully at the patterns of pieces, you will find you can make a limited number ot subassemblies (possibly only two) and use some creative circular patterns in horizontal bands of the assembly.
John Richards Sr. Mech. Engr.
Rockwell Collins Flight Dynamics
There's no place like 127.0.0.1
RE: Breaking a surface of a Sphere in to Triangles?
If you then take each hexagon and divide it into 6 equal triangles, and divide each pentagon into 5 equal triangles, you now have 720 peices total. The two long legs of each new triangle will be equal, but longer than the original side so that the vertex will fall on the sphere surface.
If each triangle is now divided into 4 equal triangles, this yields 2,880 pieces. Again, the common vertex should fall on the sphere surface.
Take it yet another step and this will yield 11,520 pieces.
Does this make any sense? Once you understand it, you'll find its much easier to do than it is to explain.
Good luck
RE: Breaking a surface of a Sphere in to Triangles?
Close ... but no cigars. I just tried your method using unity as the side length of Pentagon & Hexagon, but could not get the 5th Hex to mate.
Have you succesfully tried this?
RE: Breaking a surface of a Sphere in to Triangles?
I thought SW was good.
:)
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
Incidently, I designed a few of these, the first of which was done in Autocad in 3D wireframe. They have been used as integrating spheres from (20 inch diameter to 3 Meter diameter) to measure light output of large lamps.
RE: Breaking a surface of a Sphere in to Triangles?
Do you have a Pentagon with 5 Hexagons modeled (or sketched) & mated? If so would you please send it to the email in my profile. I would like to see what I am doing wrong! Thanks.
RE: Breaking a surface of a Sphere in to Triangles?
It’s not a big model I could email it to anyone that’s interested
RE: Breaking a surface of a Sphere in to Triangles?
I am trying to make these work.
http://www.zxys.com/swparts/
I am not giving up. I am on a mission.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
Yes please ... email address is in my profile. Thanks.
RE: Breaking a surface of a Sphere in to Triangles?
you got Mail
RE: Breaking a surface of a Sphere in to Triangles?
Thanks for the models ... I see you had the same problem that I did with the mates ... it should work with all sides being Coincident ... but it doesn't. Could be a SW bug/limitation caused by approximations. If you zoom in extremely close, you can see that edges/sketch lines/poiints do not actually coincide.
manxJim
Thanks also for the GeoSphere ... Great model, someone has put a lot of thought & effort into it. I look forward to disecting it.
Penguin221
You should get & disect these models from NHpilot & especially manxJim.
They should answer your original question.
RE: Breaking a surface of a Sphere in to Triangles?
When you get it worked out to your liking,
please let us know. I would like to see your final config.
Good luck. In my spare time, I am also trying to work it out...just to see if I can.
RE: Breaking a surface of a Sphere in to Triangles?
Would you both mind emailing me your files?
Please make sure they are zipped, because our sever may delete them if they are not zipped.
My email address is
s.getsy@silganplastics.com
Thanks.
Stephen Getsy
Product Development Engineer
Silgan Plastics
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
I just checked out that website and got more and more interested the more I read along. Is it too late to be a part of the design work? How to get involved?
Thanks,
Brian
RE: Breaking a surface of a Sphere in to Triangles?
'Thanks for the models ... I see you had the same problem that I did with the mates ... it should work with all sides being Coincident ... but it doesn't. Could be a SW bug/limitation caused by approximations. If you zoom in extremely close, you can see that edges/sketch lines/poiints do not actually coincide.'
I'm not sure what problems you mean. Do you have mate errors when you open my model? Are the parts not fully constrained?
Also, as far in as I can zoom, everything looks fine. Might you be seeing a video glitch?
RE: Breaking a surface of a Sphere in to Triangles?
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
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
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.
RE: Breaking a surface of a Sphere in to Triangles?
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
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
Regards,
Scott Baugh, CSWP

http://www.3dvisiontech.com
http://www.scottjbaugh.com
FAQ731-376
RE: Breaking a surface of a Sphere in to Triangles?
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
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
You are correct.
RE: Breaking a surface of a Sphere in to Triangles?
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
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
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
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
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?
RE: Breaking a surface of a Sphere in to Triangles?
RE: Breaking a surface of a Sphere in to Triangles?
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
www.silganplastics.com
RE: Breaking a surface of a Sphere in to Triangles?
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.
RE: Breaking a surface of a Sphere in to Triangles?
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.
RE: Breaking a surface of a Sphere in to Triangles?
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