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Breaking a surface of a Sphere in to Triangles?

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?

You can export it into STL format, but the triangle orientation won't necessarily be predictable.  Adjust the resolution settings to get what you want.

(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?

If you want uniform triangles, you will need to do it manually.  Perhaps use a 3D sketch to place points on he sphere and then connect with lines.

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.

Due to illness, the part of The Tick will be played by... The Tick.
http://www.EsoxRepublic.com

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
I want to be able to create geometry from the trangular surfaces.

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?

One more thought:

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.

Due to illness, the part of The Tick will be played by... The Tick.
http://www.EsoxRepublic.com

RE: Breaking a surface of a Sphere in to Triangles?

Make a single or a double triangular section, and use a circular pattern and other types of patterns to continue the Spherical shape. I hope you follow what I'm after.

Regards,

Scott Baugh, CSWP
http://www.3dvisiontech.com
http://www.scottjbaugh.com

FAQ731-376

RE: Breaking a surface of a Sphere in to Triangles?

I don't know if this will work for you. I did something similar once. I created the sphere and did triangle extrude cuts, with the last sketch showing as reference for the next cut. Each triangle piece was saved as a separate named part. Then all parts brought together as an assy.

RE: Breaking a surface of a Sphere in to Triangles?

That's not a bad idea, wish I would have thought of it!

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?

(OP)
Well I guess that might work for a few triangles, but I need to breack the sphere into 11,520 equal 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?

penguin221,

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?

(OP)
I gotcha ya.

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?

It's a tough one. Ask a civil engineer or an architect. They may have an idea.

RE: Breaking a surface of a Sphere in to Triangles?

If its a geodesic sphere, you would have at least two sizes of triangles. Both their bases would be the same length but there would be two different heights. The shorter ones would make a hexagon with all vertices on the sphere.  The taller ones would make pentagons with all vertices on the sphere.  Take a look at a soccer ball and imagine dividing up the hex's and pent's into 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?

(OP)
A geodesic dome is what I am going for.

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?

Penguin221,

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?

Whell, I don't know if this work but...
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?

(OP)
macPT

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?

penguin,

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?

(OP)
Creigbm,

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?

very nice. How was the dome created in the pics? Looks like helix sweep/cut...or something else?

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
That was actually done in another piece of software that gives you the ability to create a geosphere.  Then you just create a pyramid on top of each triangle.

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?

Let me get this straight.  you really want a geodesic sphere?  So you do not want a sphere cut into triangles.  You actually want a spherical looking thing made up of flat pieces - over 11k pieces.  (Are you some kind of masochist? - just kidding.)

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?

A geodesic sphere consists of 20 hexagons and 12 pentagons.  Each pentagon is surrounded by 5 hexagons.  Both will have the same length per side.  Mate these together and the sphere will form itself.  You can then correlate the sphere radius to the lenght of each side.

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?

NHPilot
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?

from (the City of) Barrie, Ontario.

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

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
After all the suggestions, I have still not been able come even close to any of this.  Maybe SW can add a geosphere feature to a next generation release.

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?

It is ... how many people do you know that want to draw a Geodesic sphere? If there was a big demand for it SW would add it in. Remember SW is basically geared toward mechanical engineering ... not civil or architectural.

from (the City of) Barrie, Ontario.

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

RE: Breaking a surface of a Sphere in to Triangles?

SW is good. There is probably a way to do it. Just need to figure out the method. One of us will eventually get it. Don't give up.

RE: Breaking a surface of a Sphere in to Triangles?

Yes, I saw an overcontraint originally in SolidWorks 2001Plus.  As you start mating tiles, only the first one will be fixed.  All others should be underconstrained so as to 'find their own' place.  The parts do have to be placed relatively close to were they will end up or SolidWorks starts to flip things around unexpectedly.  Spheres like this came up a while ago as a question to which I sent in only one of many solutions, some time back in SolidDigital digest magazine.
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?

NHPilot
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.

from (the City of) Barrie, Ontario.

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

RE: Breaking a surface of a Sphere in to Triangles?

I have a model of a Geo Sphere I down loaded from some were probable solidworks library I can’t remember exactly
 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?

(OP)
I found this site that has a dodecahedron and an icosahedron.

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?

manxJim
Yes please ... email address is in my profile. Thanks.

from (the City of) Barrie, Ontario.

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

RE: Breaking a surface of a Sphere in to Triangles?

@ CorBlimeyLimey
you got Mail

RE: Breaking a surface of a Sphere in to Triangles?

NHPilot
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.

from (the City of) Barrie, Ontario.

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

RE: Breaking a surface of a Sphere in to Triangles?

Penguin221
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?

(OP)
NHpilot and manxJim

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?

penguin221,

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?

CorBlimeylimey,

'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?

(OP)
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
www.silganplastics.com

RE: Breaking a surface of a Sphere in to Triangles?

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?

RE: Breaking a surface of a Sphere in to Triangles?

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

Quote (CBL):

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

RE: Breaking a surface of a Sphere in to Triangles?

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?

RE: Breaking a surface of a Sphere in to Triangles?

I'm fine with that.

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
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
www.silganplastics.com

RE: Breaking a surface of a Sphere in to Triangles?

Penguin221,
You are correct.  

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
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
www.silganplastics.com

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
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
www.silganplastics.com

RE: Breaking a surface of a Sphere in to Triangles?

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?

RE: Breaking a surface of a Sphere in to Triangles?

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?

RE: Breaking a surface of a Sphere in to Triangles?

(OP)
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
www.silganplastics.com

RE: Breaking a surface of a Sphere in to Triangles?

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?

RE: Breaking a surface of a Sphere in to Triangles?

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.

RE: Breaking a surface of a Sphere in to Triangles?

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

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