How do you create mathematical models?

I made another video of the creation of this object in Blender 2.74, with audio narration for you. You can find the video on my Youtube channel here:

https://youtu.be/_RQ3oCliF68

This contains the entire process form start to finish, with audio. Hope you can follow along much easier. If you have any questions, please let me know.

Hey Hey!

Following the tutorial as I write.

Attached is Before and After the update.

The update makes it SOOOO much easier
to get it right.

Not finished yet, but, I'm probably better than
two thirds along the way.

Looks really good.

I think they both have their aestetics.

But yours is CONSIDERABLY smaller.

The Render to go with it.

Thanx

(I posted an update at Blender Artists so you'll get credit there
as well.

http://blenderartists.org/forum/showthread.php?369241-Rotate -Edge-Loops-Think-Spaghetti-on-a-fork

Very nice.)

Mostly the same process applies to a truncated icosahedron as well.

See the attached file.

The blend is too big to upload.

Uploaded pic instead.

Have fun.

P.S. I've added the Blend file, annotated, with MOST of the work done. It's ready for the
Bevel point in the process.

Small enough to upload. That should give you an idea of how it works, what it looks like.

And I've updated this to reflect that it's a "truncated icosahedron" - under the Custom Menu
NOT the Icosahedron - my apologies.

Just added image - completed, using luxxeon's method:

They look great! Love the detail on that last one. Be careful of crossing edges on those more detailed types though. Not sure if that would impact the result of printing or not. Probably wouldn't, but never know. Do an STL check first to be sure.

Just want it to be clear. The credit is yours, luxxeon.

I just wanted to see if it was possible to do with another
shape.

Took FOREVER to select all those little nooks and crannies
before the last inset. No "similar" selection seemed to work.

As it is, the finished product is 37.5 MB. (STL)

Also, ran it through Netfabb (Basic) and uploaded it to
Shapeways. Passed all the tests. At 45mm it prices
at about $ 15,00. Not bad.

Could probably pare that down by decreasing the size in
the solidify step.

That would've meant a boat load of rework given the
time it took to wrap it up the first time around.

Also wondering, luxxeon, why not Alt-P after the subdivide?

Looks like it gets you to the same point as the first inset
without the extra effort of reducing to zero.

Other than that, having done it twice now, I think we've
well covered proof of concept.

Again, thanx.

Everywhere I bring this up, I try to give credit where it's
due. It's due to you.

Just for "fun" I may pick another, less complex polyhedron
and see if it works. I would think it should. If I have any success,
I'll share it here.

Also wondering, luxxeon, why not Alt-P after the subdivide

Good question. ALT-P, or the "poke" tool, is something I had completely forgot about in the Blender toolset at the time of the tutorial. It seems that it would fit that particular task well, and you can use it as a quicker means to achieve the topology.

In addition, you could also skip the step of doing an inset by region on the border polygons between each star "arm", after adding the solidify modifier. The solidify mod in Blender has it's own "edge hardening" or crease options built into it, so creating additional support edges with inset aren't actually necessary.

On Stellation / Antistellation:

Antistellate Polygons (Blender / Openscad / TopMod)
http://blenderartists.org/forum/showthread.php?372547-antist ellate-polygons&highlight=antistellate

An example of what can be done using these methods (Blender file 0 attached)

RID = Rhombicosidodecahedron

Unkerjay, were you ever able to print the star ball? Were there errors or any problems with the stl check or print inspection?

The attached should answer your question.

Haven't printed it yet, but, it, very successfully, passed print inspections.

It's just a little (emphasis "little") expensive for me to print right now.

Looking great! Take your time, but keep us posted. Very interesting.

Not sure if this object is of interest, but it also falls into the mathematical category.



Modeling A Voronoi-Style Bracelet In Blender 2.74

Here's the same object done in 3dsmax:

Voronoi-Style Bracelet Tutorial For 3dsmax

And finally, a hyperbolic star object, also done with 3dsmax, but could be translated to other packages:

Trefoil Star Pendant Tutorial For 3dsmax

Hope someone finds them useful. I'll be doing many more in the near future for both 3dsmax and Blender. Enjoy.

Here's what I got



and what I used (attached).

Cool!

btw - shared it:

Math Art - Voronoi
https://blenderartists.org/forum/showthread.php?373260-Math-A rt-Voronoi

not to mention:

[SOLVED] antistellate polygons (bottom of Page 1 and Page 2)
https://blenderartists.org/forum/showthread.php?372547-antist ellate-polygons&p=2880798&highlight=#post2880798

(THIS may take some work to print as its got all those edges ALL of which must meet printability standards. The simple bracelet
may be less involved. I've just uploaded my model. I'll keep you posted as to the results. My model came in at about 200,000 verts
and about 20MB. It takes a "little" more effort and I used thicker twists than Luxxeon did in order to have more to work with. Play around
with the twists width, the amount of solidify as well as smoothing to keep the size down.)

Update: Yep, I was right. Got wall thickness issues. Looks nice. Won't print - at least not without adjustments. It's also 45mm
(a little less than 2 in). to keep the cost down - about $ 5.00. So getting it to print (1) and at a wearable size (2) will drive the cost
up.)

After having "fixed" it, using Shapeways system, it went from part count of 1 to part count of 4.

And, as always, regardless of the results, Shapeways gives me the "seal of confusion" informing me that my model is "Now Ready to Order".

I'ma try it one more time with an adjusted (in Blender) model to see if I get better results.

An idea of what works:

Thickened in Blender.

"Fixed" in Shapeways for Stainless Steel.
(Reguires thicker model than plastics. Figure if
it works for Stainless Steel, it'll work for Plastics.
Although, YES, in the process, I'm sacrificing detail
for printability.

Does it show?

'nuther way to put it:

Does this fix make my model look fat?)

Very interesting result, unkerjay! I think your version of the model is certainly far more complex, and mathematically challenging. The added thickness creates a very unique visual aesthetic, which makes it quite fascinating in it's own right. I wouldn't say it's too thick; however, my only concern is that the inner radius does seem to contain some protruding edges that might make the bracelet uncomfortable to wear, but you might be able to file them down a little.

I was able to apply a certain degree of wall thickness to the original design, in Blender, using another instance of the Solidify modifier on top of the finished model. I'm not sure you could see it clearly in this image, but the screencap shows the wireframe of the object with that final Solidify modifier creating an inner wall thickness (outlined in red), which passed successfully through Netfabb tests. Not sure it would work on a more complex version of the object though.

Well at the dimension I print at (for cost's sake), 45mm,
a little less than 2 in, it's not much of a bracelet. It's more
like a pendant.

And at shapeways minimum thicknesses, it's just an exercise
in frustration trying to preserve FINE detail.

Guess that's why nobody in their right mind has EVER modeled
a workable printable knife because it would never pass printability
analysis.

Looks nice.

Can you make it thicker?

Doesn't look so nice anymore.

But it PRINTS!

yay.

P.S. Nevermind knives as weapons. Before they were weapons,
they were and ARE cutlery. Yeah, a bat is a weapon too, before
that they were and are used for a national past time

Worked on this:

Trefoil Star Pendant Tutorial For 3dsmax
https://youtu.be/RI2Wfcfrp5s

Came up with this
(attached)

Looks good.

Apply the subsurf / solidify modifiers and observe how
quickly it all falls apart.

Started out with a 6 sided mesh circle.
Extruded, inset, poked, subdivided, extruded,
and scaled. Duplicated and joined in Edit mode.
Deleted all the appropriate faces, joined
(vertices) using Alt-M (Center) and deleted
a TON of unnecessary vertices.

What's that saying, "close but no cigar".

Think it applies here.

(I see 3dsMax has followed Adobe's lead and decided
to lease their software. Why sell it when you can subscribe
indefinitely? Kind of like cars, where you pay twice the price
of ownership, and it's still theirs.)

P.S. I misspoke. I can buy a perpetual license for the low,
low price of about $ 4,000. Okay, $ 3,675 to be EXACT,
but that 's like saying someone with a net worth of 999,999.99
isn't a millionaire. Technically true, but, quibbling.

Your blend file of the trefoil looks very good, but I think I'd need to figure out another approach to creating this in Blender than what is used in the 3dsmax tutorial. The techniques used in 3dsmax do not translate well to Blender, as you've discovered at this point in the process. For example, the Solidify modifier in Blender works in only one direction at a time (inner or outer); in 3dsmax, the Shell modifier can be adjusted to affect the inner and outer parts at once, evenly. That's actually a crucial step to creating this shape. So, in Blender, you need to apply two instances of Solidify, each with opposing thicknesses in the modifier stack, but the result of this procedure still doesn't seem correct. Also, I haven't found an equivalent modifier to represent what the Squeeze modifier in 3dsmax does to the mesh. If you try the Cast modifier, and adjust the Factor and Radius, it only affects the object from the center point outward; while the Squeeze modifier in 3dsmax works from the outside perimeter inward. So you'd need to create that squeeze effect manually in Blender, with proportional modeling, to get the same results. Unless there's another modifier option I'm missing which could work in that manner.

All in all, I think it's possible to create this same object in Blender, or course, but not by the same series of techniques. I'd have to consider a different approach to produce the same result.

I used your blend file and came up with this, using Designspark Mechanical http://tinyurl.com/q273xcw it's free. Version 1 has a blend option, but it can be done in Version 2 using the pull tool with guides. The software automatically joins the solids together.
I scaled the model down to have 1mm thick walls. The secret to get the edges right is to create a 'pipe, tube' around all of the wire frame.

Thanks for sharing your knowledge on the rest of the thread.

It looks REALLY nice.

I bring it in to Blender and apply:

sub surface modifier
solidify modifier

or

go into edit mode and apply subdivide smooth

it just doesn't work.

Even with your model as is, I looked at the website you provided.

Nice that they have a free version. Can you do something comparable
to the Squeeze modifier in 3dsMax?

The other file: the RSDoc file, is that a default file for DesignSpark Mechanical?

Couldn't do anything with that.

Also, some files imported into Blender have a disjointed origin, well removed
from the main geometry.

Ctrl-Alt-Shift-C (Set Origin) Fixes that. When I opened it, the origin was at the 0-0-0 xyz
axis point. Using Ctrl-Alt-Shift-C and selecting "geometry to origin" pulls the
geometry from wherever it is, to the 0-0-0 mark. After that, it can be scaled down
to fit on screen.

Between Ctrl-Alt-Shift-C and Shift-S (the Snap Options Menu), can come in
handy to move geometry, the origin, and the cursor as you need to.

Thanx for sharing.

Glad it's all proving useful.

Unkerjay, attached to this reply, please find my revision of your blend file. I was able to apply a certain degree of thickness with two instances of Solidify, and Subdivision Surface, which can be increased even more if you desire. However, I still haven't had success creating the proper squeeze effect to the object. This is as far as I was able to go tonight. Please take a look, and you'll see the original mesh in edit mode. I haven't had time to experiment with proportional modeling yet, which I believe will be the way to achieve the proper squeeze to get the same shape as my 3dsmax result.

I found several unwelded vertices, and left over faces, on the object in your example blend file which were creating problems when the Solidify and Subsurface modifiers were added. I created a new object here, with the issues of welding corrected. For some reason, the remove doubles command didn't work on these vertices, and they needed to be welded by hand.