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Create torus with ALL surface polygons squares. 
niculaegeorge 
1. In 3dsmax when I choose the correct configuration of sides/segments to make the torus inner hole surface polygons, squares, the polygons on the outer circumference of the torus, are now rectangles. Or vice versa. I want all the surface polygons squares, or ALL polygons on the torus surface, are a rectangle that is ALWAYS deformed everywhere on the surface with aspect ratio!! 2. Second approach I've tried, is by using a plane and bend it twice to make it a torus. However, the polygons of the plane must be unevenly distributed on the plane surface, following an exponential formula. More squeezed towards the center or towards the sides of the plane, depending on how the two bend modifiers are applied. How can I split this plane in uneven segments the right way? I don't want to calculate anything. Can't there be an easier solution to my problem? 3. Third approach is to make a circle with uneven segments (more segments towards a side of the circle), and lathe the entire circle around a distant pivot point to make it a torus. Right... How on earth can I split the circle in uneven segments? Obviously, I don’t want to do it manually by hand, calculating all the segments for a particular torus. To make perfect squares on the torus surface, the circle segments size depends on the lathe pivot point distance…right…. but I don’t want to manually calculate anything. The software is supposed to do that all for me…or not? These words keep ringing into my ear: "Mesh", "Wave" and "bias"(like in a helix), but I can't seem to make the head and tails of things. My intuition tells me that there must be a RIGHT configuration of modifiers applied to standard primitives or splines to get what I want. Which basically put in 6 simple words is this: "TORUS WITH ALL SURFACE POLYGONS SQUARES".
If there isn’t a straight forward solution to this problem, I will be satisfied with approximations. Something like a setting I manually adjust to visually approximate ALL the surface polygons of the torus to a square or a certain rectangle (aspect ratio). I can go with that. But how can it be done?
read 768 times 11/26/2015 11:31:21 AM (last edit: 11/26/2015 11:31:21 AM)

Garp 
> torus with ALL surface polygons squares
Mathematically not possible.
read 763 times 11/26/2015 12:08:15 PM (last edit: 11/26/2015 12:08:15 PM)

niculaegeorge 
I beg to differ. You don’t understand what I want to do. It can be done. Imagine increasing the number of sides of the torus (in a crosssection of the torus, it increases the number of sides of the NGon of radius r2). Now imagine the same NGon crosssection, which has uneven size sides. Towards the center of the torus, the sides are shorter, towards the outside, they are longer. That will generate the torus I’m after.
read 755 times 11/26/2015 12:27:03 PM (last edit: 11/26/2015 12:27:03 PM)

niculaegeorge 
I’ve kind of manage a workaround, without avoiding manual calculation in excel of the poloidal angles required, calculated obviously based on circle arc length formula. It turns out that only a few toroids get close to what I want. Made a pie slice arc for each poloidal angle calculated in excel. Refined a splinecircle with points aligned to the vertexes of these arcs. And then lathe the resulted spline. Hope the pictures are explanatory. But damn, it’s hard and complex! Maybe someone can enlighten me with a simpler more straight forward method…
Wow, all perfect squares, not a trapezoid in sight. LOL
https://drive.google.com/file/d/0ByyeIdK8FssyazJRSktvTWRCMEE/view?usp=sharing https://drive.google.com/file/d/0ByyeIdK8FssyM0djVjE1dXlfY1U/view?usp=sharing https://drive.google.com/file/d/0ByyeIdK8FssycHU3UlRGdmNUXzg/view?usp=sharing
read 735 times 11/26/2015 2:45:35 PM (last edit: 11/30/2015 10:21:27 AM)

herfst1 
I beg to differ. Garp is always right.
read 727 times 11/26/2015 4:02:44 PM (last edit: 11/26/2015 4:02:44 PM)

Garp 
@herfst: Good to know! Thanks :))
@niculaegeorge: Look at what you're asking from a construction point of view. If you start with a square, another square connected to it would have the same size. To make a closed mesh, connected squares have to be at an angle that is a multiple of 90°. You can never form a torus this way. With rectangles, the reasoning is the same but with two sets of edges.
read 719 times 11/26/2015 8:01:58 PM (last edit: 11/26/2015 8:01:58 PM)

niculaegeorge 
Yes. I beg to differ. From a construction point of view it can be done. The links above prove it. That is if someone just bother to check them out and see my work, you will see I already constructed the torus I’m after. I am looking at what I'm asking. It is you who is not looking into what I'm asking and what I've done. Thank you anyway, for encouraging me.
read 694 times 11/27/2015 3:45:11 PM (last edit: 11/27/2015 4:12:44 PM)

niculaegeorge 
Oh…and here is another impossible torus whose all faces, are the same rectangle deformed with aspect ratio. All surface polygons of the torus are a rectangle which is always the same everywhere on the torus surface, just smaller, but always deformed in respect with aspect ratio:
Wow, all same rectangle, not a square in sight. https://drive.google.com/file/d/0ByyeIdK8FssyMi1YdnJoTEhuejA/view?usp=sharing It’s using the same calculations in angles.xlsx excel file of mine, that nobody cares to look at, in the links above, because EVERYBODY ALREADY KNOWS THAT WHAT I’M DOING IS IMPOSSIBLE (This is the story of my life). So, yeah… don’t even bother looking into my foolishness… just don’t.
read 687 times 11/27/2015 4:37:45 PM (last edit: 11/30/2015 12:54:23 AM)

niculaegeorge 
You might say: Yeah, but what you have done is an approximation, the squares/rectangles on the outside circumference are not exactly perfectly the same as the rest, proving my point, that what you are asking, is indeed a mathematical impossible construction. I say: Oh…I see that you have decided to look at my calculations, but you are not really listening to me. Didn’t I said in my first original post “I will be satisfied with approximations”? I did. So now that I’ve build my torus with all surface polygons APPROXIMATELY squares, I am satisfied. Thank you for your kind support and encouragement. You might say: Cut the bullshit sarcasm. Strictly speaking from a mathematical point of view, IN THEORY, what you are asking is impossible. There is no such torus. It can’t be done. I say: I beg to differ. It’s just a matter of feeding the formula for these poloidal angles in my calculations, the right set of parameters. If you just bother to look at the following excel file: https://drive.google.com/file/d/0ByyeIdK8FssycGpXa3k1NktndEU/view?usp=sharing Or jpg picture: https://drive.google.com/file/d/0ByyeIdK8FssyTF9UWkxaOHdTLU0/view?usp=sharing Even if there is a decimal limit precision in excel for calculation, perfect squares all the way can be achieved. This is the final proof that EVEN the mathematical THEORETICAL perfect model of a torus with ALL/ENTIRE/EVERYTHING/ALL surface polygons/faces PERFECTLY/EXACTLY squares is REAL, POSSIBLE, PRACTICAL, and CONSTRUCTIBLE.
I’m sorry to waste your valuable time with my foolishness…
read 684 times 11/27/2015 5:36:28 PM (last edit: 11/28/2015 3:43:58 AM)

Dave 
It's cool that you've decided to argue with yourself, saves anyone else the hassle.
"I flew over Egypt once"
read 677 times 11/27/2015 5:47:24 PM (last edit: 11/27/2015 5:47:24 PM)

niculaegeorge 
Thank you. I'm a one man forum.
read 677 times 11/27/2015 5:47:57 PM (last edit: 11/27/2015 8:19:50 PM)

herfst1 
I'm sure there's a masturbation joke in there somewhere.
read 655 times 11/27/2015 9:43:29 PM (last edit: 11/27/2015 9:43:29 PM)

niculaegeorge 
Someone might say: Look, dude, if you're so smart, and think you have all the answers, why did you even come to this forum to ask for help? I would reply: Because I’m lazy and wanted a quick easy fix. A simpler solution.
read 641 times 11/28/2015 3:34:04 AM (last edit: 11/28/2015 3:50:15 AM)

niculaegeorge 
I'm sure there's a junkie joke in there somewhere.
read 635 times 11/28/2015 3:46:35 AM (last edit: 11/28/2015 3:46:35 AM)

Garp 
I understand what you're trying to do. I was just pulling your leg a little, playing on the rigor of your argumentation vs. the sloppy terminology.
I'm afraid there is no simple solution. The maths are a little tricky. I can think of several approaches, with a tradeoff between precision and ease of computation. If it's something you're going to need often, the best thing to do imo would be to write a geometry plugin in maxscript.
read 632 times 11/28/2015 6:30:59 AM (last edit: 11/28/2015 6:30:59 AM)


