/sci/ - Science & Math » Thread #12368714

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Cargo Net Problem

Anonymous Sat 21 Nov 04:23:04 2020 No.12368714 View Reply Original Report

Quoted By: >>12368743 >>12369119 >>12369169 >>12369270

So I have perhaps discovered an unsolved problem in geometry that I'm dubbing the Cargo Net Problem

Using a continuous line(not cutting the rope) with or without a frame
what is the most efficient use of a rope, that maintains the most symmetry for making a functional net?

Which I guess means has kind of small pockets, probably some ratio to be determined later Vs the overall perimeter, or some fraction of the area.

Suppose a circular net has a different solution?

You'll be racing to beat the nerds I tagged on twitter here: if you wish to partake.

https://twitter.com/LordStreetGuru/status/1329999395274649601

Anonymous

Anonymous Sat 21 Nov 2020 04:27:40 No.12368726 Report

Quoted By:

all I can think of now is, that when you cut holes into a net, with scissors for example, you reduce the number of holes.
thank you.

Anonymous

Anonymous Sat 21 Nov 2020 04:32:27 No.12368743 Report

Quoted By:

>>12368714
I should also note that the finished formula would also be very useful for figuring out exactly how much rope is needed as well.

Anonymous

View Same Google iqdb SauceNAO Point to Point Net.jpg, 567KiB, 2048x1536

Anonymous Sat 21 Nov 2020 04:43:29 No.12368786 Report

Quoted By: >>12368796 >>12369169 >>12369717

Newest model goings from point to point instead of in the middle of points

also with a 2:1 ratio for the size of the triangles, really small holes may not be totally necessary.

Anonymous

Anonymous Sat 21 Nov 2020 04:45:44 No.12368796 Report

Quoted By: >>12368804

>>12368786
What's with the big hole in the centre?

Anonymous

Anonymous Sat 21 Nov 2020 04:47:15 No.12368804 Report

Quoted By:

>>12368796
hadn't decided how to close it up, just went every other point and made some Xs, should be good enough

Now we just need someone to build a formula to figure out what the length of rope needed is for what kind of pattern you want

Anonymous

Anonymous Sat 21 Nov 2020 05:01:00 No.12368842 Report

Quoted By: >>12369151

AND IN ADDITION

If someone does figure out a formula for this, and the formula could apply to 3D objects, using triangles or cubes, it would be extremely useful in 3D printing applications for leaving things hollow, saving plastic use.

Anonymous

Anonymous Sat 21 Nov 2020 07:37:36 No.12369119 Report

Quoted By: >>12369138

>>12368714
This is a bit pedantic, but you need to better define the shape restrictions for the net, otherwise the problem is too open.

Anonymous

Anonymous Sat 21 Nov 2020 07:49:46 No.12369138 Report

Quoted By:

>>12369119
All that really matters is the ratio you want to use to form the pattern

Probably 2 odd numbers always

can possibly even just divide up a circle in the same manner.

The most useful application is a formula for 3D printing slicers

Anonymous

Anonymous Sat 21 Nov 2020 07:56:29 No.12369151 Report

Quoted By: >>12369164

>>12368842
The 3d case seems like a pretty different problem to me, I'm not sure they'll connect all that well.

Anonymous

View Same Google iqdb SauceNAO 3D.png, 256KiB, 745x475

Anonymous Sat 21 Nov 2020 08:02:37 No.12369164 Report

Quoted By:

>>12369151
It's the same problem, because 3D printing is just a bunch of 2D layers really, so you could either just stack the 2D pattern straight vertically

or you would make the next layer slightly smaller/larger, or double the lines and put them at new angles, to stack everything towards a point, and kind of stair case it.

but with a pre baked formula for the calculation you could just control the triangle's angle/size, and the angle it went upward and how it had to scale.

Anonymous

Anonymous Sat 21 Nov 2020 08:04:32 No.12369169 Report

Quoted By: >>12369182 >>12369185 >>12369258

>>12368714
>a functional net
How do you determine whether a given net is functional?

>>12368786
What's happening at the points here? Is the rope just hinging on itself and on the frame? Is there something preventing the rope from sliding?

Anonymous

Anonymous Sat 21 Nov 2020 08:09:53 No.12369182 Report

Quoted By: >>12369185 >>12369258 >>12369365

>>12369169
It's whatever size you want to make the holes

all that really matters here is the ratio you want for the points it touches itself again

I'm just using 2 knots so it doesn't slide, could make more loops if I wanted to, but that uses slightly more material, not sure how much rope I need, hence the problem.

Anonymous

View Same Google iqdb SauceNAO Cargo Net 1.jpg, 550KiB, 996x2048

Anonymous Sat 21 Nov 2020 08:10:54 No.12369185 Report

Quoted By: >>12369365

>>12369169
>>12369182
damn it

Anonymous

Anonymous Sat 21 Nov 2020 08:31:57 No.12369258 Report

Quoted By: >>12369365

>>12369169
>>12369182
and the pattern obviously is important, I don't know if I came up with the best one already, but it seems pretty fine for the net, and for 3D printing

Anonymous

Anonymous Sat 21 Nov 2020 08:35:54 No.12369270 Report

Quoted By: >>12369274

>>12368714
Can you phrase this in terms of mongorian basket weaving so I better understand?

Anonymous

Anonymous Sat 21 Nov 2020 08:36:32 No.12369274 Report

Quoted By:

>>12369270
Ima be so pissed if some ancient bastard already solved MY math problem

Anonymous

Anonymous Sat 21 Nov 2020 09:17:22 No.12369365 Report

Quoted By: >>12369384

>>12369182
>It's whatever size you want to make the holes
So you determine a shape and/or area which all holes must fit into? Let's say you use circles, triangles, squares etc. with a area in relation to the frame area (and/or shape), or simply an area which can take any shape? A basic case would be with a square frame and a given ratio of the area of the frame and area of a hole.

>all that really matters here is the ratio you want for the points it touches itself again
Do you mean having a set/max/min number of times it touches itself again at the same point?

>>12369185
>I'm just using 2 knots so it doesn't slide, could make more loops if I wanted to, but that uses slightly more material, not sure how much rope I need, hence the problem.
So rope is fixed at points/nodes (what about to the frame?), but you don't know how much rope you're using to achieve this? With IRL ropes it depends on the thickness of the rope, the type of knots, how many times the rope is going in and out the node (the degree of the node is increasing by 2 each time). In printing you don't need to tie knots as plastic melts together, but you probably need to use more material as the degree of the node increase. Maybe model it with some function $f : \mathbb{N} \to \mathbb{R}$ where domain is the degree of the node divided by 2 and codomain is the amount of material spent? Start with $f(n) = 0$ ?

>pic
Wait, are you actually in need of a cargo net?

>>12369258
>and the pattern obviously is important
Symmetry right? Could you elaborate on this? Should the net have the same symmetries as the frame? Imagine having a circle frame, then it would be difficult to reach the same symmetries as the frame. With a low symmetry frame it would be easy for the net to surpass the symmetry of the frame.

Anonymous

Anonymous Sat 21 Nov 2020 09:27:48 No.12369384 Report

Quoted By: >>12369608

>>12369365
It doesn't really matter how many times it knots to the same point depending on the pattern.

The main point for me, is to make the webbing/net portion as efficient as possible, with the least material used. In reality of course you add like X% to the length, depending on how much you lose knotting it and crossing it back on itself in a few places.

And of course, not having to cut the rope, which would be way easier, because you could just make straight lines, but my method with the triangles slowly creeping towards the center seems pretty good for a first try.

you can just make a rectangle/square and see what kind of pattern forms if you try to use one continuous line.

Anonymous

View Same Google iqdb SauceNAO SquareFrame.png, 8KiB, 500x500

Anonymous Sat 21 Nov 2020 11:42:02 No.12369608 Report

Quoted By: >>12369637

>>12369384
>It doesn't really matter how many times it knots to the same point depending on the pattern.
Is that $f(n) = 0$ ?

>The main point for me, is to make the webbing/net portion as efficient as possible, with the least material used.
From this I take that you don't really care about symmetry, and I think symmetry is sometimes efficient for symmetric frames. And from your previous comment
>It's whatever size you want to make the holes
I take that you only care about area of the hole, and not the shape. Just to point it out, this doesn't line up with the application that is a cargo net because the things that the net is holding can have any shape that fits inside the frame, correct? That's completely fine though. But still I think this isn't perfectly clear. Let's say you also care about the distribution of the areas of the holes or something like that. What do you care about exactly? Take a look at my picture. Is this the kind of solutions you would be ok with for larges holes? I think rope length is approaching zero as hole area is approaching 1.

>In reality of course you add like X% to the length, depending on how much you lose knotting it and crossing it back on itself in a few places.
Why would it be dependent on the total rope length? By the way I think I was misguided when I said it is dependent on rope thickness. It might be better to model the rope as infinitely thin first.

Anonymous

View Same Google iqdb SauceNAO SquareFrame.png, 8KiB, 500x500

Anonymous Sat 21 Nov 2020 11:44:26 No.12369616 Report

Quoted By: >>12369637

Anonymous

Anonymous Sat 21 Nov 2020 11:55:56 No.12369637 Report

Quoted By: >>12370354

>>12369608
>>12369616
If an asymetrical design produces the best result then that's fine by me. Symmetry just seems like it would be easier.

I care about the line that is being drawn with, like a game of snake or something.

The 3D printer application can go without a frame, and just scrape the edges. Unless not using a frame is more efficient for the net part.

Like it's actually for a cargo net, but I'm looking for a formula where you put in the perimeter of the frame, and with the optimal pattern, get out the length of rope needed to fill that perimeter, with say fist sized holes or something, but those exact numbers aren't important.

Then it's about figuring out what relationship everything has with everything else in the problem. Like what angle you make the pattern/triangle move from point to point with.

Anonymous

View Same Google iqdb SauceNAO dc.jpg, 54KiB, 500x375

Anonymous Sat 21 Nov 2020 11:58:30 No.12369643 Report

Quoted By: >>12369651 >>12370354

Anonymous

Anonymous Sat 21 Nov 2020 12:02:35 No.12369651 Report

Quoted By: >>12369688 >>12369822 >>12370064

>>12369643
Yes, but A. I'm not sure how efficient it is as a cargo net.

B, still need a formula out of it for use with 3D printing.

Also those may not all use a continuous line/string/rope.

Anonymous

Anonymous Sat 21 Nov 2020 12:17:05 No.12369688 Report

Quoted By: >>12369717 >>12370354

>>12369651
its single strand and pattern is simple when weaving, not sure about 3d printing
dont know what is your formula for efficiency but if its something like (average hole size/used thread length) you generally want pattern with holes getting smaller closer to center if you are using continuous strand

Anonymous

Anonymous Sat 21 Nov 2020 12:28:23 No.12369717 Report

Quoted By: >>12370557

>>12369688
My example
>>12368786
has most of the spaces being close to the same size, meaning the whole thing is equally useful, and the rope only rarely has to cross back over itself, losing little length in the process.

Which is the one I'm currently physically making

Anonymous

Anonymous Sat 21 Nov 2020 13:27:11 No.12369822 Report

Quoted By: >>12370557

>>12369651
If how efficient it is as a cargo net playes a role, you can not solve this with pure math.
You need physics to find a solution, and will also be a 3d not a 2d problem probably.
You also need mechanics for that

Anonymous

Anonymous Sat 21 Nov 2020 15:21:14 No.12370064 Report

Quoted By: >>12370557

>>12369651
>I'm not sure how efficient it is as a cargo net
Then this isn't a math problem

Anonymous

Anonymous Sat 21 Nov 2020 17:06:53 No.12370354 Report

Quoted By: >>12370454

>>12369637
>If an asymetrical design produces the best result then that's fine by me. Symmetry just seems like it would be easier.
You may be right about that

>I'm looking for a formula where you put in the perimeter of the frame
>perimeter
That's quite interesting. Also give area of frame without shape. Also give perimeter of the holes.

>The 3D printer application can go without a frame, and just scrape the edges.
And here I suppose you need to give the exact shape and size.

> Like what angle you make the pattern/triangle move from point to point with.
What do you mean?

>>12369643
>its single strand and pattern is simple when weaving
What the name of this?
>>12369688
>average hole size/used thread length
1/((average hole size)*(thread length)) ?

Anonymous

Anonymous Sat 21 Nov 2020 17:28:00 No.12370454 Report

Quoted By: >>12370806

>>12370354
>What the name of this?
https://www.youtube.com/watch?v=PcY_60sg0w0

>1/((average hole size)*(thread length)) ?
yes

Anonymous

Anonymous Sat 21 Nov 2020 17:49:34 No.12370557 Report

Quoted By: >>12370985

>>12369822
>>12370064
since op said
>has most of the spaces being close to the same size, meaning the whole thing is equally useful (>>12369717)
im assuming he dont care about mechanical stress only about creating single thread pattern that have highest number of roughly equally sized holes so stuff cant fall through while minimizing length of the thread

its still very poorly defined problem since he did not specify how much he want to prioritize # of holes vs length, so there is no "solution"

Anonymous

Anonymous Sat 21 Nov 2020 19:01:22 No.12370806 Report

Quoted By:

>>12370454
Thanks. That's a cool weaving.

Anonymous

View Same Google iqdb SauceNAO Single Line Cargo Net Pattern.webm, 3MiB, 1112x540

Anonymous Sat 21 Nov 2020 19:35:54 No.12370909 Report

Quoted By:

Okay here, this is why it's important for 3D printing, it would allow you to make one continuous line for better strength in the part.

Doubles as an effective cargo net too though.

ignoring my first mistake there of course.

So the geometric equation/formula whatever, needs to shape the single line by, number of sides, angle of the "infill" pattern, shape of that infill pattern, ect.

Anonymous

View Same Google iqdb SauceNAO Zig Zag Infill Pattern.webm, 2MiB, 1112x540

Anonymous Sat 21 Nov 2020 19:57:35 No.12370985 Report

Quoted By:

>>12370557
>its still very poorly defined problem since he did not specify how much he want to prioritize # of holes vs length, so there is no "solution"
No lol, I need an equation or whatever that spits out, a customized pattern, for whatever the user wants.

Regardless of the physical dimensions.

The main things that matter in my mind, are the number of points it touches the frame, making one without a frame as well, and then the angle you draw the shapes in the pattern.

Whichever pattern ends up being most efficient for making spaces that are all roughly the same area inside the thing.

The video shows it also doesn't need to cross back over itself for the 3D printing application.

although you would want something more like flat triangles/zig zag pattern for real parts.

Something with flat edges and very sharp angles, although maybe this requires even steps? as I'm doing 9:7 right now

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