Wall width x cylinder radius = Hollow percentage (or similar math?)

[Shrouded Blackheart]

Okay so I admit that I'm a bit of a perfectionist when it comes to building and I like to be as accurate as possible.  So I was wondering if there was some sort of formula that I could do in order to find out the percentage that I need to hollow an object.

 

For example I have a wall that is 0.15m thick and a cylinder with a radius of 3.3m.  Is there a way that I can determine how hollow the cylinder would need to be in order to match the walls thickness?

 

I can do it manually but I prefer to be accurate as I said xD

[Freya Mokusei]

Yes.

You may need to give me a little margin for error, as I can't get in-world at present. I am way more of a mental mathematist, explaining my process doesn't always help.

I'm going to use wall 'depth' rather than 'thickness' for consistancy.

If the cylinder is 3.3m radius (half way across the shape), then 0.15m = 3.30 / 0.15 = 22. There are 22 wall-depths inside the radius.

Now the maximum value for hollow is 1.00. 1.00 / 22 = 0.04545454...

But since hollow works inversely, (0.95 = very hollow, not very solid), you need 1.00 - 0.04545 = 0.954545.

This... might cause you trouble since the maximum hollow is 0.95 and you are 0.004545 short of this - enough to drive my inner-perfectionist crazy. The important thing is that this means your maximum wall depth is 5% (1/20th) of your cylinder radius. But that's how it's done (I think).

Note also when using a torus, ring or tube your maximum is 0.5, rather than 1.00 since you use a different parameter (I forget its name). The minimum is also 0.05 (10%, rather than 5%). I can't remember if you need to invert this (I don't think you do - if I remember correctly 0.5 is 'very solid')

To simplifiy:-

t - (t / (r / w))

Where

t = maximum hollow (typically a constant of 1.00).

r = radius

w = wall depth

 

[Shrouded Blackheart]

Now I'm even more confused lol.

 

Let me just absorb this

 

Okay i think i understand... Guess I'll have to mess around with it or maybe you can explain it better once you can get in.

[Freya Mokusei]

Dammit. Uh. I'll try again.

In your example:-

t = 1.0

r = 3.3

w = 0.15

Therefore:-

(r / w) = (3.3 / 0.15) = 22

t / (r / w) = 1.00 / (22) = 0.04545...

t - (t / (r / w)) = 1.00 - (0.04545...) = 0.954545

OR

1.0 - (1.0 / (3.3 / 0.15)) = 0.954545

The area shaded grey is the calculation carried out in the line above it.

Maybe ignore the torus stuff for now.

Or try it with an easier sum.

If the cylinder radius is 1.0m, and the wall depth is 0.25m (total remains 1.0), then:-

1.0 / 0.25 = 4

4 / 1.0 = 0.25

1.0 - 0.25 = 0.75 <- Hollow of 0.75 will match.

[Shrouded Blackheart]

I'm translating between the grid in 3DS Max and such so i set the grid spacing to be 1.5m, maybe i should try working with a more even number lol.

 

Working on a little theory is all

[Freya Mokusei]

A more even number would help.

Also, I'm using the Build tab in-world with primitive cylinder and cube. The hollow parameter in SL goes from 0.0 (not hollow) to 0.95 (almost entirely hollow). I had assumed you were doing the same since this is the Building and Texturing forum and not the Mesh forum.

It's been a long time since I used 3DS Max, I can't off-hand remember how the hollow function works, sorry. You should've mentioned what you were using in your original post. All you should have to do is reduce the total (1.00 in SL, since 0.95 is 'almost' entirely hollow) by w / r as a fraction of the total.

Something like: t / (w / r)

 

[Shrouded Blackheart]

I'm not making mesh, i am experimenting with snapping to grids and such.. I am building just using 3DS to help with the measurements

[Freya Mokusei]

Well, good luck.

[Shrouded Blackheart]

Thanks

[Dora Gustafson]

The wall: W, is what is left when you subtract the hollow part from the full cylinder

for a cylinder with radius 1:

W = 1 - hollow

for a cylinder with radius R:

W = R( 1 - hollow )

solving for hollow you get:

hollow = 1 - W/R

in your example where W=0.15 and R=3.3 you get:

hollow = 1 - 0.15/3.3

so

hollow = 0.954545... which equals 95.45%

:smileysurprised::smileyvery-happy:

(anyway this is how hollow is used in Second Life)

[Freya Mokusei]

---

Dora Gustafson wrote:

hollow = 0.954545...

which equals

95.45%

---

Whew, we got the same answer!

 

[LepreKhaun]

All that theory would be great if it fit practicle application. [Edited for poor choice of words]

It might help to show the theory in practicle application. [Goes to get more coffee for self]

 

[Freya Mokusei]

Sure. I don't know why your hollow differs from the answer provided above. As I said originally I am unable to get into SL today.

Thanks for adding pics.

[LepreKhaun]

And there's the difference when the radius is at 3.3m, just won't reach with the limit of 0.95 on hollow.

[LepreKhaun]

---

Freya Mokusei wrote:

Sure. I don't know why your hollow differs from the answer provided above. As I said originally I am unable to get into SL today.

Thanks for adding pics.

---

No, I just added pics showing it in practicle use, which agrees with the theory. Of course, diameter = 2*radius.

[Freya Mokusei]

Yeeeap, confused myself. Caught that after you posted the second series of pics.

Cool stuff!

[steph Arnott]

It just a ratio of what is left and halved, has nothing to do with radius. You have $10.00 some one takes 80%  you have $2.00 left, the object has two ends so it is 1.0 It is a percentage of that axis.

BTW: The wall thickness is only an approximation by the server. SL primitives were never meant to be that accurate, face it that goes back to the start of SL, nothing has changed. Maybe CAD would suit some.

[steph Arnott]

"Okay so I admit that I'm a bit of a perfectionist"

This SL not a 3D CAD. Imperfect is much more attractive.

[Freya Mokusei]

I don't know what you're trying to say, sorry. None of it sounds right. Maybe you're replying to the OP?

I understood this issue yesterday (check page 1), but thanks.

[steph Arnott]

Sorry I was replying to OP, my fault. I was saying the hollow percentage is axis relevant only.

 

[Freya Mokusei]

No problem.

[LepreKhaun]

Ahh, Steph brought up a good point- radius for a cylinder has two parameters. Picture time!

I'll leave it to math majors to figure out the depth of the wall on a non-orthogonal angle....

[steph Arnott]

Unless one is calculating major and minor axes of an ellipse, you answer is simply a length minus the hollow percentage divided by two.

If you want a set wall thickness times it by two and  just workout what its percentage would be of its length. Forget all the pi stuff. Forget its a cylinder, 10m in diameter is just a 10 meter line across it. Talk about making something simple so complicated.

 

[Rolig Loon]

Right.  What Steph said ^^ .  :smileywink:

[Drongle McMahon]

Apologies in advance, but I'm going to be ridiculously pedantic.  "Cylinders" in SL are not actually cylinders. They are 24-sided polygonal prisms. The consequence of this, and of the way the path cut works, is that the thickness across a radial cut depends upon the position of the cut relative to the vertices of the polygon. The top picture is two inworld hollow cylinders, identical except that the blue one has a pathcut as nearly as possible half way between polygonal vertices. Note that the pathcut code does not calculate a new cut face at the proper radius, but simply cuts across the existing trapezoidal face. It is simple then to calculate that the ratio of the lengths of the cut at this point, with that of a cut through the vertex is cos(7.5 degrees). This is seen more easily in the construction velow, made in Blender. Thus the optimal hollow to fit exactly against  certain wall thickness depends on the position of the pathcut. The most extreme difference is with the cut half way between vertices, as shown. Then it is about 1%. (Not that anyone needs to care about that! :matte-motes-smile:)