# Thread: Mosaic Sphere. How? I hate to eyeball stuff =)

1. ## Mosaic Sphere. How? I hate to eyeball stuff =)

I'm trying to make a sphere made out of "squares" like if it was a mosaic.

Here's a pic explaining.

(I'll have to try 32x32)

Now... I eyeballed each loop of this sphere with Multushift (saved a profile ) but its preety innacurate and i cant apply that profile to circle different thatn 32 sides.

Question: is there a way to make this kind of sphere with input parameters, choosin the aspect ratio of the target square/rectangle, without having to eyeball it?

Again, this mosaic sphere is worst than LW sphere for subdivision and all. But if you want to make a sphere of LCD screens it's probably the better way to go.

Cheers

2. Or try to make a cube with enough segments and use spherize.

3. the first thing that comes in my mind is;

-build a ball and keep it as ref in BG
-make a square ( a single mosaic piece ) and start to clone it with ARRAY ( radial, and number of clones should be; circumference at its height / horizontal length of a mosaic )
-keep doing this for other rows ( but before you proceed with array, you should correct the angle of the first mosaic piece; it should see always the center. that's why you should have a ball in BG as a reference)
- when you arrive at the top, cheat ... =)

p.s.: fortunately you do not need thousands of mosaic pieces ... and have a MIRROR tool ... =P

4. This was my attempt.

Quite a long winded method but kinda worked. Let me know if you want the details.

5. ## in action ...

Originally Posted by zarti
the first thing that comes in my mind is;

-build a ball and keep it as ref in BG
-make a square ( a single mosaic piece ) and start to clone it with ARRAY ( radial, and number of clones should be; circumference at its height / horizontal length of a mosaic )
-keep doing this for other rows ( but before you proceed with array, you should correct the angle of the first mosaic piece; it should see always the center. that's why you should have a ball in BG as a reference)
- when you arrive at the top, cheat ... =)

p.s.: fortunately you do not need thousands of mosaic pieces ... and have a MIRROR tool ... =P
screen and video capture in the middle of process ...

Attachment 84386

video ( XVID, < 5MB )
Attachment 84387

6. Originally Posted by zarti
screen and video capture in the middle of process ...

Attachment 84386

video ( XVID, < 5MB )
Attachment 84387
_ty for the time zarti, i think your approach is quite cool for real world construction job reproduction, since the tiles would be all of the same size. But thats not my objective here.

_Cagey, ty too. Bring it on those shamefull details

The objective here is to make a sphere which each polygon has the same aproximated aspect ratio (im going with squares now, cause it's easier to see if things are correct)

Was trying to use a function to profile a Lathe. But i don't know wich function is the correct one. Anyone knows? (x^2)*3,14?

Cheers

7. Originally Posted by zarti
screen and video capture in the middle of process ...

Attachment 84386

video ( XVID, < 5MB )
Attachment 84387
this is what you are pointing to zarti, and it's very cool.

8. Originally Posted by probiner
_ty for the time zarti, i think your approach is quite cool for real world construction job reproduction, since the tiles would be all of the same size. But thats not my objective here.

_Cagey, ty too. Bring it on those shamefull details

The objective here is to make a sphere which each polygon has the same aproximated aspect ratio (im going with squares now, cause it's easier to see if things are correct)

Was trying to use a function to profile a Lathe. But i don't know wich function is the correct one. Anyone knows? (x^2)*3,14?

Cheers
My solution was similar to this i.e. forming a profile and lathing. To get the point spacing I took the points from the top section of and existing ball and stretched them back to a vertical column. so that the density of the points were denser towards the top and then re-bent that column by 90 deg before lathing.

Hopefully that's reasonably clear. I'd include a picture but I don't have LW on this comp.

9. -.š_ itthh'ss ccfflleeaarrr eeffnoughhf. Ttffhhannkkfss..

10. Ok, i think i have found a quite good math solution for the "issue". If i keep doing the 3-Sides Equal Trapezium i will get the intended result: The most possibly regular quads in a Globe Sphere.

Now, if there was a function that would generate the heights i could just Bend and Lathe them

11. After stealing all your ideas, I came up with this...

Create a cone.
Create a plane in a new layer.
Array 25 times in the y direction.
Use the bend tool on the left points and then the right.
Drill/slice the cone with your 25 planes.
Delete the bottom poly off the cone.
Mirror y.
Spherize.

12. hi XswampyX, again ty for your time you took looking into this. Your solution doesn't seem to make what i intend here, unfortunetly for me. I am looking for quads that resemble squares in the most possible way.

I ended up doing by hand the concept shown in my previous post (stacks of 3-sides equal trapeziums). It's not yet showing up perfect, but I think the image above is a nice proof of concept.
Extrude and WrapSphere was used instead of Bend and Lathe.

I also went math forums asking for expressions, where i was only told to look at Non-Euclidean geometry mainfolds, geodesic, etc. I brainfarted trying to understand those expressions and apply them to my objective.

Kudos to Artsphere's LineXLine and PointAtAngle made this taks possible. Thanks art! (by the way sometimes the LineXLine would tell me that no intersection was found, why?)

Anyway, it's looking better now, at least it's not eyeballed, but it still needs that expression to make it faster and properly =) If anyone would like to take a look there is a sample attached (i didn't finish the pole because it was getting really boring...)

Cheers

13. I think you missed the point of my post.

You set the ratio by the amount of planes you create. The first one was 50 sides on the cone and 25 cuts across it. If you want squares just create 50 cut planes.

Here's a sphere made out of 180,000 polys, square polys! That's 300 sides on the cone and 300 cut planes.

Cheers!

14. Originally Posted by XswampyX
I think you missed the point of my post.
Probably i did. Argh, ty for insisting on this with me, but i'm not really seeing how that procedure will produce apparent squares. Your examples do not show apparent squares, but a difference in proportions from equator to pole, i gues due to the type of projection.

Although, this type of finite approaches, alike previous ones in the thread are friendly, since an actual tessellation of 3-side equal trapezium will be infinite on the top, and thats not practical .

Even if i come out with an equation (which i'm not even close ), it should stop at some point before the pole.

Cheers

15. ## new puzzle

Well, boys, that was fun.

Now that you got that out of your system, , a related puzzle:

RW disco balls probably use the same size mirror over the whole surface. How would one construct a sphere efficiently covered with squares of n size?

Let's make it real rectangular solids of a given thickness. Mirrors should remain flat (planar) and square. Whether to include 'grout' is up to you--- that is: the mirrors can be 'stuck' to an underlying sphere, or the gaps between can be filled with 'virtual grout'.

Perhaps a convenient way to specify the size of the squares would be in degrees of latitude. The longitude would vary of course.

(BTW, reading an article on "Rio", apparently Blue Sky wrote an elaborate shader just to do this, to depict a specific sidewalk in the real Rio de Janeirro. They prefer procedurals(!!!) at Blue Sky to image maps.)

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