### Author Topic: Algorithm: Draw ball  (Read 4193 times)

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#### well20152016

• Newt
• Posts: 88
##### Algorithm: Draw ball
« on: April 06, 2019, 10:56:09 PM »
Known: 1. Radius of the sphere
2. Side Length of Hexagon or Pentagon (Approximate Value)

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #1 on: April 07, 2019, 12:26:24 AM »
If you want lisp, you should firstly analyze construction - it's called truncated icosahedron...
Here is my video with construction :

HTH., M.R.
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #2 on: April 07, 2019, 10:03:49 AM »

Thank you! It's just a situation! I wonder if LISP can handle more situations?

#### BIGAL

• Swamp Rat
• Posts: 580
• 30 + years of using Autocad
##### Re: Algorithm: Draw ball
« Reply #3 on: April 07, 2019, 09:11:30 PM »
If you can work out the maths then theorecticaly anything is possible. There is a mathmatical theorem for the soccer ball.

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #4 on: April 08, 2019, 01:05:15 AM »
The surface of a football ball ball ball is a sphere made up of 12 regular pentagons and 20 regular hexagons.

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #5 on: April 09, 2019, 05:50:05 AM »
dwg

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #6 on: April 09, 2019, 09:39:17 AM »
You generated different ball then I was expecting... It's not based on truncated icosahedron... I tried to get 3DSOLID, but some lines aren't touching exactly with each others and beside all this, to make 3DSOLID those lines have to make exact planar polygons - sorry it was close - my routine recognized some polygons and converted them to regions, but major of them were not processed, so final surfsculpt was not good...
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #7 on: April 10, 2019, 10:19:22 AM »

It's sphere constructed of 12 regular pentagons and 60 irregular hexagons... There are variants with 12 pentagons and 200 hexagons and 12 pentagons and 620 hexagons... Pentagon centers are positioned always at vertices of corresponding regular icosahedron...
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #8 on: April 10, 2019, 10:38:12 AM »
There is also this picture - extended dodecahedra...
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #9 on: April 10, 2019, 06:18:37 PM »
Thank you. I'm studying, too.

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #10 on: April 12, 2019, 09:34:51 AM »
It's sphere constructed of 11 regular pentagons and 80 irregular hexagons.

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #11 on: April 12, 2019, 10:33:18 AM »
Well it's almost the same as your first example... I would say 12 regular pentagons and 80 irregular hexagons... I guess I counted wrong - thought 60 hexagons... But the same - no success in converting 3d lines to 3d solid... Only pentagons were good, but then again I think that not all were processed - not even single hexagon is good - you have to check their planar characteristics... Still not perfect...
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### well20152016

• Newt
• Posts: 88
##### Re: Algorithm: Draw ball
« Reply #12 on: April 12, 2019, 12:21:07 PM »
Are there any programs that can automatically generate sphere boxes?

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #13 on: April 12, 2019, 01:05:51 PM »
Look I've counted your last example - it seems 12 regular pentagons and 110 irregular hexagons... I'll attach my counted version - you can check if you want...
To answer your question : there are lisps for geodesic spheres and also there are lisps for all kind of dense covered spheres with regular triangles, quads, pentagons and hexagons based on uniform polyhedrons...
M.R.
« Last Edit: April 13, 2019, 07:46:24 AM by ribarm »
Marko Ribar, d.i.a. (graduated engineer of architecture)

#### ribarm

• Water Moccasin
• Posts: 2452
• Marko Ribar, architect
##### Re: Algorithm: Draw ball
« Reply #14 on: April 14, 2019, 04:38:12 AM »
Here is my version of the same ball - 12 pentagons + 110 hexagons... I constructed based on dodecahedron - the problem still exist - we don't know ratio : edge of pentagon/hexagon : radius of sphere... I almost did it visually, but then the problem occurred when 2 cups had to be connected (bottom and top cup)... It seems that edge of pentagon should be little bigger, but we don't know how to determine that accurately...

Regards, M.R.

[EDIT : DWG removed due to lack of interest - not even single download up to now... See date of edit below post...]
« Last Edit: April 15, 2019, 12:17:12 PM by ribarm »
Marko Ribar, d.i.a. (graduated engineer of architecture)