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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: n-poly from a line...
Date: Tue, 1 Apr 2025 13:10:59 -0700
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On 4/1/2025 3:46 AM, sobriquet wrote:
> Op 01/04/2025 om 06:54 schreef Chris M. Thomasson:
>> On 3/31/2025 9:48 PM, Chris M. Thomasson wrote:
>>> On 3/31/2025 3:53 PM, sobriquet wrote:
>>>> Op 31/03/2025 om 23:05 schreef Chris M. Thomasson:
>>>>> On 3/31/2025 6:40 AM, sobriquet wrote:
>>>>>> Op 30/03/2025 om 08:24 schreef Chris M. Thomasson:
>>>>>>> Well, according to some AI's, lol, my ability to find an n-poly 
>>>>>>> from a single line, its incircle, outcircle and center point is 
>>>>>>> supposedly something good. Some of them claim it's not enough 
>>>>>>> info to gain the poly from the line and number of vertices alone. 
>>>>>>> Well, my function only takes two points (p0, p1) and a number of 
>>>>>>> vertices (n) for the result. Then renders all of them. Does this 
>>>>>>> sound like anything worthwhile to you? I just did it for a new 
>>>>>>> fractal I am tinkering around with for fun. I did not think it 
>>>>>>> was anything all that special. Fwiw, here is a render:
>>>>>>>
>>>>>>> https://i.ibb.co/Y7G4C80t/image.png
>>>>>>>
>>>>>>> Notice how the red circles are all tangent along a "path". The 
>>>>>>> green circles intersect. The number of polys are decreased as 
>>>>>>> they extend out. This starts from a single line and the number of 
>>>>>>> vertices. I am thinking about doing something interesting with 
>>>>>>> it. It might look fairly nice.
>>>>>>>
>>>>>>> :^)
>>>>>>>
>>>>>>> Thanks.
>>>>>>>
>>>>>>> Kind of interesting at all? Or been there, done that. :^)
>>>>>>
>>>>>> Nice! Looks a bit like a polyhedron that has been unfolded.
>>>>>>
>>>>>> Not sure how you scaled it relative to the unit circle.
>>>>>>
>>>>>> https://www.desmos.com/calculator/3izjfv3yma
>>>>>
>>>>> Thanks. Well, my algorithm starts off with only three relevant inputs:
>>>>>
>>>>> p0 = start of line
>>>>> p1 = end of line
>>>>> n = the n in n-poly
>>>>>
>>>>>  From that information alone, I create the fractal. So, it's not 
>>>>> scaled to the unit circle, its basically scaled from that line (p0, 
>>>>> p1). So, it can grow out of bounds, if we treat the unit circle as 
>>>>> a sort of "boundary". Now, you read my mind a bit. I have a way to 
>>>>> scale the fractal as a whole inside of any circle. Just need to 
>>>>> port my older code to this. Fwiw, these types of things can get 
>>>>> pretty dense, using the tangent circles instead of n-poly. 
>>>>> Actually, its a different generator algo using the same 
>>>>> intersection avoidance algo:
>>>>>
>>>>> https://www.facebook.com/photo? 
>>>>> fbid=1377765076715820&set=pcb.1377765353382459
>>>>>
>>>>> Can you get to that FB link? Sorry... ;^o
>>>>
>>>> Yes, looks cool.. Can you also shade those fractals?
>>>>
>>>> In desmos it's a bit cumbersome, but still kinda cool effect:
>>>>
>>>> https://www.desmos.com/calculator/kuw9d9ftim
>>>>
>>>
>>> I got it in 3d now. Here is an example:
>>>
>>> https://i.ibb.co/CkHZ98P/ct-p4-Copy.png
>>
>> https://www.facebook.com/photo/? 
>> fbid=1378008770024784&set=pcb.1378008916691436
>>
> 
> Would be nice if you can zoom and view it from all sides. But I guess 
> you can put it on sketchfab for an interactive version.
> 
> https://www.desmos.com/3d/0oepmeegkq

Starting small here. I isolated my spherical projection in a little 
function. It ported fine. Now, all I need to do is hook it up to my 
expand and avoid algorithm... Here is a render of my little test 
function. Green spheres are all tangent to the red sphere. No sphere 
intersects:

https://i.ibb.co/99rvy3Gg/ct-pov.png