On 15.09.2024 11:21, yesbird wrote:
> Hi,
> 
> I found following paper this morning, authors are offering new
> approach to space filling, calling it a 'soft tilings':
> 
> https://academic.oup.com/pnasnexus/article/3/9/pgae311/7754698?login=false
> 

I don't quite see an "innovation". In rectangular bitmap tiling there is 
a well known trick based on "wraparound" processing, allowing to do 
anything, including distortions, producing what the authors called 
"soft" tiling (surely, tiling symmetry remains the same but it's harder 
to see). I did it for web backgrounds before it became a mainstream ;-) 
In fact, I did something like this for "puzzle" preset for my POVRay 
Mosaic, there "thingie" object is defined as:

#declare pin_rad = 0.2;
#declare pin_off = 0.1;
#declare thingie = difference {
     union {
         box{
             <-0.5, -0.5, -0.5>, <0.5, 0.5, 0.5>
         }
         cylinder {
             <-0.5-pin_off, 0, -0.5>, <-0.5-pin_off, 0, 0.5>, pin_rad
         }
         cylinder {
             <0, -0.5-pin_off, -0.5>, <0, -0.5-pin_off, 0.5>, pin_rad
         }
     }
     union {
         cylinder {
             <0.5-pin_off, 0, -1>, <0.5-pin_off, 0, 1>, pin_rad
         }
         cylinder {
             <0, 0.5-pin_off, -1>, <0, 0.5-pin_off, 1>, pin_rad
         }
     }
   scale 0.99
}

  Easy to see that cylinders for pins at one side and cylinders for 
holes at another side are internally linked though "pin_off" variable, 
providing wraparound movement. Now, if one dare to replace cylinders 
with prism control points...

-- 
Ilyich the Toad
https://dnyarri.github.io/

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