POV-Ray : Newsgroups : povray.general : Fitting a gothic trefoil into an equilateral triangle : Re: Fitting a gothic trefoil into an equilateral triangle Server Time
4 Aug 2024 08:22:12 EDT (-0400)
  Re: Fitting a gothic trefoil into an equilateral triangle  
From: LinuxLibrarian
Date: 13 Jun 2003 09:01:27
Message: <3ee9cb27@news.povray.org>

> // Hi LibraryMan,
> //
> // here is some code for you to play with; the radius of the circles
> // can be specified:
> //
> //    Side * (sqrt(3)-1)/4   circles are mutually touching
> //    Side * sqrt(3)/9       circles intersect in midpoint ("true gothic")
> //    Side * sqrt(3)/6       circles have max. size (all are equal)
> //
> // The distance of the centers (distance AB as named in your link) is
> //
> //    Side-2*sqrt(3)*Radius
> //
> //
> //
> // Sputnik
> //
> //
> // ----------------------------

> // fr### [at] computermuseumfh-kielde
> // ----------------------------
> 
> 
> // +W640 +H480 -F +D +A0.1
> 
> // macro for trefoil ====================================================
> 
> #macro Trefoil (Side, Radius) // lower left corner at origin
> 
>   #local R = 0.005; // "Linewidth"/2
> 
>   #local Height  = sqrt(3)/2*Side;
> 
>   #local Corner1 = <Side/2, Height, 0>; // top corner
>   #local Corner2 = 0; // bottom left corner
>   #local Corner3 = Side*x; // bottom right corner
> 
>   #local Center  = <Side/2, Height/3, 0>; // triangle
> 
>   #local Center1 = <Side/2, Height-2*Radius, 0>; // top circle
>   #local Center2 = <sqrt(3)*Radius, Radius, 0>; // bottom left circle
>   #local Center3 = <Side-sqrt(3)*Radius, Radius, 0>; // bottom right circle
> 
>   union {
>     union {
>       sphere { Corner1, R }
>       sphere { Corner2, R }
>       sphere { Corner3, R }
>       cylinder { Corner1, Corner2, R }
>       cylinder { Corner2, Corner3, R }
>       cylinder { Corner3, Corner1, R }
>       texture { pigment { color green 1 } finish { ambient 1 } }
>       }
>     union {
>       torus { Radius, R rotate 90*x translate Center1 }
>       torus { Radius, R rotate 90*x translate Center2 }
>       torus { Radius, R rotate 90*x translate Center3 }
>       texture { pigment { color red 1 } finish { ambient 1 } }
>       }
>     // "}" omitted to allow application of transformations
> 
>   #end//macro Trefoil
> 
> 
> // simple scene with trefoils ===========================================
> 
> Trefoil ( 1  , 1*(sqrt(3)-1)/4 ) translate <-1.6,  0.2  , 1> } // small
> Trefoil ( 2  , 2*sqrt(3)/9     ) translate <-1  , -1    , 1> } // gothic
> Trefoil ( 1  , 1*sqrt(3)/6     ) translate < 0.6,  0.2  , 1> } // large
> 
> light_source { <-1500, 2500, -2000>, color rgb 1 }
> 
> camera { orthographic up 3*y right 4*x }
> 
> 
> // END ==================================================================
> 
> 
Thanks, I'll play with this too! (not to confuse people, but LibraryMan 
and LinuxLibrarian are the same person, but LibraryMan is my screen name 
for when I'm posting via the web interface to the newsgroup)
--LinuxLibrarian


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