Pattern function for an n-foil (like a trefoil, but with more Ns). Fits within a
unit circle.

// +fn -f +a0.3 +am2 +r2

#version 3.7;
global_settings{assumed_gamma 1.}
#default{ finish{emission 1} }

#declare CScale = 1.2;
camera{
 orthographic
 right x*2 up y*2
 location -32*z
 look_at 0
 scale CScale
}

/*
 N  = angular symmetry
 CT = circle thickness
 PO = texture z offset
*/
#macro N_Foil(N, CT, PO)

 // angle map for rotation & repetition
 #local A =
  function(x, y){
   floor(atan2(x, y)/pi/2*N+.5)/N*pi*2
  }

 // distance between two rotated points
 #local Dst = vlength(<0, 1>-vrotate(<0, 1>, z*360/N));

 // adjustment for radius and y-translation
 #local Scale = (1-CT) / (1+Dst/2);

 // pattern function
 #local PF =
  function{
   pattern{
    pigment_pattern{
     pigment_pattern{
      planar
      translate -y
      scale CT
     }
     pigment_map{
      [0 rgb 0]
      [.025/CT granite scale .5 translate PO*z]
     }
     translate y*((Dst/2)*Scale+CT)
    }
   }
  }

 // function before repetition
 #local F =
  function{
   pattern{
    function{
     PF(0, sqrt(x*x+pow(max(y, 0), 2)), 0)
    }
    rotate -z*180/N
    translate y*Scale
   }
  }

 // function repeated radially with mirrored x
 F(abs(x*cos(A(x, y)) - y*sin(A(x, y))), x*sin(A(x, y)) + y*cos(A(x, y)), 0)
#end

plane{
 z, 0
 pigment{
  function{N_Foil(7, .075, 1)}
 }
}

torus{1, 1. * CScale / image_width rotate x*90 pigment{rgb<1, .05, .1>}}

Post a reply to this message

Attachments:
Download 'nfoil.jpg' (70 KB)

Preview of image 'nfoil.jpg'

"Samuel B." <stb### [at] hotmailcom> wrote:
> Pattern function for an n-foil

Ideally, the center would be empty, but I don't know how to approach that
problem atm :P

Post a reply to this message

"Samuel B." <stb### [at] hotmailcom> wrote:
> "Samuel B." <stb### [at] hotmailcom> wrote:
> > Pattern function for an n-foil
>
> Ideally, the center would be empty, but I don't know how to approach that
> problem atm :P

#declare Radius = 0.2;
#declare Circle = function {sqrt (x*x + y*y)}

/ function before repetition
 #local F =
 function {
  pattern {
   function{
    //PF(0, sqrt(x*x+pow(max(y, 0), 2)), 0)
    PF(0, max (sqrt(x*x+pow(max(y, 0), 2)), Circle (x, y, z) - Radius), 0)
   }
   rotate -z*180/N
   translate y*Scale
  }
 }


Gives me an N-sided hole in the center.
Not sure how to get it to be an actual circle....

- BW

Post a reply to this message

hi,

"Bald Eagle" <cre### [at] netscapenet> wrote:
> > "Samuel B." <stb### [at] hotmailcom> wrote:
> > > Pattern function for an n-foil

nice, thanks.


> ...
> Not sure how to get it to be an actual circle....

use many "foils" ?  </grin>  (appreciate is not what was meant)


regards, jr.

Post a reply to this message

Attachments:
Download '230806-be.png' (191 KB)

Preview of image '230806-be.png'

"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Samuel B." <stb### [at] hotmailcom> wrote:
> > "Samuel B." <stb### [at] hotmailcom> wrote:
> > > Pattern function for an n-foil
> >
> > Ideally, the center would be empty [...]
>
> [Bald Eagle's code]
>
> Gives me an N-sided hole in the center.
> Not sure how to get it to be an actual circle....
>
> - BW

It's not an easy function to alter, but your solution looks pretty good! I bet
it would help when making rose windows.

I was hoping to make a more traditional shape, but 'tradition' can be a flexible
idea :P

Here's what I came up with this afternoon (with added border):

/*
 N = angular symmetry
 CT = circle/frame thickness
 YC = y-cutoff
 PO = texture z offset
*/
#macro N_Foil(N, CT, YC, PO)

 // angle map for rotation & repetition
 #local A =
  function(x, y){
   floor(atan2(x, y)/pi/2*N+.5)/N*pi*2
  }

 // distance between two rotated points
 #local Dst = vlength(<0, 1>-vrotate(<0, 1>, z*360/N));

 // adjustment for radius and y-translation
 #local Scale = (1-CT) / (1+Dst/2) - CT;

 // pattern function
 #local PF =
  function{
   pattern{
    pigment_pattern{
     pigment_pattern{
      planar
      translate -y
      scale CT
     }
     pigment_map{
      [0 rgb 0]
      [.025/CT granite scale .5 translate PO*z]
     }
    }
   }
  }

 // function before repetition
 #local F =
  function{
   max(
    PF(0, sqrt(x*x+pow(max(y-Scale, -YC), 2))-(Dst/2)*Scale-CT, 0),
    PF(0, -sqrt(x*x+y*y)+1-2*CT, 0)
   )
  }

 // function repeated radially with mirrored x
 F(abs(x*cos(A(x, y)) - y*sin(A(x, y))), x*sin(A(x, y)) + y*cos(A(x, y)), 0)
#end

The eventual plan was to make this work for height_fields or isosurfaces.

Sam

Post a reply to this message

Attachments:
Download 'fnfoilb.jpg' (38 KB)

Preview of image 'fnfoilb.jpg'

"jr" <cre### [at] gmailcom> wrote:
> hi,
>
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> > > "Samuel B." <stb### [at] hotmailcom> wrote:
> > > > Pattern function for an n-foil
>
> nice, thanks.
>

Np.

>
> > ...
> > Not sure how to get it to be an actual circle....
>
> use many "foils" ?  </grin>  (appreciate is not what was meant)
>
> regards, jr.

I see you're using it as intended `;P

Sam

Post a reply to this message

"Samuel B." <stb### [at] hotmailcom> wrote:
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> > "Samuel B." <stb### [at] hotmailcom> wrote:
> > > "Samuel B." <stb### [at] hotmailcom> wrote:
> > > > Pattern function for an n-foil
> > >
> > > Ideally, the center would be empty [...]
> >
> > [Bald Eagle's code]
> >
> > Gives me an N-sided hole in the center.
> > Not sure how to get it to be an actual circle....
> >
> > - BW
>
> Here's what I came up with this afternoon (with added border):
>

And its usage:

plane{
 z, 0
 pigment{
  function{N_Foil(4, .1, .15, 1)}
 }
}

Post a reply to this message

"Samuel B." <stb### [at] hotmailcom> wrote:
>
> Here's what I came up with this afternoon (with added border):
>

And here's the realized object. It uses a height_field for its relief, and CSG
for everything else. It fits within a box of width=.5; height=.5; depth=object
depth.

/*
 N = angular symmetry (int)
 CT = frame/circle thickness
 YC = y-cutoff for inner points
 PO = texture z offset
 RD = relief depth (height field)
 OD = object depth
 Res = height_field resolution x & y (int)
*/
#macro N_Foil_Obj(N, CT, YC, PO, RD, OD, Res)

 #declare Eps = .002; // a small value (for CSG)

 // angle map for rotation & repetition
 #local A =
  function(x, y){
   floor(atan2(x, y)/pi/2*N+.5)/N*pi*2
  }

 // distance between two rotated points
 #local Dst = vlength(<0, 1>-vrotate(<0, 1>, z*360/N));

 // circle y-position, will be also used for radius adjustment
 #local CirY = (1-CT) / (1+Dst/2) - CT;

 // circle radius
 #local CirR = (Dst/2) * CirY;

 #macro N_Foil(N, CT, YC, PO)

  // pattern function
  #local PF =
   function{
    pattern{
     pigment_pattern{
      pigment_pattern{
       planar
       translate -y
       scale CT
      }
      pigment_map{
       [0 rgb 0]
       [.025/CT granite scale .5 translate PO*z]
      }
     }
    }
   }

  // function before repetition
  #local F =
   function{
    max(
     PF(0, sqrt(x*x+pow(max(y-CirY, -YC), 2))-CirR-CT, 0),
     PF(0, -sqrt(x*x+y*y)+1-2*CT, 0)
    )
   }

  // function repeated radially with mirrored x
  #local F_ =
   function{ F(abs(x*cos(A(x, y)) - y*sin(A(x, y))), x*sin(A(x, y)) + y*cos(A(x,
y)), 0) }

  F_(2*(x-.5), 2*(-y+.5), 0)
 #end

 difference{

  // height field
  intersection{
   height_field{
    function Res, Res {
     N_Foil(N, CT, YC, PO)
    }
    smooth
    rotate x*270
    scale <1+Eps, 1+Eps, RD>
    translate -.5*(x+y)
   }
   cylinder{-z*(RD+Eps), z*OD, .5-Eps}
  }

  // x position of inner box cutout (doesn't seem to be 100% correct...)
  #local XP = abs(pow(YC, 2)-pow(CirR, 2));

  // cut out from center from previous object
  #for(I, 0, N-1)
   cylinder{<0, CirY/2, -(RD+Eps)>, <0, CirY/2, OD+Eps>, (CirR-CT)/2+Eps rotate
z*360/N*I}
   box{<-XP-Eps, 0, -(RD+Eps)>, <XP+Eps, CirY/2, OD+Eps> rotate z*360/N*I}
  #end

  // take out objects from between major circle and minor circle
  #if(true)
   intersection{
    cylinder{<0, 0, -(RD+Eps)>, <0,0, OD+Eps>, .5-CT+Eps}
    #for(I, 0, N-1)
     cylinder{<0, CirY/2, -RD>, <0, CirY/2, OD>, (CirR+CT)/2-Eps rotate
z*360/N*I inverse}
    #end
   }
  #end

  translate -z*OD
 }
#end

object{
 N_Foil_Obj(6, 0.1, 0.1, 4.0, 0.05, 0.15, 1024)
 pigment{rgb .75}
}

Post a reply to this message

Attachments:
Download 'fnfoilb-object.jpg' (102 KB)

Preview of image 'fnfoilb-object.jpg'