OpenSCAD User Manual/undersized circular objects

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When using cylinder() with difference() to place holes in objects, the holes will be undersized. This is because circular paths are approximated with polygons inscribed within in a circle. The points of the polygon are on the circle, but straight lines between are inside. This is discussed in some detail at http://hydraraptor.blogspot.com.au/2011/02/polyholes.html

While the standard cylinder() and circle() generate inner (inscribed) polygons, here are modules to produce outer (circumscribed) and mid ( 1/2 way between) polygons.

cylinder[edit]

 module cylinder_outer(height,radius,fn){
   fudge = 1/cos(180/fn);
   cylinder(h=height,r=radius*fudge,$fn=fn);}
 module cylinder_mid(height,radius,fn){
   fudge = (1+1/cos(180/fn))/2;
   cylinder(h=height,r=radius*fudge,$fn=fn);}
Example of outer and mid cylinder
partial view
 //example script to show differences
 cylinder_outer(5,100,6);
 %cylinder_mid(5.5,100,6);
 cylinder(6,r=100,$fn=6);        // standard
 #cylinder(5.75,r=100,$fn=60);   // reference
 //CSG tree for this example
 group() {
   group() {
     cylinder($fn = 6, $fa = 12, $fs = 2, h = 5, r1 = 115.47, r2 = 115.47, center = false);
   }
 % group() {
     cylinder($fn = 6, $fa = 12, $fs = 2, h = 5.5, r1 = 107.735, r2 = 107.735, center = false);
   }
   cylinder($fn = 6, $fa = 12, $fs = 2, h = 6, r1 = 100, r2 = 100, center = false);
 # cylinder($fn = 60, $fa = 12, $fs = 2, h = 5.75, r1 = 100, r2 = 100, center = false);
 }

cone[edit]

For cylinders with different top and bottom radii

 module cone_outer(height,radius1,radius2,fn){
   fudge = 1/cos(180/fn);
   cylinder(h=height,r1=radius1*fudge,r2=radius2*fudge,$fn=fn);}
 module cone_mid(height,radius1,radius2,fn){
   fudge = (1+1/cos(180/fn))/2;
   cylinder(h=height,r1=radius1*fudge,r2=radius2*fudge,$fn=fn);}
 cone_outer(5 ,10 ,5 ,6);
 cone_mid(5 ,10 ,5 ,6);

circle[edit]

And lastly not to forget the 2D world

   module circle_outer(radius,fn){
     fudge = 1/cos(180/fn);
     circle(r=radius*fudge,$fn=fn);}
   module circle_mid(radius,fn){
     fudge = (1+1/cos(180/fn))/2;
     circle(r=radius*fudge,$fn=fn);}
 circle_outer(20,6);
 circle_mid(20,6);