MetaFun - Pragma ADE

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A few more details Curve construction
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Just in case you are interested in how such graphical simulations can be organized, we show simplified
versions of the macros used here. (In the previous examples we minimized the complexity
of the code by using buffers, but describing this mechanism is out of the scope of this section.)
We need to loop over all segments of a curve, where for each segment the left and right side sub
curves are handled recursively, upto the requested depth (denoted as n). For this we define the
following macros.
vardef dodrawmidpoints (expr a, b, c, d, n) =
save e, f, g, h, i, j ; pair e, f, g, h, i, j ;
e := .5[a,b] ; f := .5[b,c] ; g := .5[c,d] ;
h := .5[e,f] ; i := .5[f,g] ; j := .5[h,i] ;
draw j ;
if n>1 :
dodrawmidpoints(a, e, h, j, n-1) ;
dodrawmidpoints(j, i, g, d, n-1) ;
fi ;
enddef ;
vardef drawmidpoints (expr p, n) =
save a, b, c, d ; pair a, b, c, d ;
for x=0 upto length(p)-1 :
a := point x of p ; b := postcontrol x of p ;
d := point x+1 of p ; c := precontrol x+1 of p ;
dodrawmidpoints(a, b, c, d, n) ;
endfor ;
enddef ;
We apply this macro to a simple shape:
drawmidpoints (fullcircle xscaled 300pt yscaled 50pt, 1) ;
When drawn, this results in the points that makes up the curve:
We now add an extra iteration (resulting in the yellow points):
drawmidpoints (fullcircle xscaled 300pt yscaled 50pt, 2) ;
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