Nice work! Will the source be available?

(I'm getting an error on the link)

Looks really great. Would it be too much to suggest some kind of tension parameter, to move from squarer – rounder versions of the font?

Edit: Actually is that what this "half' command is: superhalfs. Or your nilus arc,

Which by the way what was the correction you made with that exactly? I'm also trying to do italics in Metafont and finding it difficult to compensate correctly)

Also what is -randup?

2nd Edit: you may be interested in Dexter Sinister's metafont, 'Meta-the-difference-between-the-two-Font' – which looks like it's Metafont logo derived.

There is already a global parameter ("superness") that makes the font squarer or rounder. E. g. the script styles have superness=0.75 instead of superness=0.8. After having published the sources, everyone may produce easily new font styles by just redefining the global parameters.

"half" is nothing really special, it is just the concatenation of two arcs and arcs are not really special (nilus arcs are a bit more complex) as the font is penbased. Have a look at the following picture and then you may have a look at the definitions of "arc", "half" and "circle":


%this is for arc, it is just the algebraic solution of
%zi+whatever*diri=zj+whatever*dirj
%but I did not want to save any variables here
def corner(expr zi,diri,zj,dirj) =
(
xpart(zi)
-xpart(diri/length(diri))/(ypart(diri/length(diri))
*xpart(dirj/length(dirj))-xpart(diri/length(diri))
*ypart(dirj/length(dirj)))*(xpart(dirj/length(dirj))
*(ypart(zi)-ypart(zj))+ypart(dirj/length(dirj))
*(xpart(zj)-xpart(zi)))
,
ypart(zi)
-ypart(diri/length(diri))/(ypart(diri/length(diri))
*xpart(dirj/length(dirj))-xpart(diri/length(diri))
*ypart(dirj/length(dirj)))*(xpart(dirj/length(dirj))
*(ypart(zi)-ypart(zj))+ypart(dirj/length(dirj))
*(xpart(zj)-xpart(zi)))
)
enddef;


%a quarter of a superellipse
def arc(expr zi,diri,zj,dirj) =
zi{diri}
...zi
+superness*(corner(zi,diri,zj,dirj)-zi)
-(1-superness)*(corner(zi,diri,zj,dirj)-zj)
...zj{dirj}
enddef;


%half a superellipse
def half(expr zi,diri,zj,dirj,zk,dirk) =
arc(zi,diri,zj,dirj)
& arc(zj,dirj,zk,dirk)
enddef;


%full superellipse
def full(expr zi,diri,zj,dirj,zk,dirk,zl,dirl) =
arc(zi,diri,zj,dirj)
& arc(zj,dirj,zk,dirk)
& arc(zk,dirk,zl,dirl)
& arc(zl,dirl,zi,diri)
enddef;


The "-randup" is just like the direction "(0,-1)" but with some noise (which is only applied for the script styles). I was too lazy to define a "random down" so it is kind of "- random up".

To the nilus arc: I have worked out a clearer solution of it a long time ago but never wrote it down in METAFONT. But the principle stays the same, so here is the old code snippet (and I am aware that it is ugly, sorry):


vardef computearcpoints(suffix $,$)(expr lsupcorr,rsupcorr) = % private definition for computations of arcpoints
pair originall,originalr,centerl,centerr,cornerl,cornerr,betweenl,betweenr,extremuml,extremumr;
if (xpart(z$r-z$r)>0) and (ypart(z$r-z$r)<0) %lower left
or (xpart(z$r-z$r)<0) and (ypart(z$r-z$r)>0): %upper right
originall=(1/(length(up slanted slant)))[.5[z$l,z$r],z$l]; %later there will be some slanting calculations and we redo them now
originalr=(1/(length(up slanted slant)))[.5[z$l,z$r],z$r];
%originall=z$l;
%originalr=z$r;
centerl=(x$l,ypart(originall));
centerr=(x$r,ypart(originalr));
cornerl=(xpart(originall),y$l);
cornerr=(xpart(originalr),y$r);
else: %lower right and upper left
originall=(1/(length(up slanted slant)))[.5[z$l,z$r],z$l];
originalr=(1/(length(up slanted slant)))[.5[z$l,z$r],z$r];
centerl=(x$l,ypart(originall));
centerr=(x$r,ypart(originalr));
cornerl=(xpart(originall),y$l);
cornerr=(xpart(originalr),y$r);
fi
betweenr=(length(((z$r-z$r)/length((z$r-z$r)))slanted slant)*0.5+0.5)
[((1+rsupcorr)*superness)[centerl,cornerl],
((1+rsupcorr)*superness)[centerr,cornerr]];
betweenl=(length(((z$l-z$l)/length((z$l-z$l)))slanted slant)*0.5+0.5)
[((1+lsupcorr)*superness)[centerr,cornerr],
((1+lsupcorr)*superness)[centerl,cornerl]];
%--calculate extrema for slanted bows:---
if slant>0:
if (xpart(z$r-z$r)>0) and (ypart(z$r-z$r)<0): %lower left
extremuml=directionpoint (slant,-1) of (z$l{cornerl-z$l}...betweenl{z$l-z$l});
extremumr=directionpoint (slant,-1) of (z$r{cornerr-z$r}...betweenr{z$r-z$r});
elseif (xpart(z$r-z$r)<0) and (ypart(z$r-z$r)>0): %upper right
extremuml=directionpoint (-slant,1) of (z$l{cornerl-z$l}...betweenl{z$l-z$l});
extremumr=directionpoint (-slant,1) of (z$r{cornerr-z$r}...betweenr{z$r-z$r});
fi
else:
if (xpart(z$r-z$r)>0) and (ypart(z$r-z$r)<0) %lower left
or (xpart(z$r-z$r)<0) and (ypart(z$r-z$r)>0): %upper right
extremuml=z$l;
extremumr=z$r;
fi
fi
enddef;


vardef pulled_arc.l(suffix $,$)(expr lsupcorr,rsupcorr) = % inside of arc
computearcpoints($,$,lsupcorr,rsupcorr);
z$l{cornerl-z$l}...betweenl{z$l-z$l}
...{z$l-cornerl}z$l
enddef;


vardef pulled_arc.r(suffix $,$)(expr lsupcorr,rsupcorr) = % outside of arc
computearcpoints($,$,lsupcorr,rsupcorr);
z$r{cornerr-z$r}...betweenr{z$r-z$r}
...{z$r-cornerr}z$r
enddef;


vardef arc.l(suffix $,$) = % inside of arc
pulled_arc.l($,$,0,0)
enddef;


vardef arc.r(suffix $,$) = % outside of arc
pulled_arc.r($,$,0,0)
enddef;


Meanwhile, I have published the font on CTAN.