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celticb.mf
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% a font devised for typesetting certain "Celtic paths"
% (see program CELTIC-PATHS for more details)
% --- Don Knuth, August 2010
mode_setup;
quad#:=13u#;
define_pixels(u,d);
font_size 13u#;
pickup pencircle scaled d;
thick_pen=savepen;
numeric s; s=1.5u*sqrt2;
z0l=(s,13u); z0=(0,13u); z0r=(0,13u-s);
z1l=(8u,13u); z1=(6.5u,13u); z1r=(5u,13u);
z2l=(13u,13u-s); z2=(13u,13u); z2r=(13u-s,13u);
z3l=(13u,5u); z3=(13u,6.5u); z3r=(13u,8u);
z4l=(13u-s,0); z4=(13u,0); z4r=(13u,s);
z5l=(5u,0); z5=(6.5u,0); z5r=(8u,0);
z6l=(0,s); z6=(0,0); z6r=(s,0);
z7l=(0,8u); z7=(0,6.5u); z7r=(0,5u);
z10=dir -45;
z11=down;
z12=dir -135;
z13=left;
z14=dir 135;
z15=up;
z16=dir 45;
z17=right;
path p[][];
for i=0 upto 7:
for j=0 upto 7:
if i<>j:
if (i-j) mod 8 <> 1:
if (j-i) mod 8 <> 1:
if (i mod 2 = 1) or (j mod 2 = 1):
p[i][j]=z[i]l{z[i+10]}...z[j]r{-z[j+10]};
fi
fi
fi
fi
endfor
endfor
path p[][]l;
for j=0 step 2 until 6:
p[j][(j+3)mod 8]l=p[j][(j+3)mod 8]--z[(j+2)mod 8]--cycle;
p[j][(j+5)mod 8]l=p[j][(j+5)mod 8]--z[(j+4)mod 8]--z[(j+2)mod 8]--cycle;
p[j+1][(j+3)mod 8]l=p[j+1][(j+3)mod 8]--z[(j+2)mod 8]--cycle;
p[j+1][(j+4)mod 8]l=p[j+1][(j+4)mod 8]--z[(j+2)mod 8]--cycle;
p[j+1][(j+5)mod 8]l=p[j+1][(j+5)mod 8]--z[(j+4)mod 8]--z[(j+2)mod 8]--cycle;
p[j+1][(j+6)mod 8]l=p[j+1][(j+6)mod 8]--z[(j+4)mod 8]--z[(j+2)mod 8]--cycle;
p[j+1][(j+7)mod 8]l=p[j+1][(j+7)mod 8]--z[(j+6)mod 8]
--z[(j+4)mod 8]--z[(j+2)mod 8]--cycle;
endfor
def filland(expr p,q) =
begingroup picture regp,regq;
regp:=nullpicture;
addto regp contour p;
addto regp doublepath p withpen currentpen;
cull regp keeping (1,infinity);
%display regp inwindow currentwindow; errmessage "regp";
regq:=nullpicture;
addto regq contour q;
addto regq doublepath q withpen currentpen;
cull regq keeping (1,infinity);
%display regq inwindow currentwindow; errmessage "regq";
addto regp also regq;
%display regp inwindow currentwindow; errmessage "regp";
cull regp keeping (2,2);
%display regp inwindow currentwindow; errmessage "regp";
addto currentpicture also regp;
endgroup
enddef;
def begincchar(expr c) =
beginchar(c,quad#,quad#,0);
pickup thick_pen;
z0l=(s,13u); z0=(0,13u); z0r=(0,13u-s);
z1l=(8u,13u); z1=(6.5u,13u); z1r=(5u,13u);
z2l=(13u,13u-s); z2=(13u,13u); z2r=(13u-s,13u);
z3l=(13u,5u); z3=(13u,6.5u); z3r=(13u,8u);
z4l=(13u-s,0); z4=(13u,0); z4r=(13u,s);
z5l=(5u,0); z5=(6.5u,0); z5r=(8u,0);
z6l=(0,s); z6=(0,0); z6r=(s,0);
z7l=(0,8u); z7=(0,6.5u); z7r=(0,5u);
z10=dir -45;
z11=down;
z12=dir -135;
z13=left;
z14=dir 135;
z15=up;
z16=dir 45;
z17=right;
enddef;
boolean charstopping;
charstopping:=false;
def endcchar =
if charstopping:
showit;
errmessage decimal charcode;
fi
endchar;
enddef;
begincchar(oct"40");
fill z0--z2--z4--z6--cycle;
draw z0--z2--z4--z6--cycle;
endcchar;
def singlechar(expr c,i,j) = % "white" is on left of p[i][j]
begincchar(c);
draw p[i][j]l;
fill p[i][j]l;
draw p[j][i]l;
fill p[j][i]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
endcchar;
begincchar(c+1);
draw p[i][j];
filldraw p[j][i]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
endcchar;
enddef;
singlechar(oct"44",3,0);
singlechar(oct"46",5,0);
singlechar(oct"50",1,3);
singlechar(oct"52",1,4);
singlechar(oct"54",1,5);
singlechar(oct"56",1,6);
singlechar(oct"60",1,7);
singlechar(oct"62",2,5);
singlechar(oct"64",2,7);
singlechar(oct"66",3,5);
singlechar(oct"70",3,6);
singlechar(oct"72",3,7);
singlechar(oct"74",4,7);
singlechar(oct"76",5,7);
def doublecharwbw(expr c,i,j,ii,jj) = % two arcs, no overlap, middle black
begincchar(c);
fill p[i][j]l;
draw p[i][j]l;
filland(p[j][i]l,p[jj][ii]l);
fill p[ii][jj]l;
draw p[ii][jj]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+1);
draw p[i][j];
filland(p[j][i]l,p[jj][ii]l);
fill p[ii][jj]l;
draw p[ii][jj]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+2);
fill p[i][j]l;
draw p[i][j]l;
filland(p[j][i]l,p[jj][ii]l);
draw p[ii][jj];
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+3);
draw p[i][j];
filland(p[j][i]l,p[jj][ii]l);
draw p[ii][jj];
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
enddef;
def doublecharbwb(expr c,i,j,ii,jj) = % two arcs, no overlap, middle white
begincchar(c);
draw p[j][i]l;
fill p[j][i]l;
filland(p[i][j]l,p[ii][jj]l);
draw p[jj][ii]l;
fill p[jj][ii]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+3);
draw p[j][i]l;
fill p[j][i]l;
draw p[i][j];
draw p[ii][jj];
draw p[jj][ii]l;
fill p[jj][ii]l;
if j mod 2 = 0: draw z[j]l--z[j]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
enddef;
doublecharwbw(oct"100",5,7,1,3);
doublecharbwb(oct"104",1,7,5,3);
doublecharwbw(oct"110",5,0,1,3);
doublecharbwb(oct"114",2,7,5,3);
doublecharwbw(oct"120",5,7,1,4);
doublecharbwb(oct"124",1,7,6,3);
doublecharbwb(oct"130",3,0,7,5);
doublecharbwb(oct"134",1,7,5,2);
doublecharwbw(oct"140",4,7,1,3);
doublecharbwb(oct"144",1,6,5,3);
doublecharwbw(oct"150",5,0,1,3);
doublecharbwb(oct"154",2,7,6,3);
doublecharbwb(oct"160",3,0,7,4);
doublecharbwb(oct"164",1,6,5,2);
path cuttings; % what got cut off
tertiarydef a cutbefore b = % tries to cut as little as possible
begingroup save t;
(t, whatever) = a intersectiontimes b;
if t<0:
cuttings:=point 0 of a;
a
else: cuttings:= subpath (0,t) of a;
subpath (t,length a) of a
fi
endgroup
enddef;
tertiarydef a cutafter b =
reverse (reverse a cutbefore b)
hide(cuttings:=reverse cuttings)
enddef;
def doublechar(expr c,i,j,ii,jj) = % i j under ii jj; (i ii j jj) ctrclkwise
begincchar(c);
filland(p[i][j]l,p[jj][ii]l);
filland(p[i][j]l,p[ii][jj]l);
filland(p[j][i]l,p[jj][ii]l);
filland(p[j][i]l,p[ii][jj]l);
draw p[ii][jj];
draw p[jj][ii];
if ii mod 2 = 0: draw z[ii]l--z[ii]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+1);
draw p[i][j] cutafter p[jj][ii];
filland(p[i][j]l,p[ii][jj]l);
filland(p[j][i]l,p[jj][ii]l);
filland(p[j][i]l,p[ii][jj]l);
draw p[ii][jj];
draw p[jj][ii];
if ii mod 2 = 0: draw z[ii]l--z[ii]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+2);
filland(p[i][j]l,p[jj][ii]l);
filland(p[i][j]l,p[ii][jj]l);
filland(p[j][i]l,p[jj][ii]l);
draw p[j][i] cutafter p[ii][jj];
draw p[ii][jj];
draw p[jj][ii];
if ii mod 2 = 0: draw z[ii]l--z[ii]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
begincchar(c+3);
draw p[i][j] cutafter p[jj][ii];
filland(p[i][j]l,p[ii][jj]l);
filland(p[j][i]l,p[jj][ii]l);
draw p[j][i] cutafter p[ii][jj];
draw p[ii][jj];
draw p[jj][ii];
if ii mod 2 = 0: draw z[ii]l--z[ii]r; fi
if jj mod 2 = 0: draw z[jj]l--z[jj]r; fi
endcchar;
enddef;
doublechar(oct"170",4,1,0,3);
doublechar(oct"174",5,2,6,3);
doublechar(oct"200",7,4,0,5);
doublechar(oct"204",6,1,7,2);
doublechar(oct"210",5,1,0,3);
doublechar(oct"214",5,2,7,3);
doublechar(oct"220",5,1,7,4);
doublechar(oct"224",6,1,7,3);
doublechar(oct"230",7,3,0,5);
doublechar(oct"234",5,1,7,2);
doublechar(oct"240",4,1,7,3);
doublechar(oct"244",5,1,6,3);
doublechar(oct"250",6,1,0,3);
doublechar(oct"254",5,2,0,3);
doublechar(oct"260",5,2,7,4);
doublechar(oct"264",6,1,7,4);
doublechar(oct"270",7,1,0,5);
doublechar(oct"274",4,1,7,2);
doublechar(oct"300",4,1,6,3);
doublechar(oct"304",6,3,0,5);
doublechar(oct"310",7,1,0,3);
doublechar(oct"314",3,1,5,2);
doublechar(oct"320",5,3,7,4);
doublechar(oct"324",6,1,7,5);
doublechar(oct"330",7,1,0,5);
doublechar(oct"334",3,1,7,2);
doublechar(oct"340",4,1,5,3);
doublechar(oct"344",6,3,7,5);
doublechar(oct"350",6,1,0,5);
doublechar(oct"354",7,2,0,3);
doublechar(oct"360",4,1,5,2);
doublechar(oct"364",6,3,7,4);
def lambdachar(expr a,b,c,d) =
begincchar(8a+4b+2c+d);
draw p[3][7]; draw p[7][3];
if a=0: filland(p[1][5]l,p[3][7]l); else: draw p[1][5] cutbefore p[3][7]; fi
if b=0: filland(p[3][7]l,p[5][1]l); else: draw p[5][1] cutafter p[3][7]; fi
if c=0: filland(p[5][1]l,p[7][3]l); else: draw p[5][1] cutbefore p[7][3]; fi
if d=0: filland(p[7][3]l,p[1][5]l); else: draw p[1][5] cutafter p[7][3]; fi
endcchar;
enddef;
lambdachar(0,0,0,0);
lambdachar(0,0,0,1);
lambdachar(0,0,1,0);
lambdachar(0,0,1,1);
lambdachar(0,1,0,0);
lambdachar(0,1,0,1);
lambdachar(0,1,1,0);
lambdachar(0,1,1,1);
lambdachar(1,0,0,0);
lambdachar(1,0,0,1);
lambdachar(1,0,1,0);
lambdachar(1,0,1,1);
lambdachar(1,1,0,0);
lambdachar(1,1,0,1);
lambdachar(1,1,1,0);
lambdachar(1,1,1,1);
font_quad:=13u#;
font_normal_space:=13u#;
font_normal_stretch:=0;
font_normal_shrink:=0;
font_identifier:="CELTICB";
font_coding_scheme:="bizarre";
bye.
showit; errmessage "blank";
charstopping:=true;
secondarydef p then q =
begingroup pair t; t=p intersectiontimes q;
subpath (0,xpart t) of p & subpath(ypart t,1) of q
endgroup
enddef;