manfnt.mf

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

% Special font for the TeX and METAFONT manuals
% This file was prepared "hastily" and hasn't been "polished".
% In particular, some characters won't work when aspect_ratio<>1.

font_size 10pt#;
em#:=10pt#; ht#:=250/36pt#;
mode_setup;

font_identifier "MANFNT";
font_coding_scheme "PI";

message "Hex symbols";
width1#=.4pt#*(ht#/(100/36pt#));
width2#=.6pt#*(ht#/(100/36pt#));
define_blacker_pixels(width1,width2);

beginchar(1,2ht#,ht#,0); "Original hex";  % \hexa
pickup pencircle scaled width1;
w:=2good.x .5w;
x1=x4=good.x 0; x2=x5=.5w; x3=x6=good.x w;
y1=y2=y3=good.y h; y4=y5=y6=good.y 0;
draw z1..z6; draw z2..z5; draw z3..z4;
for k=1 upto 6: drawdot z[k]; endfor
labels (1,2,3,4,5,6); endchar;

beginchar(2,2ht#,ht#,0); "Top/bot adjusted hex";  % \hexb
pickup pencircle scaled width1;
w:=2good.x .5w;
x1=x4=good.x 0; x2=x5=.5w; x3=x6=good.x w;
top y1=h; y1=y2=y3; bot y4=0; y4=y5=y6;
draw z1..z6; draw z2..z5; draw z3..z4;
for k=1 upto 6: drawdot z[k]; endfor
labels (1,2,3,4,5,6); endchar;

beginchar(3,2ht#,ht#,0); "Bold top/bot adjusted hex";  % \hexc
pickup pencircle scaled width2;
w:=2good.x .5w;
x1=x4=good.x 0; x2=x5=.5w; x3=x6=good.x w;
top y1=h; y1=y2=y3; bot y4=0; y4=y5=y6;
draw z1..z6; draw z2..z5; draw z3..z4;
for k=1 upto 6: drawdot z[k]; endfor
labels (1,2,3,4,5,6); endchar;

beginchar(4,2ht#,ht#,0); "Bold top/bot/lft/rt adjusted hex";  % \hexd
pickup pencircle scaled width2;
w:=2good.x .5w;
lft x1=0; x1=x4; x2=x5=.5w; rt x3=w-1; x3=x6;
top y1=h; y1=y2=y3; bot y4=0; y4=y5=y6;
draw z1..z6; draw z2..z5; draw z3..z4;
for k=1 upto 6: drawdot z[k]; endfor
labels (1,2,3,4,5,6); endchar;

beginchar(5,2ht#,ht#,0); "Hex corrected for darkness in the center"; % \hexe
pickup pencircle scaled width1;
w:=2good.x .5w;
top z1=(0,h); top z2=(.5w,h); top z3=(w,h);
bot z4=(0,0); bot z5=(.5w,0); bot z6=(w,0);
for k=1 upto 6: drawdot z[k]; endfor
z1'=.25[z1,z6]; z6'=.75[z1,z6]; theta1:=angle(z6-z1)+90;
z3'=.25[z3,z4]; z4'=.75[z3,z4]; theta3:=angle(z4-z3)+90;
z7=z8=.5[z1,z6];
penpos1'(width1,theta1); penpos6'(width1,theta1); penpos7(.6width1,theta1);
penpos3'(width1,theta3); penpos4'(width1,theta3); penpos8(.6width1,theta3);
draw z1..z1'; penstroke z1'e{z6'-z1'}..z7e..{z6'-z1'}z6'e; draw z6'..z6;
draw z2..z5;
draw z3..z3'; penstroke z3'e{z4'-z3'}..z8e..{z4'-z3'}z4'e; draw z4'..z4;
penlabels(1,1',7,2,3,3',8,4,4',5,6,6'); endchar;

message "Stick A's";
b#:=250/36pt#; a#:=150/36pt#; s#:=30/36pt#;
standardwidth#:=.4pt#;
darkwidth#:=.8pt#; lightwidth#:=.2pt#;
define_blacker_pixels(standardwidth,darkwidth,lightwidth);
define_pixels(b,a,s);
def stick_A(expr alpha)(text pentype)=
beginchar (incr(charcode),s#+a#+s#,b#,0);
pickup pentype;
bot z1=(good.x s,0); z5=z1+(a,0);
z3=(1/2[x1,x5],good.y b);
z2=alpha[z1,z3]; z4=alpha[z5,z3];
draw z1..z3; draw z3..z5; draw z2..z4;
drawdot z1; drawdot z5; drawdot z3;
labels(1,2,3,4,5); endchar; enddef;
charcode:=5; % the first A will be number 6

stick_A((3-sqrt5)/2, % (area above bar / area below) = golden ratio % \Aa
 pencircle scaled standardwidth);

for alpha=.2 step .05 until .5+10epsilon:
 stick_A(alpha,pencircle scaled standardwidth); endfor % chars 7..13

beginchar(14,s#+a#+s#,b#,0);
pickup pencircle scaled standardwidth;
bot z1=(good.x s,0); z5=z1+(a,0);
z3=(1/2[x1,x5],good.y b);
z4-z2=whatever*dir20; 1/2[y2,y4]=2/3[y3,y1];
z2=whatever[z1,z3]; z4=whatever[z3,z5];
draw z1..z3; draw z3..z5; draw z2..z4;
drawdot z1; drawdot z5; drawdot z3;
labels(1,2,3,4,5); endchar;

stick_A((3-sqrt5)/2,pencircle xscaled darkwidth yscaled lightwidth); % \Ab=15
stick_A((3-sqrt5)/2,
 pencircle xscaled darkwidth yscaled lightwidth rotated 30); % \Ac=16

message "Kidney beans";
standardwidth#:=.4pt#;
darkwidth#:=.8pt#; lightwidth#:=.2pt#;
define_blacker_pixels(standardwidth,darkwidth,lightwidth);
b#:=100/36pt#;
define_pixels(b);
def bean(text pentype)=
beginchar (incr(charcode),2b#,1.5b#,0);
pickup pentype;
z1=(0,b); z2=(b,b); z3=(2b,b);
z4=(0,0); z5=(b,0); z6=(2b,0);
draw z5..z4..z1..z3..z6..cycle;
labels(1,2,3,4,5,6); endchar; enddef;
charcode:=16; % the first bean will be number 17

bean(pencircle scaled standardwidth);  % \beana=17
bean(pencircle scaled darkwidth);  % \beanb=18
bean(pencircle xscaled darkwidth yscaled lightwidth); % \beanc=19
bean(pencircle xscaled darkwidth yscaled lightwidth rotated 30); % \beand=20

message "Pen nibs";
bigthickwidth#:=8pt#; littlethickwidth#:=2pt#;
define_blacker_pixels(bigthickwidth,littlethickwidth);

beginchar(21,bigthickwidth#,0,0);  % \niba
pickup pencircle xscaled bigthickwidth yscaled littlethickwidth;
lft z1=(0,good.y 0);
drawdot z1;
labels(1); endchar;

beginchar(22,bigthickwidth#,0,0);  % \nibb
pickup pencircle xscaled bigthickwidth yscaled littlethickwidth rotated 30;
lft z1=(0,good.y 0);
drawdot z1;
labels(1); endchar;

beginchar(23,littlethickwidth#,0,0);  % \nibc
pickup pencircle yscaled bigthickwidth xscaled littlethickwidth;
lft z1=(0,good.y 0);
drawdot z1;
labels(1); endchar;

message "Ionian letters";
em#:=10pt#; cap#:=7pt#;
thin#:=1/3pt#; thick#:=5/6pt#;
slab#:=.8pt#;
stem#:=.9pt#;
o#:=1/5pt#;

define_pixels(em,cap);
define_blacker_pixels(thin,thick,slab,stem);
define_corrected_pixels(o);

curve_sidebar=round 1/18em;

%vardef pentaper@#(expr lt,rt) = % dropped from PLAIN
% x@#l:=lt[x@#l,x@#]; x@#r:=rt[x@#r,x@#];
% y@#l:=lt[y@#l,y@#]; y@#r:=rt[y@#r,y@#] enddef;


% ill-fated example wasn't attractive enough by itself:
%bar:=slab;
%beginchar(24,0.6em#,cap#,0); % "The letter T"; \IOT=24
%penpos1(bar,70);
%penpos2(bar,35);
%penpos4(bar,35);
%penpos5(bar,55);
%x1=0; y1r=h; y2r=y4r=.2[y1r,y1]; y5l=.3[y1l,y1];
%x2l=1/3[x1l,x5l]; x4l=2/3[x1l,x5l]; x5=w;
%penpos6(stem,20); pentaper6(.1,0);
%penpos3(x6r-x6l,0);
%penpos7(stem,10);
%y3=y2; x3=.5w;
%x6r=x3r; y6=2/3h;
%x7=x6; y7=0;
%penstroke z1e{curl infinity}..z2e..z4e..{curl infinity}z5e;
%penstroke z3e..z6e{down}..z7e;
%labels.top(1r,2l,2,2r,4l,4,4r,6);
%labels.lft(1,1l,6l);
%labels.rt(5,5r,5l,6r);
%labels.bot(3l,3,3r,7,7r,7l);
%endchar;

beginchar(25,5/9em#,cap#,0); % "The letter S"; /IOS=25
penpos1(slab,70);
penpos2(.5slab,80);
penpos3(.5[slab,thick],200);
penpos5(.5[slab,thick],210);
penpos6(.7slab,80);
penpos7(.25[slab,thick],72);
x1=x5; y1r=.94h+o;
x2=x4=x6=.5w; y2r=h+o; y4=.54h; y6l=-o;
x3r=.04em; y3=.5[y4,y2];
x5l=w-.03em; y5=.5[y4,y6];
.5[x7l,x7]=.04em; y7l=.12h-o;
path trial; trial=z3{down}..z4..{down}z5;
pair dz; dz=direction 1 of trial;
penpos4(thick,angle dz-90);
penstroke z1e..z2e{left}..z3e{down}..z4e{dz}..z5e{down}..z6e{left}..z7e;
labels.lft(2,3r,5r,6,7);
labels.rt(1,3l,4,5l);
labels.top(1r,2r,3,4l,5,6r,7r);
labels.bot(1l,2l,4r,6l,7l);
endchar;

beginchar(26,0.8em#,cap#,0); % "The letter O"; \IOO=26
 penpos1(thick,10); penpos2(.1[thin,thick],90-10);
 penpos3(thick,180+10); penpos4(thin,270-10);
 x1l=w-x3l=curve_sidebar; x2=x4=.5w;
 y1=.49h; y2l=-o; y3=.51h; y4l=h+o;
 penstroke z1e{down}..z2e{right}..z3e{up}..z4e{left}..cycle;
 penlabels(1,2,3,4); endchar;

beginchar(27,.35em#,cap#,0); % "The letter I"; \IOI=27
 penpos1(stem,15); penpos2(.9stem,12); penpos3(stem,10);
 x1=x2=x3=.5w; y1=h; y2=.55h; y3=0; x2l:=1/6[x2l,x2];
 penstroke z1e..z2e{down}..z3e;
 penlabels(1,2,3); endchar;

%ligtable 24: 24 kern .05em#, 26 kern -.05em#; % TT and TO are adjusted

message "Cubes and such";
s#:=5pt#; define_pixels(s); % side of the square
beginchar(28,5/3s#,4/3s#,0); % "Possible cube"; \cubea=28
z1=(-epsilon,-epsilon);  z2=(s+epsilon,-epsilon);
  z3=(-epsilon,s+epsilon); z4=(s+epsilon,s+epsilon);
for k=1 upto 4: z[k+4]=z[k]+(2/3s,1/3s); endfor
pickup pencircle scaled .4pt;
draw z5--z6--z8--z7--cycle;
pickup pencircle scaled 1.6pt;
erase draw z2--z4--z3;
pickup pencircle scaled .4pt;
draw z1--z2--z4--z3--cycle;
for k=1 upto 4:  draw z[k]--z[k+4]; endfor
labels.top(1,2,5,6);
labels.bot(3,4,7,8);
endchar;

beginchar(29,5/3s#,4/3s#,0); % "Impossible cube"; \cubeb=29
z1=(-epsilon,-epsilon);  z2=(s+epsilon,-epsilon);
  z3=(-epsilon,s+epsilon); z4=(s+epsilon,s+epsilon);
for k=1 upto 4: z[k+4]=z[k]+(2/3s,1/3s); endfor
pickup pencircle scaled .4pt;
draw z3--z4; draw z5--z6;
cullit; pickup pencircle scaled 1.6pt;
undraw z7--1/2[z7,z5];
 undraw z2--1/2[z2,z4];
cullit; pickup pencircle scaled .4pt;
draw z3--z1--z2--z4;
 draw z5--z7--z8--z6;
for k=1 upto 4:  draw z[k]--z[k+4]; endfor
labels.top(1,2,5,6);
labels.bot(3,4,7,8);
endchar;

beginchar(30,10pt#,7pt#,2pt#); % bicentennial star
pair center; center=(.5w,2pt);
numeric radius; radius=5pt;
for k=0 upto 4: z[k]=center+(radius,0) rotated(90+360/5k); endfor
def :: = ..tension 5.. enddef;
path star; star=z0::z2::z4::z1::z3::cycle;
pickup pencircle scaled .4pt; draw star;
cullit;  pickup pencircle scaled 1.6pt;
for k=0 upto 4: undraw subpath(k+.55,k+.7) of star; endfor
cullit;  pickup pencircle scaled .4pt;
for k=0 upto 4: draw subpath(k+.47,k+.8) of star; endfor
labels(0,1,2,3,4); endchar;

beginchar(31,2/3*11pt#,.5*11pt#,0); % \oneu=31
pickup pencircle scaled 3/4pt yscaled 1/3 rotated 30;
save ww; ww=3/2w;
save t; transform t;
t=identity rotatedaround((.5ww,h),-90);
x2=.35ww; x3=good.x .6ww;
y2=good.y .2h; top y3=round .8h+eps;
save p; path p; p=z2{right}...{up}z3;
top z1=point .5 of p transformed t;
draw (z1...p);
labels(1,2,3); endchar;

beginchar(38,11pt#,11pt#,0); % \fouru=38
pickup pencircle scaled 3/4pt yscaled 1/3 rotated 30;
save t; transform t;
t=identity rotatedaround((.5w,.5h),-90);
x2=.35w; x3=good.x .6w;
y2=good.y .1h; top y3=round .4h+eps;
save p; path p; p=z2{right}...{up}z3;
top z1=point .5 of p transformed t;
draw (z1...p);
addto currentpicture also currentpicture transformed t;
addto currentpicture also currentpicture transformed(t transformed t);
labels.bot(1,3); labels.rt(2); endchar;

beginchar(39,11pt#,11pt#,0); % \fourc=39
pickup pencircle scaled 3/4pt yscaled 1/3 rotated 30;
save t; transform t;
t=identity rotatedaround((.5w,.5h),-90);
x2=.35w; x3=good.x .6w;
y2=good.y .1h; top y3=round .4h+eps;
save p; path p; p=z2{right}...{up}z3;
top z1=point .5 of p transformed t;
draw (z1...p) rotatedaround((.5w,.5h),-45)
 withpen pencircle scaled 3/4pt yscaled 1/3 rotated-15;
addto currentpicture also currentpicture transformed t;
addto currentpicture also currentpicture transformed(t transformed t);
labels.bot(1,3); labels.rt(2); endchar;

message "Circle variations";

beginchar(32,5pt#,5pt#,0); "Quarter circle";  % \circa
pickup pencircle scaled (.4pt+blacker);
draw quartercircle scaled 10pt; endchar;

beginchar(33,5pt#,5pt#,0); "Filled quarter circle";  % \circb
fill ((0,0)--quartercircle--cycle) scaled 10pt; endchar;

beginchar(34,5pt#,5pt#,0); "Rotated quarter circle";  % \circc
pickup pencircle scaled (.4pt+blacker);
draw quartercircle rotated 90 scaled 10pt shifted (5pt,0); endchar;

beginchar(35,5pt#*sqrt2,5pt#,0); "Cone";  % \circd
pickup pencircle scaled (.4pt+blacker);
draw ((0,0)--quartercircle--cycle)
 rotated 45 scaled 10pt shifted (.5w,0); endchar;

beginchar(36,10pt#,7.5pt#,2.5pt#); "Concentric circles";  % \circe
pickup pencircle scaled (.4pt+blacker);
for D=.2w,.6w,w:
 draw fullcircle scaled D shifted (.5w,.5[-d,h]);
 endfor endchar;

beginchar(37,10pt#,7.5pt#,2.5pt#); "Concentric diamonds";  % \circf
pickup pencircle scaled (.4pt+blacker);
for D=.2w,.6w,w:
 draw unitsquare shifted -(.5,.5) rotated 45
  scaled (D/sqrt2) shifted (.5w,.5[-d,h]);
 endfor endchar;

message "Miscellaneous symbols"; % mostly from the old manfnt

beginchar(oct"171",15pt#,7.5pt#,2.5pt#); % arrow for errata lists
curve#:=30/36pt#; dcurve#:=60/36pt#; bar#:=25/36pt#;
define_whole_blacker_pixels(curve,dcurve,bar);
penpos1(curve,90); penpos2(curve,90); penpos3(dcurve,90);
penpos4(dcurve,90); penpos5(curve,90); penpos6(curve,90);
y1r=vround(y1r-(y1-.5[-d,h])); y2=y5=y6=y1=y0; y4l=-d; y3r=h;
x1=0; x2=.1w; x3=.2w; x4=.55w; x5=.65w;
x2l:=x2l+.25curve; x5r:=x5r-.25curve;
penstroke z1e--z2e--z3e--z4e--z5e;    % crooked arrow
penpos13(bar,0); penpos14(bar,0); x0=w;
y13-y0=y0-y14=.24h+eps; x13=x14=7/8w-eps;
penpos15(.5bar,angle(z14-z0)); z15l=z0; penpos16(.5bar,angle(z13-z0)); z16l=z0;
z19=.381966[.5[z13,z14],z0];
numeric t; path p; p=z14l{z19-z14}..z16r;
t=xpart(p intersectiontimes((0,y6l)--(w,y6l))); x6=xpart point t of p;
filldraw z0..{z14-z19}z14r--subpath (0,t) of\\(z14l{z19-z14}..z16r)
 --z6l--z5l--z5r--z6r--subpath (t,0) of\\(z13l{z19-z13}..z15r)
 --z13r{z19-z13}..z0 & cycle;  % arrowhead and link
penlabels(range 1 thru 19); endchar;

beginchar(oct"170", 5pt#, 6.25pt#, 0); "Triangle for exercises";
x1=x2=w-x3=round .43pt; y3=.5+floor.5h;
z1-z2=(z3-z2) rotated 60;
y1:=.5sqrt3+round(y1-.5sqrt3); y2:=h-y1;
fill z1--z2--z3--cycle;
labels(1,2,3); endchar;

beginchar("6",256/36pt#,250/36pt#,0); % upper triangle for Addison-Wesley logo
x1=round 5/36pt; x2=round .5w; x2-x1=x3-x2=(y2-y1)/(sqrt 3);
y1=y3=0; fill z1--z2--z3--cycle; labels(1,2,3); endchar;

beginchar("7",256/36pt#,250/36pt#,0); % lower triangle for Addison-Wesley logo
x1=round 5/36pt; x2=round .5w; x2-x1=x3-x2=(y1-y2)/(sqrt 3);
y1=y3; y2=0; fill z1--z2--z3--cycle; labels(1,2,3); endchar;

def font_setup=
define_pixels(u,tiny,axis,hheight,border);
define_blacker_pixels(hair,thin,thick,rulethickness);
pickup if tiny<.5: nullpen else: pencircle scaled tiny fi;
tinypen:=savepen;
currenttransform:=identity yscaled aspect_ratio slanted slant;
enddef;

% typical cmr10 parameters
u#:=20/36pt#;
tiny#:=0;
axis#:=90/36pt#;
hheight#:=250/36pt#;
border#:=20/36pt#;
hair#:=8/36pt#;