Can I visualize the Bezier control points of a letter ... in TeX?

Question

Without knowing anything about fonts, I innocently read an article on Postscript/Truetype Bezier curves.

The first picture in the article shows the letter Q, and it's Bezier control points. I'd like to look at more letters (also greek letters) and their Bezier construction.

I therefore installed the program fontforge and loaded a letter from the computer modern font (I belive) in /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb

This visualization is perhaps technically useful, but not very pleasing. So, I wonder, could it be done inside TeX? Maybe using TikZ controls function: .

Clarification for this option: The letter can be drawn with TikZ as well, but I'm more interested in a nice visualization of the control points.

It surely isn't easy, as the font is stored in a binary format. Perhaps it can be converted?

EDIT

• @g.kov shows a nice visualization using Asymptote.
• I modified Andrew Stacy's script from this question, and am quite happy with it. See below.

Answer 1

Control points of a glyph path(s) can be extracted with texpath() function in Asymptote:

// glyph.asy :
//
size(7cm);
import fontsize;

defaultpen(fontsize(9pt));

real wd=0.6bp;
pen dotPen=deepblue+wd;
pen dotFill=dotPen;

pen dotPenB=blue+wd;
pen dotPenC=red+wd;

pen linePen=deepblue+wd;
pen fillPen=lightgreen+opacity(0.1);

pen thinLinePen=black+wd/2;


guide[] g;

g=texpath("$\Omega$");

filldraw(g,fillPen,linePen);

pair a,b,c,d;
pair labdir;
int pointNo=0;

for(int i=0;i<g.length;++i){
  for(int j=0;j<size(g[i])-1;++j){
    a=point(g[i],j);
    d=point(g[i],j+1);
    if(straight(g[i],j)){
      draw(a--d,thinLinePen);    
    }else{
      b=postcontrol(g[i],j);
      c=precontrol(g[i],j+1);
      draw(a--b--c--d,thinLinePen);
      dot(b,dotPenB,UnFill);
      dot(c,dotPenC,UnFill);
    }
    dot(a,dotPen,Fill(dotFill));
    labdir=rotate(-90)*dir(g[i],j);
    label("$\scriptsize "+string(pointNo)+"$",a,labdir);
    ++pointNo;
  }
  dot(d,dotPen,Fill(dotFill));
  labdir=rotate(-90)*dir(g[i],size(g[i])-1);
  label("$\scriptsize "+string(pointNo)+"$",d,labdir);
}

To get glyph.pdf, run:

asy -f pdf glyph.asy

Answer 2

After modifying Andrew's script, I get:

How to do it:

1. fontforge script font2svg.fontforge

   #! /usr/bin/env fontforge
   Open($1)
   Generate($1:t:r + ".svg")
   

2. running (chmod +x font2svg.fontforge)

   ./font2svg.fontforge /usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
   

   Puts a file cmr10.svg into your folder. E.g. letter 'Omega':

   <glyph glyph-name="Omega" unicode="&#x2126;" horiz-adv-x="722"              
   d="M677 162l-33 -162h-159c-23 0 -26 0 -26 21c0 69 32 159 47 201c29 82 56 158 56 233c0 156 -106 228 -202 228c-91 0 -201 -68 -201 -228c0 -75 28 -154 49 -212c23 -64 54 -152 54 -222c0 -21 -3 -21 -25 -21h-160l-33 162h25c5 -25 10 -51 18 -74c5 -15 8 -23 66 -23
   h80c-13 56 -45 104 -89 170c-47 71 -88 140 -88 219c0 137 133 251 305 251c169 0 304 -112 304 -251c0 -79 -41 -148 -88 -219c-45 -66 -76 -114 -89 -170h80c58 0 61 8 66 24c9 24 13 47 18 73h25z" />
   

   Nice, these are the path specifications.

3. Running the modified script

   ./svgtopgf_mime.pl crm10.svg tmpstr
   

   My changes to Andrew's. It now writes (for each glyph), three files

   • chars/gly_<prefix>N, where N is the decimal unicode number. This file contains the glyph path (almost identical output of original script).
   • chars/bezier_<prefix>N containing the bezier control handles. TikZ 3.0 arrows.
   • chars/pts_<prefix>N containing all the points on the glyph outline (not used)

4. Then, drawing a new glyph is as easy as including them in a tex file:

   \documentclass[a4paper]{article}
   \usepackage{tikz} % loads xcolor
   \usetikzlibrary{arrows.meta}
   \begin{document}
   \definecolor{solbglight}{HTML}{FDF6E3}
   \definecolor{solblue}{HTML}{268BD2}
   \definecolor{solmagenta}{HTML}{D33682}
   \pagecolor{solbglight}
   
   %Omega
   \begin{tikzpicture}[scale=18]
   \input{chars/gly_tmpstr8486}
   \pgfusepath{fill}%
   \begin{scope}[thick,solblue]
     \input{chars/bezier_tmpstr8486}
   \end{scope}
   \end{tikzpicture}
   
   %Percent sign
   \begin{tikzpicture}[scale=15]
   \input{chars/gly_tmpstr37}
   \pgfusepath{fill}%
   \begin{scope}[thick,solblue]
     \input{chars/bezier_tmpstr37}
   \end{scope}
   \end{tikzpicture}
   
   %g
   \begin{tikzpicture}[scale=25]
   \input{chars/gly_tmpstr103}
   \pgfusepath{fill}%
   \begin{scope}[thick,solblue]
     \input{chars/bezier_tmpstr103}
   \end{scope}
   \end{tikzpicture}
   
   \end{document}
   

Answer 3

Metapost also lets you do this, using the glyph operator.

This was produced by the glyph visualization program from section 9 of the MP manual, changed to show an Ω from "cmr10", and shown below.

The names of the fonts are those defined in the relevant map file (usually pdftex.map) and the names of the glyphs are the usual PostScript names (see Appendix E of the PS Language Reference Manual for a list).

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);
  picture q;
  path p;
  interim ahlength := 9bp;
  interim ahangle := 25;
  q := glyph "Omega" of "cmr10" scaled .2;
  for item within q:
    p := pathpart item;
    drawarrow p withcolor (.6,.9,.6) withpen pencircle scaled 1.5;
    for j=0 upto length p:
      pickup pencircle scaled .7;
      draw (point j of p -- precontrol  j of p) dashed evenly withcolor blue;
      draw (point j of p -- postcontrol j of p) dashed evenly withcolor blue;
      pickup pencircle scaled 3;
      draw precontrol j of p withcolor red;
      draw postcontrol j of p withcolor red;
      pickup pencircle scaled 2;
      draw point j of p withcolor black;
    endfor
  endfor
endfig;
end.