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  <!-- Created with AOLpress/2.0 -->
  <!-- AP: Created on: 23-Jun-2001 -->
  <!-- AP: Last modified: 23-Jul-2001 -->
  <TITLE>MetaFont -- Standard Transformations on Fonts</TITLE>
</HEAD>
<BODY>
<H1 ALIGN=Center>
  MetaFont<BR>
  Standard Transformations on Fonts
</H1>
<P>
The MetaFont dialog (obviously the name is a rip-off of
<A HREF="http://www.tug.org/">Knuth's work</A>) will try to find important
features of a font and a character and allow you to modify them. The features
searched for are:
<UL>
  <LI>
    The X-Height.<BR>
    A font-wide attribute, making the X-Height larger relative to the Cap-Height
    will often make the font appear to have a larger point-size (PfaEdit will
    also search out the Cap-Height, Ascendor-Height and Descender, but modification
    of those is less common. Though it is feasible)
  <LI>
    Stems and their widths<BR>
    Modification of a Stem's width makes the font appear Bolder or Lighter
  <LI>
    Counters and their widths (a counter is the white space between stems)<BR>
    Modification of a Counter's width makes the font appear Expanded or Condensed
  <LI>
    Left and Right Side Bearings<BR>
    Behavior similar to Counter's
</UL>
<P>
The results will probably always need to be examined and fixed up by the
human eye, but they may provide a help in changing a font's attributes. At
the moment the command is pretty primitive.
<P>
It "works" best on sans serif, non-Oblique fonts. 
  <HR>
<H3>
  Bold
</H3>
<P>
Bold fonts have thicker stems and are slightly more extended than normal
fonts. In Knuth's Computers &amp; Typesetting, the bold fonts have a stem
width that is approximately 1.6 (1.68(at 12pt)-1.5(at 5pt)) times the stem
width of the normal font. This is very similar to the 1.75 suggested by
Microsoft's ratio of 700/400 (700 being the numeric weight of a bold font,
and 400 being the numeric weight of a normal font).
<P>
In Knuth's Computer Modern Bold Extended Roman, the "m" character is extended
to 1.15 times the width of the "m" in Computer Modern Roman, and the x-height
is 1.03 times higher.
<P>
<TABLE BORDER CELLPADDING="2">
  <TR>
    <TD>Font</TD>
    <TD>Ratio of Bold/Regular Stems</TD>
    <TD>Ratio of DemiBold/Regular</TD>
    <TD>Expansion</TD>
    <TD>Bold serif height/Regular serif</TD>
    <TD>Bold serif width/regular</TD>
  </TR>
  <TR>
    <TD>Arial</TD>
    <TD>1.5</TD>
    <TD></TD>
    <TD>1</TD>
    <TD></TD>
    <TD></TD>
  </TR>
  <TR>
    <TD>Times New Roman</TD>
    <TD>1.7</TD>
    <TD></TD>
    <TD></TD>
    <TD>1</TD>
    <TD>.98</TD>
  </TR>
  <TR>
    <TD>Computer Modern Roman</TD>
    <TD>1.68(at 12pt) - 1.5(at 5pt)</TD>
    <TD></TD>
    <TD>1.15</TD>
    <TD></TD>
    <TD></TD>
  </TR>
  <TR>
    <TD>Adobe Helvetica</TD>
    <TD>1.6</TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
  </TR>
  <TR>
    <TD>Adobe Times</TD>
    <TD>1.56</TD>
    <TD></TD>
    <TD>1.17</TD>
    <TD>1.10</TD>
    <TD>.97</TD>
  </TR>
  <TR>
    <TD>Garamond Antiqua</TD>
    <TD></TD>
    <TD>1.5</TD>
    <TD></TD>
    <TD>1.05</TD>
    <TD>.90</TD>
  </TR>
  <TR>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
  </TR>
</TABLE>
<P>
<H3>
  Point Size
</H3>
<P>
At first glance this does not seem like much of a transformation, after all
postscript and truetype fonts can be drawn at any pointsize. But traditionally,
as the point-size decreases the boldness (thickness of the stems) increases
slightly, the counters and side bearings also change. For metal type there
were generally three drawings for a character in a given font, one for pointsizes
less than 10, one for pointsizes 10,11 and 12, and one for display sizes
(above 12). Most computer vector fonts do not show this change, while Knuth's
Computer Modern fonts have a continuum:
<TABLE CELLPADDING="2">
  <CAPTION>
    Stem width, scaled by point size, made relative to 12pt
  </CAPTION>
  <TR>
    <TD></TD>
    <TH>17pt</TH>
    <TH>12pt</TH>
    <TH>10pt</TH>
    <TH>9pt</TH>
    <TH>8pt</TH>
    <TH>7pt</TH>
    <TH>6pt</TH>
    <TH>5pt</TH>
    <TD></TD>
    <TH>(12pt compared to cmr 12pt)</TH>
  </TR>
  <TR>
    <TH>cmr</TH>
    <TD>83%</TD>
    <TD>100%</TD>
    <TD>109%</TD>
    <TD>116%</TD>
    <TD>120%</TD>
    <TD>124%</TD>
    <TD>130%</TD>
    <TD>139%</TD>
    <TD>Computer Modern Roman</TD>
    <TD>100%</TD>
  </TR>
  <TR>
    <TH>cmti</TH>
    <TD></TD>
    <TD>100%</TD>
    <TD>106%</TD>
    <TD>112%</TD>
    <TD>115%</TD>
    <TD>122%</TD>
    <TD></TD>
    <TD></TD>
    <TD>Computer Modern Text Italic</TD>
    <TD>94%</TD>
  </TR>
  <TR>
    <TH>cmbx</TH>
    <TD></TD>
    <TD>100%</TD>
    <TD>105%</TD>
    <TD>108%</TD>
    <TD>112%</TD>
    <TD>117%</TD>
    <TD>120%</TD>
    <TD>123%</TD>
    <TD>Computer Modern Bold Extended</TD>
    <TD>170%</TD>
  </TR>
  <TR>
    <TH>cmtt</TH>
    <TD></TD>
    <TD>100%</TD>
    <TD>109%</TD>
    <TD>116%</TD>
    <TD>120%</TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD>Computer Modern Typewriter</TD>
    <TD>100%</TD>
  </TR>
  <TR>
    <TH>cmss</TH>
    <TD>99%</TD>
    <TD>100%</TD>
    <TD>102%</TD>
    <TD>109%</TD>
    <TD>113%</TD>
    <TD></TD>
    <TD></TD>
    <TD></TD>
    <TD>Computer Modern Sans Serif</TD>
    <TD>120%</TD>
  </TR>
</TABLE>
<!--<TABLE CELLPADDING="2">
<CAPTION>
Stem width, scaled by point size
</CAPTION>
<TR>
<TD></TD>
<TH>17pt</TH>
<TH>12pt</TH>
<TH>10pt</TH>
<TH>9pt</TH>
<TH>8pt</TH>
<TH>7pt</TH>
<TH>6pt</TH>
<TH>5pt</TH>
</TR>
<TR>
<TH>cmr</TH>
<TD>1.9</TD>
<TD>2.3</TD>
<TD>2.5</TD>
<TD>2.67</TD>
<TD>2.75</TD>
<TD>2.85</TD>
<TD>3</TD>
<TD>3.2</TD>
<TD>Computer Modern Roman</TD>
</TR>
<TR>
<TH>cmti</TH>
<TD></TD>
<TD>2.17</TD>
<TD>2.3</TD>
<TD>2.44</TD>
<TD>2.5</TD>
<TD>2.64</TD>
<TD></TD>
<TD></TD>
<TD>Computer Modern Text Italic</TD>
</TR>
<TR>
<TH>cmbx</TH>
<TD></TD>
<TD>3.9</TD>
<TD>4.1</TD>
<TD>4.2</TD>
<TD>4.37</TD>
<TD>4.57</TD>
<TD>4.67</TD>
<TD>4.8</TD>
<TD>Computer Modern Bold Extended</TD>
</TR>
<TR>
<TH>cmtt</TH>
<TD></TD>
<TD>2.3</TD>
<TD>2.5</TD>
<TD>2.67</TD>
<TD>2.75</TD>
<TD></TD>
<TD></TD>
<TD></TD>
<TD>Computer Modern Typewriter</TD>
</TR>
<TR>
<TH>cmss</TH>
<TD>2.71</TD>
<TD>2.75</TD>
<TD>2.8</TD>
<TD>3</TD>
<TD>3.12</TD>
<TD></TD>
<TD></TD>
<TD></TD>
<TD>Computer Modern Sans
Serif
<TR>
<TH>cmssi</TH>
<TD></TD>
<TD></TD>
<TD>2.8</TD>
<TD></TD>
<TD></TD>
<TD></TD>
<TD></TD>
<TD></TD>
<TD>Computer Modern Slanted Sans Serif</TD>
</TR></TD>
</TR>
</TABLE>-->
<P>
<IMG SRC="CaslonOriginality.png" WIDTH="435" HEIGHT="300" ALIGN="Right">
<P>
To the left is an example of the same word (taken from a font specimine sheet)
printed at 3 different point sizes (8,12 and 24) and then scaled up to the
same size. The most obvious difference is that the characters are proportionally
wider at the smaller pointsizes. It is less apparent that the stems of the
letters are different:
<TABLE CELLPADDING="2">
  <TR>
    <TD></TD>
    <TH>24pt</TH>
    <TH>12pt</TH>
    <TH>8pt</TH>
  </TR>
  <TR>
    <TD>stem of the "n" (compared to 12pt)</TD>
    <TD>89%</TD>
    <TD>100%</TD>
    <TD>117%</TD>
  </TR>
  <TR>
    <TD>counter of the "n" (compared to 12pt)</TD>
    <TD>104%</TD>
    <TD>100%</TD>
    <TD>89%</TD>
  </TR>
  <TR>
    <TD>width of "originality" (compared to 12pt)&nbsp;&nbsp;&nbsp;&nbsp;</TD>
    <TD>93%</TD>
    <TD>100%</TD>
    <TD>104%</TD>
  </TR>
</TABLE>
<P>
<BR Clear=All>
<H3>
  SmallCaps
</H3>
<P>
A SmallCaps font is made by <A HREF="transform.html">scaling</A> the capital
letters to the x-height (so that they are the same height as lower case letters
without ascendors) and then adjusting the stem widths so that they too will
match stem widths of the lower case.
<H3>
  Italic
</H3>
<P>
The Italic transformation contains at least four parts: A change in the
letterforms of the lowercase letters, a <A HREF="transform.html">skew</A>,
and a condensation and a narrowing of the vertical stems..
<TABLE BORDER CELLPADDING="2">
  <TR>
    <TD></TD>
    <TD>Italic Angle</TD>
    <TD>Condensation</TD>
    <TD>Stem width change</TD>
  </TR>
  <TR>
    <TD>Computer Modern Text Italic</TD>
    <TD>14&#186;</TD>
    <TD>91%</TD>
    <TD>94%</TD>
  </TR>
  <TR>
    <TD>Times New Roman</TD>
    <TD>16&#186;</TD>
    <TD>100%</TD>
    <TD>91%</TD>
  </TR>
  <TR>
    <TD>Adobe Times</TD>
    <TD>15</TD>
    <TD>100%</TD>
    <TD>92%</TD>
  </TR>
</TABLE>
<P>
Letterform changes in Galliard:
<IMG SRC="ItalicCompGalliard.png" WIDTH="328" HEIGHT="33">
<P>
Letterform changes in
Caslon:<IMG WIDTH="368" HEIGHT="48" SRC="ItalicCompCaslon.png"> <BR>
<SMALL>(These glyphs have been deskewed to display the shape transformation
better.)</SMALL>
<P>
Cyrillic Letterform
changes:<IMG WIDTH="272" HEIGHT="45" SRC="CyrilItalicComp.png"> <BR>
<SMALL>(These glyphs are also deskewed.)</SMALL>
<P>
This is not a complete list, but it shows most of the salient features of
such a transformation.
<H3>
  Oblique
</H3>
<P>
The Oblique transformation is a simple <A HREF="transform.html">skew</A>,
<TABLE BORDER CELLPADDING="2">
  <TR>
    <TD>Computer Modern Slanted Sans Serif</TD>
    <TD>9.5&#186;</TD>
  </TR>
  <TR>
    <TD>Arial Italic (actually an oblique)</TD>
    <TD>12&#186;</TD>
  </TR>
  <TR>
    <TD>Adobe Helvetica Oblique</TD>
    <TD>12&#186;</TD>
  </TR>
  <TR>
    <TD></TD>
    <TD></TD>
  </TR>
</TABLE>
<H3>
  Extended/Condensed
</H3>
<P>
In these two transformations the stem width is held constant but the horizontal
counter sizes and side bearings are increased (or decreased for condensed).
<H3>
</H3>
</BODY></HTML>