units.md

Units

Written because the author confused themselves and wanted to be sure they now understand.

There are three main classes of variation axis coordinates in variable fonts:

1. Design coordinates
   • Used by the type designer and design tool
   • Not directly present in the font binary at all
   • For example, in a .designspace file
2. User, aka External, coordinates
   • The values in fvar, for example Weight 400
   • What you would expose to an end user in a document editor or manipulate via CSS
3. Internal, or normalized, coordinates
   • Values in [-1, 1], used internally by the font
   • The default must be at 0 in these terms

Any unit can be converted to any other unit using a piecewise linear function.

Design : Internal

Given that we have at least one design coordinate, and we know what the design coordinate for the default outline is:

Design coord	Internal coord	Notes
min design value	-1	If min < default master location
default master location	0	Mandatory
max design value	1	If max > default master location

User : Internal

User coordinates run through a piecewise linear function, to get internal coordinates. avar captures this in the font binary, derived from the User:Design mapping typically captured in the sources.

User : Design

Both Glyphs and .designspace files capture mappings from user to design coordinates:

• The set of elements for an axis capture it in .designspace sources, for example (from Noto Sans Thai):

  <axes>
      <axis tag="wght" name="Weight" minimum="100" maximum="900" default="400">
        <map input="100" output="26"/>
        <map input="200" output="39"/>
        <map input="300" output="58"/>
        <map input="400" output="90"/>
        <map input="500" output="108"/>
        <map input="600" output="128"/>
        <map input="700" output="151"/>
        <map input="800" output="169"/>
        <map input="900" output="190"/>
      </axis>
      <axis tag="wdth" name="Width" minimum="62.500000" maximum="100" default="100">
        <map input="62.500000" output="70"/>
        <map input="75" output="79"/>
        <map input="87.500000" output="89"/>
        <map input="100" output="100"/>
      </axis>
  </axes>

• The custom key "Axis Mappings" captures it in .glyphs sources, for example (from Lexend)

   {
   name = "Axis Mappings";
   value = {
       HEXP = {
           0 = 0;
           100 = 100;
       };
       wght = {
           100 = 22;
           200 = 50;
           300 = 78;
           400 = 108;
           500 = 130;
           600 = 150;
           700 = 170;
           800 = 198;
           900 = 216;
       };
   };
   }
  

Since design trivially maps to internal coordinates this readily yields the mapping needed for the avar table, as is the intent.

References

See also @anthrotype's writeup in googlefonts/glyphsLib#568 (comment).