Implementing Fractions in OpenType Fonts

Fractions are essential in typography for displaying mathematical expressions, measurements, and more. The frac feature in OpenType fonts replaces figures (digits) separated by a slash (U+002F) or a fraction slash (U+2044) with “common” (diagonal) fractions.

Common Method for Implementing Fractions

One of the more common ways to implement the frac feature is as follows:

@figures = [zero one two three four five six seven eight nine];
@figuresNumerator = [zero.numr one.numr two.numr three.numr four.numr five.numr six.numr seven.numr eight.numr nine.numr];
@figuresDenominator = [zero.dnom one.dnom two.dnom three.dnom four.dnom five.dnom six.dnom seven.dnom eight.dnom nine.dnom];
@slash = [slash fraction];

feature frac {
    sub @figures by @figuresNumerator;
    sub [@slash @figuresDenominator] @figuresNumerator' by @figuresDenominator;
    sub slash by fraction;
} frac;

Issues with the Common Method:

While this method effectively formats fractions, it can inadvertently affect non-fractional digits and slashes within text blocks. For example:

1/2 123/456 4 5/8 m/s

Potential Problems:

• The slash in "m/s" would be substituted with the fraction slash.
• Digits not intended to be part of a fraction (like the "4") would be converted to numerator forms.
• This leads to incorrect rendering and affects readability.

New Approach Using Reverse Chaining Single Substitution (rsub)

To address these issues, we can use a more precise method that only affects actual fractions, leaving other parts of the text untouched. One effective approach is using GSUB LookupType 8 (Reverse Chaining Contextual Single Substitution), a technique we developed in June 2021.

Here is the proposed solution:

@figures = [zero one two three four five six seven eight nine];
@figuresNumerator = [zero.numr one.numr two.numr three.numr four.numr five.numr six.numr seven.numr eight.numr nine.numr];
@figuresNumeratorEx = [fraction @figuresNumerator];
@figuresDenominator = [zero.dnom one.dnom two.dnom three.dnom four.dnom five.dnom six.dnom seven.dnom eight.dnom nine.dnom];
@figuresDenominatorEx = [fraction @figuresDenominator];

feature frac {
    sub @figures slash' @figures by fraction;
    rsub @figures' @figuresNumeratorEx by @figuresNumerator;
    sub @figuresDenominatorEx @figures' by @figuresDenominator;
    sub @figures space' @figuresNumerator by space.frac;
} frac;

Advantages of the New Method:

• Contextual Precision:
  • Only affects digits and slashes that are part of actual fractions.
  • Leaves other digits and slashes in the text untouched.
• Preservation of Non-Fraction Content:
  • Units like "m/s" remain correctly formatted.
  • Mathematical expressions or measurements not intended as fractions are displayed as intended.

Summary of Benefits

• Avoids Unintended Substitutions:
  • The common method alters all digits and slashes, which can be problematic in running text.
  • The new method selectively applies substitutions, enhancing typographic accuracy.
• Enhances Readability:
  • Readers can correctly interpret measurements and units without confusion.
  • Fractions are formatted appropriately without affecting surrounding text.
• Improves User Experience:
  • Typists and designers can input text without worrying about incorrect glyph substitutions.
  • The font behaves predictably, which is essential for professional typography.

Final Thoughts

Implementing the frac feature using rsub provides a significant advantage in handling real-world text scenarios. By focusing substitutions only where they are needed, we maintain the integrity of the text and enhance the overall typographic quality of the font.