Fine typography: Numbers


Several glyph effects relate to numbers, and simple mathematical typesetting. Note the word "simple": GX is not going to set integrals for you.

Figures

The illustration below shows a typical selection of numeric glyphs:

 

A more complete Monospaced Numbers set might also include its own monospaced mathematical and monetary symbols.

Number Spacing

The Number Spacing feature type specifies a choice for the appearance of digits. Monospaced digits have uniform width and are useful for displaying numbers in columns. Proportional digits may have individual widths, and are thus preferred for numbers within sentences.

This is an exclusive feature: numbers have to be either monospaced or proportional. Either one can be the default setting.

For the default setting (whichever one that is), you can leave the editor blank. Note that all digits must be proportional or all digits monospaced: you should not mix-and-match between the two within a givensetting.

Monospaced Numbers

Glyphs:
Proportional numbers, monospaced numbers
Effect:
Substitutes monospaced numbers for proportional numbers in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Proportional Numbers

Glyphs:
Monospaced numbers, proportional numbers
Effect:
Substitutes proportional numbers for monospaced numbers in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Number Case

The Number Case feature type specifies a choice for the appearance of digits. Number Case is independent of Letter Case. Lower Case Numbers (also called "ranging", "traditional" or "old style") are digits whose optical height is the same as that of the lower-case letters in the font, and - like the lower case letters - can have both ascenders and descenders.

Upper Case Numbers (also called "lining") on the other hand, have neither ascenders nor descenders: all digits are usually the same height as the capital letters in the font. Upper case numbers are sometimes called "modern" digits.

This is an exclusive feature: numbers have to be either uppercase or lowercase. Either one can be the default setting; that editor should have no entries, and that effect should have its "is default" checkbox checked. The default setting should correspond to the style of numeric glyphs which are normally mapped to the characters '0' to '9' in the font - don't set "Lower Case Numbers" as the default if the font contains uppercase number glyphs.

Lower Case Numbers

Glyphs:
Uppercase numbers, lowercase numbers
Effect:
Substitutes lowercase numbers for uppercase numbers in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Upper Case Numbers

Glyphs:
Lowercase numbers, uppercase numbers
Effect:
Substitutes uppercase numbers for lowercase numbers in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Vertical Position

The Vertical Position feature type controls things like superscripts and subscripts. The Superiors and Inferiors selectors are used to map numerals to alternate glyph forms, positioned differently with respect to the baseline. Superiors and Inferiors can certainly be used for letters as well as numbers, but typically these settings are only relevant in relation to numbers.

The Ordinals selector is used to contextually change attached ordinal marks (such as "st" in "1st", or "ème" in "3ème") into superior forms.

Vertical Position is an exclusive feature, for which "Normal position" must be the default setting.

There is no editor for Normal Position, as it should represent the native state of any font.

Normal Position

Glyphs:
None
Effect:
None
Editor:
There is no editor for this effect. TrueEdit automatically creates it when you create any of the other settings for Vertical Position feature.
Notes:
This is the default setting and leaves numbers and letters on the baseline.

Superiors

Glyphs:
Normal forms, superior forms
Effect:
Substitutes superior form glyphs for normal form glyphs in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Inferiors

Glyphs:
Normal forms, inferior forms
Effect:
Substitutes inferior form glyphs for normal form glyphs in all contexts.
Editor:
A standard one-to-one non-contextual editor, as shown in the "Small Capitals" example.

Ordinals

Glyphs:
Normal letters, superior letters, digits
Effect:
When a sequence of (up to 8) normal letter glyphs immediately follows a digit glyph, Line Layout substitutes superior letter glyphs for all of the normal letter glyphs.
Editor:
A unique contextual editor with three live areas for Digits, for Letters, and for Superiors.

Note:
The end of the sequence of normal letter glyphs is determined by the first glyph not in that class.

Fractions

The Fractions feature type controls the selection and/or generation of fractions. The No Fractions selector specifies that fractions should not be formed automatically. The Vertical Fractions selector will form vertical fractions when glyphs are present in the font, with horizontal fraction bars. The Diagonal Fractions synthesizes fractions using numerator and denominator glyphs.

TrueEdit doesn't let you make a table which lets the end user type a slash and have a fraction bar substituted for it. Fractions composed with the slash bar will have equal spacing of numbers and / on a single line. Such fractions cannot be affected by the settings of the Fractions feature. Fractions composed with the fraction bar (shift-option-1 on US and some other keyboards) will look ugly with the fractions feature off, but will turn into nice vertical or diagonal fractions (depending on the end user's choice of effects) when the feature is selected.

This is an exclusive feature.

There's no editor for No Fractions, as it is the native state of the font. However, any of the three fraction settings could be the default.

Note that while diagonal fractions can certainly be used for letters (for abbreviations such as c/o, t/a), they're mainly relevant in relation to numbers.

No Fractions

This setting is normally the default for a font. Selecting No Fractions will prevent any diagonal or vertical fractions from being formed. The resulting flat, or "linear", fractions are as shown below.

Note that in this case, the fraction bar is not as good a separator as the forward slash. Because the fraction bar is meant to lie between superior and inferior digits, not normal digits, it tends to overlap normal-sized figures directly to its left and right.

Glyphs:
None
Effect:
None
Editor:
There is no editor for this effect. TrueEdit automatically creates it when you create either of the other settings for the Fractions feature.

Vertical Fractions

Glyphs:
Digits, fraction bar, vertical fractions
Effect:
When the three-glyph sequence of a numerator digit glyph, the fraction bar glyph, and a denominator digit glyph occurs, a vertical fraction glyph is substituted for that sequence.
Editor:
A standard many-to-one ligature editor, as shown in Example 2: Common Ligatures. The middle glyph of the ligature should be the fraction bar, in order to allow this feature to interoperate with the Diagonal Fractions effect.
 
 
Notes:
Only fractions which exist in the font as individual glyphs can be formed by the Vertical Fractions effect.
The numerators and denominators must be single digits.

Diagonal Fractions







Glyphs:
Digits, numerators, denominators, fraction bar
Effect:
When a sequence of (up to 8) digit glyphs, the fraction bar glyph, and (up to 8) digit glyphs occurs, ·numerator glyphs are substituted for the digit glyphs before the fraction bar and denominator glyphs for the digit glyphs after the fraction bar.
Editor:
Shown in the "Diagonal Fractions" example.

Mathematical Extras

The Mathematical Extras effects are useful in setting figures and mathematics.

These features are cumulative: none, all, or any combination may be on at one time.

Hyphen To Minus

Glyphs:
Hyphen, Minus.
Effect:
Changes the hyphen in a space-hyphen-space or digit-hyphen-digit group into a minus
Editor:
A simple editor with two live areas: one for the hyphen character, the other for the minus glyph with which it should be replaced.
Notes:
This overrides the effect of the Hyphen to En Dash selector in the Typographic Extras feature type. Whichever comes first in the font's mort table will take effect.
Although the digit-hyphen-digit substitution is technically wrong, the current version of TrueEdit adds it to the "Hyphen to Minus" effect anyway. A digit-hyphen-digit group shouldn't qualify. A space(or parenthesis, etc..)-hyphen-digit should.

Asterisk to Multiply


Glyphs:
Asterisk, Multiplication sign.
Effect:
Changes the asterisk character in a space-asterisk-space group into a multiplication sign.
Editor:
A simple editor with two live areas: one for the asterisk character, the other for the multiplication-sign glyph with which it should be replaced.

Slash to Divide

Glyphs:
Forward Slash, Division sign.
Effect:
changes the slash character in a digits-slash-digits group into a division-sign glyph.
Editor:
A simple editor with two live areas: one for the forward-slash character, the other for the division-sign glyph with which it should be replaced.
Notes:
Because of a bug in TrueEdit, only a digit-slash-digit group qualifies for division-sign substitution - more correctly, space-slash-space sequences should be changed too.

Inequality Ligatures

Glyphs:
Equals, Less-than, Greater-than glyphs, Less-than-or-equal-to, Greater-than-or-equal-to.
Effect:
Changes the >= sequence into a greater-than-or-equal-to glyph and the <= sequence into a less-than-or-equal-to glyph.
Editor:
A unique editor with live areas for the equals, less-than and greater-than glyphs; and the less-than-or-equal-to and greater-than-or-equal-to glyphs:

Notes:
Due to a bug in TrueEdit, the sequences "=>" and "=<" do not work: only ">=" and "<=" will produce a greater-than-or-equal-to or less-than-or-equal-to glyph.

Exponent

Glyphs:
Caret; digits, decimal points, brackets, plus, minus, etc.; superior digits, decimal points, brackets etc.
Effect:
Takes digits immediately following a ^ and changes them into their superior forms. The ^ character itself is not displayed.
Editor:
A unique contextual editor with live areas for Caret, Digits and Superiors.

The Caret area takes only one glyph: that of the caret or exponent sign (^). The Digits live area should hold the digit glyphs, including any sign, bracket or decimal glyphs - don't forget that a comma is used in most of Europe as a decimal point. The third area, Superiors, should contain the superior forms of the glyphs in the Digits area (you can use the same superior numbers for both upper and lower case digits if the font doesn't contain uppper and lowercase superiors).

Notes:
Exponents end at 8 glyphs, or when they stop being digits (as defined in the Digits column of the editor). In theory, you could have alphabetic exponents, but that could easily interfere with normal typing. If you must do it that way, be careful.




Arleigh Movitz (movitz@apple.com)
Dave Opstad (opstad@apple.com)
Kristian Walsh (walsh.k@euro.apple.com)