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OpenType mathematics layout

Semantic box tree

GlyphKit parses a small semantic language and lays it out as a MathBox tree. The tree keeps glyph layouts, child origins, bounds, baselines and rules apart, so a backend can draw A Cobb–Douglas utility function laid out with OpenType MATH metrics and exact glyph outlines without implementing TeX.

A node's kind says what it is: text (glyphs), sequence (children side by side), script, shifted, fraction, root, limits, operator, delimited, matrix, hat and overline (accents and rules), and space. The origin of a child is its position relative to its parent, in layout units with y up, and baseline and bounds are in the node's own frame.

def walk(node, depth=0):
    print("  " * depth, node.kind, node.origin)
    for child in node.children:
        walk(child, depth + 1)


walk(box)

Script scaling

If the display size is \(s\) and ScriptPercentScaleDown is \(r\) percent, the script size is \(s_1 = s r / 100\). At the next level the ScriptScriptPercentScaleDown constant applies in the same way, and both are taken from the whole expression's size. MathStyle.script_scale and script_script_scale replace the font's values.

Constants come from the font

Shifts, gaps, rule thicknesses and the sizes of operators come from the font's MATH table: for example SuperscriptShiftUp, SubscriptShiftDown, AxisHeight, FractionRuleThickness, RadicalVerticalGap and DisplayOperatorMinHeight. Math grammar describes how each construct uses them. A constant that the font does not supply falls back to a value in points. It is not scaled a second time.

Style and constant overrides

MathStyle(
    size,
    families,
    level='display',
    script_scale=None,
    script_script_scale=None,
    constants=...,
    letter_slant='normal',
)

Controls the size, the family, the level, the slant of letters, overrides of the script scales, and overrides of other OpenType constants by name. Override values are fractions of an em, and values from the font table are scaled from font units.

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