Equations (Office Math) in layout

Office Math (OMML, ECMA-376 Part 1 §22.1) is read into a typed tree, laid out with a TeX-style box layout driven by the math font's OpenType MATH table, and painted with the paragraph it sits in. The tree is a view over the markup (nothing is rewritten); the layout is a public, queryable box.

Layers

In a paragraph

• m:oMath inside a paragraph (also inside hyperlinks, content controls and revision wrappers) is inline: text style, scripts at the script scale, limits beside n-ary signs. It is placed on the line like a word; a line break is allowed before and after it where the surrounding text allows one, never inside it. Line ascent and descent grow to the box's.
• m:oMathPara is display: each m:oMath in it gets a line of its own, in display style (m:dispDef on by default), placed by m:oMathParaPr/m:jc, else the document's m:defJc, else centred (ECMA-376 §22.1.2.57). left and right are start and end; center and centerGroup both centre each equation (a group is laid out as one equation per line). The measure is the text width minus the paragraph indents and m:lMargin/m:rMargin; the margins do not otherwise move the equation yet.
• A display equation wider than the measure breaks at binary operators and relations: m:brkBin (before, after or repeat), m:wrapIndent (default 72 pt, at most half the measure), m:wrapRight, and manual m:brk in a run. m:brkBinSub is read but not applied.
• Size, colour and text font come from the paragraph's style (the equation's own w:rPr in a math run overrides). Math letters use the math font; m:nor text uses the paragraph font.
• The paragraph's Text holds the linear text in place of the equation, so offsets, line text and extraction agree. A LayoutRun of kind Math carries the MathBox (LayoutRun.Math); its Text is the linear form.
• Table cells call the same paragraph code, so equations in tables lay out (their width counts in autofit).

Linear form (alternative text and text extraction)

UnicodeMath (Unicode Technical Note #28, v3.2) conventions: (a+b)/c fractions (parentheses only when the operand is not one atom), a/b, x^2, x_i, x_k^n, ∑_(i=1)^n▒i n-ary, √(x+1), ∛x, √(5&x) with a degree, (a+b) delimiters with separators, ■(a&b@c&d) matrices, █(x&=1@y&=2) equation arrays. Office.ExtractText returns this form for m:oMath/m:oMathPara in Word documents and in PowerPoint text bodies (a14:m), instead of the loose characters of the math runs. The painter uses it as the Alt text of the figure.

Layout rules used

All values come from the font's MATH table (units per em scaled by the size of the level). The rules are TeX's, as the OpenType specification describes the constants; the choices Word leaves unstated are in the last section.

• Levels: display, text, script (ScriptPercentScaleDown 60 % in Noto Sans Math), script-script (ScriptScriptPercentScaleDown, 50 %), then it stops. Numerators and denominators step one level in text style; in display style they stay at text size. Subscripts, denominators and radicands are cramped.
• Fractions: rule thickness FractionRuleThickness; shifts FractionNumeratorShiftUp/DenominatorShiftDown (display variants in display style) raised until the gaps FractionNumeratorGapMin/DenominatorGapMin (display variants) hold, measured from the rule's edges about AxisHeight. Skewed: numerator up and denominator down by SkewedFractionVerticalGap about a slash; linear: a/b as characters; no bar: stacked with the same shifts and no rule.
• Scripts: SuperscriptShiftUp (cramped variant), SubscriptShiftDown, SuperscriptBottomMin, SubscriptTopMax, SubSuperscriptGapMin; the script starts after the base's advance plus its italic correction (superscript) or without it (subscript). Pre-scripts mirror this on the left.
• Radicals: the sign is the smallest size variant (else an assembly) that reaches the radicand's height plus the gap (RadicalVerticalGap, display variant) and rule thickness (RadicalRuleThickness); the rule starts where the sign ends at the top of the sign. A degree is script-script size, kerned by RadicalKernBeforeDegree/RadicalKernAfterDegree and raised by RadicalDegreeBottomRaisePercent of the sign's height.
• Delimiters: grow by default (m:grow); the target is TeX's rule: twice the larger distance of the content from the axis, times 0.901, or that minus 5 pt per 10 pt em (0.5 em), whichever is taller. The smallest variant at least that tall is chosen; else the vertical assembly (parts bottom to top; extenders repeat; overlaps grow up to what the connectors allow, never below MinConnectorOverlap). Separators and empty delimiters (m:begChr empty) follow ECMA-376 §22.1.2.31.
• N-ary: in display style a large operator (sum, product, union and the like, not integrals unless m:limLoc says) takes the largest size variant; this font's DisplayOperatorMinHeight (2.3 em) is beyond its largest summation (1.34 em), so the largest variant is used. The operator is centred on the axis. Limits are above/below (undOvr) or beside (subSup): display default is above/below except integrals, m:naryLim/m:intLim in the settings change that; inline is always beside. Above/below limits are centred and kept UpperLimitGapMin/LowerLimitGapMin away.
• Accents, bars, group characters: the accent glyph is the font's combining mark (Noto Sans Math has no spacing circumflex or tilde), centred on the base by TopAccentAttachment (else the middle), raised only when the base is taller than AccentBaseHeight; wide accents use the horizontal variants. Bars are rules (OverbarVerticalGap, UnderbarVerticalGap, OverbarRuleThickness). Group characters (braces, arrows) stretch by horizontal variants or assembly to the base's width and sit below by default, m:pos on the group-character object.
• Matrices and equation arrays: columns are as wide as the widest cell, gap 1 em plus m:cGp/m:cSp; rows 1.2 em apart plus m:rSp/m:rSpRule; the box is centred on the axis. m:mcJc aligns cells per column. Equation arrays align at m:aln points: the part before an alignment point is right-aligned, the part after it left-aligned, alternating by point.
• Spacing: TeX's table between atom classes (ordinary, operator, binary, relation, opening, closing, punctuation), in 18ths of an em: 3 for thin, 4 for medium, 5 for thick; none inside scripts; a binary operator at the start or after another operator or opening delimiter is a sign and takes none. m:r literal text (m:lit) and m:nor take no class spacing.
• Characters: Latin letters are math italic (U+1D434…), Greek follows m:sty/m:scr; m:sty p plain, b bold, bi bold italic; m:scr script, fraktur, double-struck, sans-serif, monospace map to the Mathematical Alphanumeric block; digits and m:nor text are upright; function names (m:func) upright with a thin space before the argument.
• Baseline: the first baseline of the box is the baseline of the text it stands in; the box extends Ascent above and Descent below.

The math font

Cambria Math (Word's default) maps to Noto Sans Math (SIL OFL 1.1), shipped through OneRender's Fonts.Noto.Math package and loaded by FontLibrary.CreateDefault as the family and as a fallback for math characters; the note is a FontSubstitutionNote of kind approximate. STIX Two Math and Latin Modern Math map to it too. On a machine that has Cambria Math installed and registered with the library, its own MATH table is used. Metrics differ between the two fonts, so line breaks and box sizes against Word on Windows are a measured difference, not a bug: the layout differential decides how far it goes.

Notes

LayoutDocument.Notes carries equation notes as layout.math.*: layout.math.unknown-element (an element not in §22.1.2 was skipped), layout.math.depth, layout.math.size (limits of the reader and the layout), layout.math.no-math-table (the font has no MATH table; fixed ratios were used), layout.math.font-missing (the named math font is not available; the default was used), layout.math.glyph-missing (no font has a glyph for a character; the missing-glyph shape is drawn).

Choices to check against Word

These need Word's own output to settle; the layout differential inputs (80–89 in the generated set) are written for it.