MathML Operator Mirroring Explainer

HTML RTL mirroring

Modern browsers support two mirroring techniques when rendering RTL text:

Character-level via Unicode. For example LEFT PARENTHESIS U+0028 becomes RIGHT PARENTHESIS U+0029.
Glyph-level mirroring via the rtlm OpenType feature. This requires special font such as the xits-math.otf font used in this page. For example SQUARE ROOT U+221A has glyph name uni221A in that font, for which the rtlm mirrored form is the glyph called uni221A.rtlm.

Description	Mirroring	English (LTR)	Arabic (RTL)
HTML	character-level via Unicode	(1,2]	(١،٢]
HTML	glyph-level mirroring via `rtlm`	√3÷4	√٣÷٤

MathML operator stretching

Modern browsers support two special rendering modes for MathML operators. This requires special fonts with an OpenType MATH table such as the xits-math.otf font used in this page.

Stretchy operators (vertical or horizontal) such as large fences.
Large operators such as summation symbols or integrals.

Description	Attributes	English (LTR)
Normal text layout	`<mo stretchy="false" largeop="false">`	$(∲_{C}]$
Stretchy operator	`<mo stretchy="true">`	$(\frac{\frac{1}{2}}{\frac{3}{4}}]$
Large operator	`<mo largeop="true">`	$∲_{C}$

RTL math mirroring (issue #67)

Arabic mathematical notations require rendering math operator in right-to-left mode. This works when operators uses normal text layout. But when shaping a stretchy glyph or drawing a large operator, MathML Core does not define how to perform the mirroring. Some browsers (e.g. Firefox) are able to perform glyph-level/character-level mirroring of MathML operators.

Firefox can even mirror via a "negative" scale transform. This provides a fallback technique for math fonts that don't provide rtlm variants, but does not work for things like clockwise integrals and the like where the semantic would be modified by the transform.

Description	Mirroring	English (LTR)	Arabic (RTL)
MathML `<mo stretchy="false">`	character-level mirroring via Unicode	$(1, 2]$	$(١ ، ٢]$
MathML `<mo stretchy="true">`	character-level mirroring via Unicode	${\frac{5}{6})$	${\frac{٥}{٦})$
MathML `<mo largeop="true">`	glyph-level mirroring via `rtlm`	$∲_{C}$	$∲_{ج}$
MathML `msqrt`	glyph-level mirroring via `rtlm`	$\sqrt{\frac{3}{4}}$	$\sqrt{\frac{٣}{٤}}$

MathML Core amendment

Currently for <mo> element is made of a single character c, steps 2 and 3 of layout of operators determine the glyph corresponding to a given character c, and uses that glyph as an input to the MathVariant tables in order to obtain a larger glyph or a glyph assembly. The same is done for the radical symbol of the <msqrt> and <mroot> elements, using character U+221A SQUARE ROOT.

The proposal is simply to amend these steps, so that the input glyph is instead obtain by one of the HTML RTL mirroring techniques (Character-level via Unicode or Glyph-level mirroring) from the character c.

The proposed approach should work with the XITS fonts and is equivalent to what is implemented by Firefox. Internally, Firefox actually shapes the character c in RTL mode and then extracts the glyph from the output shape buffer.