Left-middle-right delimiters and unicode-math

Question

Consider the rendering of \middle| in the code below:

\documentclass[12pt,a4paper]{article}
\usepackage{unicode-math}
\setmathfont{xits-math.otf}
\begin{document}
\[ \left\lbrace p_{i,j} \, \middle| \, 1 \le i \le k_j, 0 \le j \le N \right\rbrace \]
\[ N \left[ f \right] = \left\lbrace x \in N \, \middle| \, f \cdot x = 0 \right\rbrace \]
\end{document}

XeTeX produces the following output:

On the other hand, LuaTeX produces this:

It's not hard to see that XeTeX renders only the first line correctly while LuaTeX renders only the second line correctly. A similar problem happens if I swap Asana Math for XITS, so it seems to be an engine problem rather than a font problem. The problem disappears if I change from unicode-math to mathspec, so it appears to be specific to unicode-math.

Clearly, there is an execution path which makes \middle work correctly (in the sense of being consistent with \left and \right: how do I force \middle to be rendered that way when using unicode-math?

Answer 1

I think this is a mix of minor engine differences and font issues. It is not really a difference between \left/\right and \middle but rather difference between brace and bar glyphs.

The braces in most fonts have several ascending sizes that the engine can choose from, and if no big enough brace is available it composites it from smaller building blocks, on the other hand bar in most fonts is available only in one size and if the engine wants a bigger glyph it composites it from smaller blocks, and because compositing is bit more flexible it results in more intermediate sizes than the braces, resulting in effects like this.

If you try \middle\lbrace you will see that the sizes are consistent, and if you test with a font like Lucida Bright OT Math that has glyphs for bar in the same sizes as the braces, you will see the results are consistent.

(At some point I'll do this for XITS, hopefully before TL 2012)

The differences between the two engines might be due to minor differences in calculating the required glyph sizes.