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Is there a fix for this LaTeX rendering artefact?

TeX - LaTeX Asked by Georgina Davenport on May 4, 2021

While reading this PhD thesis

David Farrell, Weak Compactness in Banach Spaces: James’ Theorem and Convex Analysis.

On page 9 I noticed rendering anomalies, reproduced below.

Double modulus rendering artefact

On closer inspection I noticed the double modulus symbol is not rendered as two single lines but rather each apparent single line is made out of five smaller subsections.

The effect is visible, below, even when using the Adobe pdf viewer. I can notice the modulus symbol is made of smaller lines which overlap and in doing so it produces artefacts.

Line rendering artefacts

The artefacts from Google’s rendering engine appear to be explained by the fact not all of those smaller subsections align properly, but in Adove even though they align properly they still don’t anti-alias smoothly, you can see bumps where the lines overlap.

This result somewhat less than what I expect from LaTeX.

Is there a way to eliminate those effects?

One Answer

This is a flaw in the Google PDF viewer. Getting proper translation of positioning text elements to pixels is not something that can do naïvely, even at high resolutions. The logic in DVItype.web goes to great lengths to manage this and as far as I know, every dvi post processor borrows Knuth's logic towards that end.

But writing to PDF, you end up swapping one virtual coordinate system (TeX's sp = 1/65536 of a TeX pt = 1/72.27in measured as integer values) for another (PDF's point = 1/72in measured as floating point values) and you're at the mercy of the PDF viewer to maintain the translation of PDF coordinates to pixels. Anecdotally, every viewer does this correctly except for Google's viewer which is actually transforming the PDF to HTML and doesn't deal with pixels at all which is why things end up looking so bad.

Growing delimiters is something that happens at a low level in TeX's typesetting engine in cooperation with special aspects of the font in question (if you ever print a font table of, e.g., cmex10 you'll notice that the delimiter pieces position themselves oddly in the table) and while finding some way to replace vertical bars with rules might solve this particular issue, other big delimiters would still suffer so I don't think that there's any work around to the limitations of the Google PDF-HTML viewer.

Correct answer by Don Hosek on May 4, 2021

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