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Another solution I quite like is highlighting the headings of all the sections that are currently on screen.

I agree…

I don’t think this is a real problem that needs solving; or I at least think it’s a problem browser vendors should solve, but lets over engineer it while still trying to keep it simple and usable…

What I might do is something similar to what you’re suggesting. I would have the anchor tag be a regular old anchor tag. Then, I’d highlight the heading (maybe just temporarily) at the same time. I’d use CSS if I could figure that out or JS if I couldn’t. The end result would send the user to the normal place and flash a highlight on the heading for users with JS support.

Keep it simple, but over engineer it to make whoever requested this happy.

Edit: After re-reading your response we probably aren’t talking about the same thing, exactly.

This seems like the obvious solution to me. You don't know what the user's eyes are looking at, so making the highlighting a visual representation of what's in the viewport seems preferable than nominating a single section as "current".

In fact the final solution is pretty bad. Sure, it looks nice when I scroll down, but when I use the alternative navigation method of clicking the sidebar items, it just scrolls to unexpected places.

Beautiful article, though.