Some things to consider:

* Widths at which shape change should start/stop (i.e. the "minimum fully-slanted" and "maximum fully-square" widths)
* Pinned tab shape: without other tabs present, with other tabs present of a similar width, with other tabs present of a dissimilar width, and the transitions between these states
* Gap between pinned and normal tabs
* Stacked tab shape
* New tab button shape, size, and gap
* Amount of padding within tab between content and side edges
* Roundedness of tab corners (they may look sharp now but are not; look at the tab with --force-device-scale-factor=4 to see, attached a screenshot), and similarly NTB corners
* Amount of space at left edge of tabstrip before tabs begin, and whether it changes as the tab shape changes
* Any transition differences that should be made as a result of opening or closing one or more tabs, versus shrinking or expanding the window

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I uploaded a WIP patch at https://chromium-review.googlesource.com/c/507049 to demonstrate how this could be implemented.  It's nowhere near ready to go, and I'm not sure whether I'll continue on it, but if someone wanted to try to implement this I hope it would give them a big leg up.

Lots to think about, +bettes for visual design.

 Issue 637343  has been merged into this issue.

Tagging with Proj-TabletChrome for tracking purposes. If implemented, I believe this would be a win for touch in the tabstrip:

* Less-angled tab borders would make tabs more touch-friendly, at least in appearance.

* Improved space efficiency would raise the number-of-open-tabs threshold at which stacked tab mode is triggered, or may even eliminate the need for stacked tabs at all.

+CC ellyjones who apparently has some WIP Mac code.  Elly, see link in comment 2 for views.

For internal folks, I created a rough prototype to expand on ainslie's explorations. Gives an idea of the extra space created for more usable tabs versus our current tab strip.

go/dynamic-tabstrip-prototype

Keep clicking the new tab button or press 'T' to keep adding tabs. Toggles to explore ideas like removing borders, expanding the tab when hovering over tiny tabs and an tab overview list.

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Working on computing dynamic control points, which intersects with some of what is required in this case as well. 

Tried the above patch from #2 with some modification. Got the following results (Does not include the modified corner curves).

When the minimum width for the tab is reached, the last tab gets pruned for paint due to its right() being greater than the tab_strip.width().

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Apparently I'm now slated to own this.

Moot; latest proposals eliminate the need for dynamic tab shape in favor of other solutions.