Possible to auto center camera on last sculpted, a la ZBrush?

In ZBrush, when sculpting, the viewport pivot point will automatically center itself around the last brushstroke location. In Blender, I know how to center the viewport on the current selection in Edit Mode, or the 3d Cursor, but having it update as you sculpt is probably the thing I’m having the hardest time getting used to moving over from ZBrush. If this isn’t currently a feature, what would be the best channel to request it?

The shortcut for that is NUMPAD PERIOD.

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It’s called “auto depth” in user preferences, navigation
And alt+MMB centers on cursor position