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I was working on a project with a large-ish terrain (7M+ faces) that I Knife Projected many curves (~70k faces) onto:
zoom out showing extent of terrain and many, many trails, and zoom in showing high complexity of topology

After a bunch of cleanup (selecting faces that hadn't been selected by Knife Project), I zoomed in and realized that there were many faces crossing the curve border; some faces that should have been inside the curve went outside, some faces that should have been outside the curve went inside. The edge was not clean:
zoom in showing resulting topology not matching edge of curve Seen above, the orange outline shows the curve that was knife projected, green shows the faces selected.

I came here to ask how to improve this, but decided I should reproduce it first and experiment with any ~threshold settings I could find. And...I cannot reproduce it. All the knife projects I make now are ~perfect. Here's the same region, with a new test knife project:
new knife project with far more vertices

I know that I did not have Auto Merge or Split Edges and Faces on when editing the mesh. In fact, I am fairly certain that I did not edit any vertex placement on the entire terrain during material assignment. So, I assume the bad result I got originally is what came out of the knife project, and not something like Merge by Distance changing my terrain after the projection occurred.

So, I assume--and I'm being clear about this assumption, because I might be wrong--that knife projection produced a sloppy edge the first time around. What controls the precision of the projection? Even now it's not perfect--as seen in the final image below--so I assume there's a threshold or similar setting I've now changed that is affecting my new tests.

one imperfectly placed vertex
one imperfectly placed vertex

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I found the ~answer in a comment on another, similar question. Horrifyingly, it depends on the zoom level when the knife project is applied. If I zoom way out in the orthographic view and then apply the knife projection, I get this horrible result:
really, really rough knife projection

So: if you want accurate knife projection, zoom in on the viewport before applying knife project. (!!)

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