Yes, you're very right, of course my aim is to find the closest point within the bounds.
I've looked into barycentric coordinates. It looks like for a quad I'll need four barycentic coordinates. Any point on a quad is the weighted sum of its corner vectors with these area coordinates, so p = A * v1 + B * v2 + C * v3 + D * v4. This of course yields a set of three equations with four unknowns. The fourth equation is A + B + C + D = 1. Then it should be possible to get the barycentric coordinates (A, B, C,
D) for the previously found closest point. (Provided the last equation holds also for points outside the quad? I'm not so sure...)
But then, how do you suppose I get the point "moved" into the quad? Really just by clamping? How does that work?
As for partitioning measures, I don't think that'll be worth the effort, as we're talking about a mesh of about 60 quads max. But it might be practical to divide the quads into triangles, as it will remove one dimension from the whole thing.