What I would like to do:

Given a Polygon (or MultiPolygon) and a Point, p, outside the Polygon, I'd
like to find the Polygon boundary line segment (p0,p1) closest to p. Then
I'd like to split that boundary segment into 2: (p0,p)(p,p1), emitting a
refined (Multi)Polygon Or possibly by (p0,pp)(pp,p1), where pp is the
projection of p onto (p0,p1).

I want to do this with the a single (Multi)Polygon with a set of points, so
an ideal strategy would compute all the split locations first, and then
refine the (Multi)Polygon in one pass.

The best idea I've come up with is so far is to imitate
com.vividsolutions.jts.densify.Densifier, replacing the on-the-fly
computation of split locations with ones that are pre-determined.

Is there a better way to do this? I'm hoping there's something that already
does this kind of refinement, via noding, snapping, unioning, or soemthing
like that, and I'm just failing to recognize it.
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