Does anyone know of a (good) algorithm to tesselate a 2D polygon?

At least I think tesselation is what I'm after - what I want to do is
distributing points evenly inside a polygon with a certain maximum distance
to each other (that is, tesselate(d) should fill the polygon with enogh
points so that no points are more separated by more than d distance), and
then make a triangular mesh out of it.

Any ideas?

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