Here's the mesh I'm using on a bunch of parallel lines, attempting to simulate water for an engraving project:
When I exit Point mode I get this, looking good for my first trial anyway:
But when I Convert to Curves, I get this:
Ooooh, ick! What's going on? Strangely, if I Export the object, with the unconverted mesh intact, as an SVG, the results are closer to the desired result but not quite as desired.