I have extruded a single-line drawing made of vertices, and want to add thickness (making a cookie cutter). When I add the Solidify modifier, the resulting shape has a lot of empty spots in it. Are my settings wrong, or is there a more appropriate modifier for this? Thanks for any help!
You most likely imported an SVG file from a vector software and that always comes with lots of errors. First you'll want to select everything and M to merge by distance, getting rid of probably a lot of double vertices. Also keep checking for flip normals, so turn on face orientation and probably leave it on while you simplify things. Because what you need to do is lower the insane poly count the import leaves you with, that's what making the mess, there are a lot of useless vertices in there that are just making everything too messy. So for simplifying your mesh, you could use a decimate modifier, or remesh. Or you could select everything and then go to Select -> Checker Deselect and then Control + X to see if that deletes lots of tight vertices and start to create gaps between them. You can do this a couple of times until things have cleared up.
Also, it's not a hard shape to redraw. You can basically do a retopo over it, trace it vertex by vertex and create a clean mesh tracing the outlines.
Thank you, Omar!
I drastically reduced the number of starting vertices, merged the crap out of everything, checked the normals, and it worked.