Turn an enclosed region into a triangle mesh I have a (2d) region defined as a list of vertices that I'm currently drawing as a line loop in opengl. I want to draw this region solidly. I started by using triangle fan, but that doesn't work if the region has vertices positioned at the same angle (relative to the center) but different radii, because then that whole region is draw solid.

So, I think I just need some general method to convert an enclosed spline/list of points into a triangle mesh. Maybe there's a better way?
If the number of vertices is not too large, I would suggest looking into "ear clipping". It's a straightforward method to triangulate possibly-concave polygons, as long as they don't have holes. However, it's $O(n^2)$ in the number of vertices, so may not a great choice if you need to handle a large number of verts. Dave Eberly has a paper on ear clipping and also an open-source implementation in C++. There are many other links available on the web, too.

The basic idea is to find an "ear" of the polygon, which is defined as a triangular subset of the polygon, formed by three consecutive vertices of the polygon. Once you find an ear, you add it to the output triangle list, and remove it from the original polygon (which reduces the number of vertices by one). Repeat this until the polygon is gone.

The reason it's $O(n^2)$ is that you have to repeatedly search the list of vertices to find another ear to remove. There are more efficient triangulation algorithms as well, but they're more difficult to implement.