Let's say I have a bunch of numbered vertices. Each vertex has a reference to the next vertex. All of these vertices define a polygon. There might be isolated vertices or a second set of numbered vertices which define a hole in the polygon.

I need to triangulate the resulting shape. But I can't think of a right approach. I've searched about that topic and it doesn't seem to be that easy... bur maybe someone has a good explanation for me.

Example (without isolated vertices and holes):


Thanks for hints