How does heavily constrained delaunay triangulation work?

In short: I’m trying to find an algorithm for performing a Delaunay triangulation of a heavily constrained polygon, with the understanding that most of the resulting triangles will be illegal (non-Delaunay) due to the constraints. Making the effort should still help reduce generation of long/thin triangles where possible.

I’m trying to understand how constrained Delaunay triangulation works, within the context of game maps where the available polygon to be triangulated is concave and extremely constrained.

I first looked into regular Delaunay triangulation, and there are multiple methods available, but they all assume a point cloud where the goal is to create ideal triangles without constraints.

Then I looked into constrained Delaunay triangulation, but there is very little available I could find beyond academic papers, and many of those simply perform a regular Delaunay triangulation, then cut triangles that intersect constraints and re-triangulate around them. This seems backwards and inefficient to me when literally ALL of the triangles I want to end up with will be constrained.

I saw a GDC video, where the Starcraft 2 devs talked about using constrained Delaunay triangulation, and you can kind of see it when you look at the pathing mesh in the Starcraft 2 editor. However, very few of the generated triangles are legal, due to the number of constraints in the map layout. Still, I am assuming the Delaunay algorithm influenced the selection of points to triangulate, in order to get the best triangle coverage.

However, I can’t find any further info on how this might work. How does one start with constraints, points connected by fixed lines, and then "fill in" the remaining lines to generate triangles that are a best-effort attempt to not be overly stretched or narrow?