Are Steiner points always the vertex in Delaunay triangulation?

Question

I'm reading up about Steiner point, and it's quite unclear whether I can use Steiner points to form the vertexes in the Delaunay triangulation. The wiki entry above doesn't seem to be clear on this.

So if I pick some points inside a polygon as Steiner points and I triangulate it via Delaunay triangulation, are those points guaranteed to end up as vertexes of the triangulation?

Answer 1

We can formulate many geometric optimization problems with or without Steiner points, and these points are simply additional points, which don't exist in the input data. This term appeared in Computational Geometry because of the Steiner tree problem, where additional points allowed us to get a shorter spanning tree for a plane point set.

So, yes, if you add Steiner points inside a polygon, you'll probably get a better triangulation, and all these additional points will be vertices in this triangulation (Delaunay or not). Questions are:

1. How to measure a quality of triangulation?
2. How many additional points are needed?
3. Where to place these additional points?

If you still need to deal with these questions please take a look at this paper.