One of the steps in inserting a constraint into a constrained delaunay triangulation is retriangulating the cavity left by removing triangles intersected by the constraint.
In the following image, constraint u (A-F) is being inserted into the triangulation, and it intersects the triangles in blue. So the blue region gets retriangulated.
This means that the triangles in blue will be removed from the triangulation, and new triangles will be added to fill the hole that was left behind when removing those triangles. Only these new triangles will have the edge A-F (which is constraint u)
Assuming that the triangulation was delaunay before inserting constraint u (except for other constrained edges), and that the triangles in green are delaunay themselves (no vertex of the green polygon is inside the circle of any other green triangle), does edge flipping need to be checked / performed on the edges connecting green triangles to the red triangles? Or is there some sort of propriety that assures that no edge flipping will happen?
In other words, is it possible that a vertex outside the cavity has become inside one of the new triangles' circle? (Note that such vertex was not previously inside any other circle, because it was previously delaunay).
Or put in a simple way, is it needed to check / perform edge flipping on the cavity edges after retriangulating it?
Reference paper used for CDT: https://infoscience.epfl.ch/record/100269/files/Kallmann_and_al_Geometric_Modeling_03
Please note that the images were hand made using GeoGebra and not the actual triangulation code, which means that the triangles in the picture may not look delaunay. Also, the pictures show only part of the triangulation for a visual example purpose.
