Triangulate a set of points with a concave domain

Question

Setup

Given some set of nodes within a convex hull, assume the domain contains one or more concave areas:

where blue dots are points, and the black li

Answer 1

One of Classic DT algorithms generates first a bounding triangle, then adds all new triangles sorted by x, then prunes out all triangles having a vertex in the supertriangle.

At least from the provided image one can derive the heuristics of pruning out also some triangles having all vertices on the concave hull. Without a proof, the triangles to be pruned out have a negative area when their vertices are sorted in the same order as the concave hull is defined.

This may need the concave hull to be inserted as well, and to be pruned out.