I am working on terrain rendering tool currently. I have to cut a piece from a given Delaunay triangulation. Suppose following triangulation is given:
The red square depicts area to cut from the original triangulation, i.e. find sub triangulation which has the same points as the original triangulation plus points on the square's border.
Is there any kind efficient algorithm to perform such cut?
I would suggest to use a constrained Delaunay Triangulation. Here, you can enforce a certain set of edges to appear in the triangulation. Thus you can enforce the edges of your cut to appear.
If you use the perspective that the Delaunay triangulation is the lower convex hull of the 2d point set lifted to the paraboloid, then in the constrained Delaunay triangulation, only non-constrained edges have a convex creasing in the paraboloid lifting. Constrained Delauney triangulations can be efficiently computed, e.g. by an improving flip sequence.