pinknation

So, I have a picture here that will help a lot with my question:


excuse the poor drawing if possible, anyways, the point here is that if I have a convex hull such as in Diagram 1, the teapot, and I slice on on that red line, from the top-down view, the slice points(otherwise the inverse of the plane) will look like that in 2D. is there any good triangulation algorithms which can a) support holes, and b) support edges/points seperated from each other creating sub polygons, but all within the same triangulation sweep;

this is important, and any information would be great, I am capable of learning, but looking for something more open-source that i can try and understand better then a PDF, but anything will do