Closing the hole after cutting a triangular mesh

Once a triangular mesh is cut by an intersecting plane, the resulting halves are no longer a water-tight mesh, because some holes are created by the cutting action of the plane.

In the image here, the volume of a [solid] hat was cut by a vertical plane, splitting it in two. In order for this half to be back a 2-manifold triangular mesh, all the triangles with black edges have been added to create a flat surface that covers what the cut plane would otherwise reveal (the inside of the hat).

The problem is how given a certain polygon, like the red polygonal line here, a collection of triangles can be created to cover entirely all the area delimited by such a perimeter (aka polygon triangulation).

The problem gets even more interesting once we consider that some meshes can present holes inside these perimeters obtained after cutting the mesh with a plane.

Fortunately, there are different algorithms to solve that problem, and I will settle with the so-called Ear clipping. Fortunately, there is an open-source java library for doing just that and this is what I used for triangulating the example in the graph.

There is a small warning though, as the code above is only suitable for Java 8 (I know because I had to backport it to an older version installed in my test system).