I am calculating points on triangulated grid(blue) and since I had idle cores I added points (red):

To do this I triangulated the original grid and then added points in the centroids of the biggest triangles. As you can see this does not result in a nice grid, but with some very uneven triangles.
How do I determine a "nice" point to add a new point, without shifting any of the old? I feel that I can do this much better manually. Are there any known schemes?