Determine whether a point is above a mesh surface with PCL

How can I determine whether a point is above an irregular mesh/surface in PCL?

I have one cloud of points that I would like to convert to a surface/mesh (not sure which terminology I should use.) Think of it as an irregular ground plane. For example:

This just shows that the surface can be sort of random, even have holes in it where data wasn't available.

Now, I have another point cloud, and I'd like to be able to filter out all the points that are below this surface.

The way I've been converting my points to a surface was by following the Fast triangulation of unordered point clouds tutorial.

If I can do this without converting the points to a surface, that would be great too. I'm new at this so I can easily imagine I'm going about this all wrong.

When I tried using straight point clouds, sparsity became a big issue. For example, in the image below, I generated a dense surface of points, and to filter the other cloud, used used getPointsInBox() (as suggested here) to search beneath the points. But as you can see, it fails with sparsity (the blue points circled in black.)

If I could create a more-or-less continuous mesh grid of points from my original points, the getPointsInBox() method would work quite well, but I also haven't been able to figure out how to do that.