Map from terrain scanning

Hi! I want to create a 3D map from a portion of the terrain like this (yes it's from Hostile Waters):

My simple solution that I use raycasting around player. These rays are moving along with player, but at map these raycasted points has a fixed position. In Hostile Waters the map grid is moving when player is moving too.

So my result:

I draw my map with OpenGL and I want this map with backface culling. I have another ideas:

1. somehow draw a portion of the terrain meshgrid (moving map, best solution I think)

2. create a plane and lift mesh's points (not moving map, complex because the triangles)

3. create 3D cubes and lift these objects according to my raycasters (not moving map)

Anyone created such map like Hostile Waters' map? Any idea?