Smoothing out blocks

So I'm looking to get some general information here, but I'm not sure where to start. I'm thinking of exploring real-time terrain deformation (by which I mean hardcore deformation like digging holes and caves and tunnels, not just heightmap), and my idea was to make a 3D array of points representing cubes which can be solid or not, and can be removed or added. I'm not looking for perf开发者_开发问答ect curvature in terrain or high precision deformation. But I want to write the engine such that the cubes (which are just points, really, not actual polygons) are smoothed out into something resembling a mesh (not a highly detailed mesh). The intent is that the limited deformability of the terrain would both simplify the algorithms necessary and hopefully reduce the processor power required.

Basically, I want to make something like Minecraft but with the visual illusion that the world isn't made of cubes, but rather of a mesh. I'm just interested in seeing if it can be done, and making a bare-bones demo of it. But I have no idea where to start, and what the current state of deformable terrain is amongst programmers. I've found a few articles on things like voxels and volumetric rendering, but I'd rather hear some input from live programmers. What do you think?

You're looking for marching cubes or marching tetrahedrons (if I'm saying the latter correctly).