I'm aware of three basic methods for rasterizing arbitrary solid volumes (from finite differencing approximation):
midpoint occupancy: If the cell (cube) centre is inside the object, it's solid.
Volume fraction: If the majority (or some other cutoff value) of the cell volume is filled by the object, it's a solid space. [requires calculating the volume of an intersection cube-parametric surface]
Point occupancy fraction: Choose a representative (or random) set of points inside the cube, test if they are inside the parametric object, on cutoff percentage declare occupied or not.
The central point method has high aliasing, so is suitable only for small voxels (which Minecraft(c) does not have). The fractional occupancy varieties can have intermediate cases linked to other cutoff values as an anti-aliasing technique. For example, one could actually consider binary Marching Cubes to be a version of point occupancy that chooses the 8 corners as its test points and has anti-aliasing.
As I've personally not gotten to rasterizing trees (and will probably go with cellular automata inside the grid confines, as an aesthetic choice) for my own project, I have no specific guides or commentary to recommend.