Space Subdivision
A 3D representation based on [see page 20, decomposing] the space into a region (grid) and then labelling what's within or outside of the region. This resolution of this approach depends on the resolution of the grid.
This approach in 3D is called voxels (equal subdivision of space into cubes).
A partial optimisation for space subdivision is the [see page 24, quadtree]. For each square in the grid we subdivide it into 4 and recurse into sub squares determining which parts of the parent grid is occupied by the object.
Another approach is Binary Space Partition [see page 27, BSP] which is like a quadtree except each
node in a single partitioning place splits the space into two.
Quadtrees and BSP trees aren't often used for 3D representation, their more useful for collision detection or raytacing.