A volumetric data structure models a particular volume representing the particular volume at a plurality of levels of detail. A first entry in the volumetric data structure includes a first set of bits representing voxels at a first level of detail, the first level of detail includes the lowest level of detail in the volumetric data structure, values of the first set of bits indicate whether a corresponding one of the voxels is at least partially occupied by respective geometry, where the volumetric data structure further includes a number of second entries representing voxels at a second level of detail higher than the first level of detail, the voxels at the second level of detail represent subvolumes of volumes represented by voxels at the first level of detail, and the number of second entries corresponds to a number of bits in the first set of bits with values indicating that a corresponding voxel volume is occupied.