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Systems and methods for providing and/or presenting, to a user, a user interface for an environment that includes virtual objects are disclosed. Exemplary implementations may: obtain, from electronic storage, information regarding virtual objects in a virtual three-dimensional space that has a virtual three-dimensional volume; determine a subset of voxels from the set of voxels such that the subset of voxels encompasses a three-dimensional volume that includes at least part of a first external surface of the first virtual object; determine proximity information for the first virtual object; determine a manipulation granularity; adjust the manipulation granularity based on the proximity information; receive particular user input from the user having a particular input magnitude; manipulate the first virtual object within the virtual three-dimensional space in accordance with the received particular user input; and effectuate …