1. A method for performing a drilling operation at a welisite having a drilling rig configured to advance a drilling tool into a subsurface, comprising: obtaining a first well trajectory associated with a first three-dimensional (3D) volume; obtaining information related to a first subsurface entity associated with a second 3D volume; using a 3D relational comparison to determine that the first 3D volume intersects the second 3D volume to define a first intersection information, wherein the 3D relational comparison comprises: dividing the first 3D volume into a first plurality of volume portions; dividing the second 3D volume into a second plurality of volume portions; and determining that at least one of the first plurality of volume portions intersects at least one of the second plurality of volume portions; updating the first well trajectory, based on the first intersection information, to obtain an updated well trajectory; and advancing the drilling tool into the subsurface based on the updated well trajectory.