1. A method for performing a drilling operation at a wellsite having a drilling rig configured to advance a drilling tool into a subsurface, comprising: obtaining a first well trajectory associated with a first volume; obtaining information related to a first subsurface entity associated with a second volume; using a three-dimensional relational comparison to determine that the first volume intersects the second volume to define a first intersection information; 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.