An augmented reality device includes a logic machine and a storage machine holding instructions executable by the logic machine to, for one or more real-world surfaces represented in a three-dimensional representation of a real-world environment of the augmented reality device, fit a virtual two-dimensional plane to the real-world surface. A request to place a virtual three-dimensional object on the real-world surface is received. For each of a plurality of candidate placement locations on the virtual two-dimensional plane, the candidate placement location is evaluated as a valid placement location or an invalid placement location for the virtual three-dimensional object. An invalidation mask is generated that defines the valid and invalid placement locations on the virtual two-dimensional plane.