Selecting objects within a three-dimensional point cloud environment

Techniques for interacting with virtual environments. For example, a virtual reality application outputs a three-dimensional virtual reality scene. The application receives a creation of a slicing volume that is positioned within the three-dimensional virtual space. The slicing volume includes virtual elements of an object within the scene. The application projects the slicing volume onto a two-dimensional view. The application displays the two-dimensional view within the three-dimensional virtual reality scene. The application associates a surface of a physical object with the two-dimensional view. The application receives an interaction with the surface of the physical object, and based on the interaction, selects one or more virtual elements.