In one embodiment, one or more computing devices access an image comprising at least a portion of a hand of a user of a head-mounted display and generate a planar representation of the hand and a height map associated with the planar representation. A first portion of the planar representation that is closer than a first portion of a virtual object to a viewpoint and a second portion of the planar representation that is farther than a second portion of the virtual object from the viewpoint is determined based on the height map and the virtual object. A display image is rendered from the viewpoint for display, the display image comprising a first set of pixels corresponding to the first portion of the planar representation and a second set of pixels corresponding to the second portion of the virtual object.