A multi-planar volumetric display system and method of operation generate volumetric three-dimensional images using a multi-surface optical device including a plurality of individual optical elements arranged in an array; an image projector for selectively projecting images on respective optical elements to generate a first volumetric three-dimensional image viewable in the multi-surface optical device; and a floating-image generator for projecting the first volumetric three-dimensional image to generate a second volumetric three-dimensional image viewable as floating in space at a location separate from the multi-surface optical device. Anti-aliasing adjusts the display of voxels in a transition between optical elements, such that color values of the voxels are modified as a function of the distance of the voxels from the optical elements, to generate a smooth transition between portions of the volumetric three-dimensional image.