A virtual image generation apparatus comprising shape data memory for storing shape data pertaining to obstacles and the like, position data specifier for specifying position data for the subjects, overlap determiner for determining, on the basis of shape data and position data, whether or not physical objects located between a visual point and a subject should overlap and be visible from the visual point, and image generator for generating virtual images wherein physical objects are processed by prescribed show-through processing (mesh processing, translucent processing, or the like) when it is determined that an overlapping state exists. Accurate overlap determinations can be made using a vector that extends from the visual point towards an object and a vector that extends from an obstacle towards the object, and mesh processing or other show-through processing used to produce a suitable display of the subject obscured by a physical object.