1. An image processing apparatus for displaying a non-planar image of a three-dimensional coordinate system mapped on a two-dimensional planar image as a video image, the image processing apparatus comprising: an indication means for designating at least one of a viewpoint direction and a zoom value, and a video image production means for producing a three-dimensional shape video image in an arbitrary viewpoint direction in accordance with at least one of the designated viewpoint direction and the zoom value using mapping information when the non-planar image is mapped to the two-dimensional plane image, wherein the video image production means comprises a means for converting omnidirectional image coordinates of each of apexes of primitives included in the omnidirectional video image mapping information into polar coordinates using the two-dimensional image mapping information, a means for converting the polar coordinates into viewpoint direction image coordinates from at least one of the viewpoint direction and the zoom value, and a means for producing a viewpoint direction image in a unit of a primitive using the omnidirectional video image as a texture.