1. A method for producing an elemental image array for three-dimensional image display in a three-dimensional image display device of a horizontal parallax type that includes a two-dimensional image display unit having a plurality of pixels arranged two-dimensionally therein, and a light-ray control element that has a plurality of exit pupils for controlling light rays emitted from the pixels in such a manner that a position for viewing image information represented by the pixels is varied for each pixel, a plurality of pixels being horizontally allocated to each one of the exit pupils, the pixels allocated to the exit pupils forming a set of elemental image display pixels, parallax information being generated in a horizontal direction by allocating image information to each of the elemental image display pixels according to directions in which the elemental image display pixels are viewed through the exit pupils, the three-dimensional image display device of the horizontal parallax type using the parallax information to cause a viewer to recognize a three-dimensional image, pixel information of multi-view images projected onto a display face of the three-dimensional image display device in various directions with respect to the horizontal direction being allocated to the elemental image display pixels according to projecting directions, thereby producing the elemental image array for three-dimensional image display, the method comprising: making a horizontal resolution of a two-dimensional image, that is k times as high as the resolution of the three-dimensional image display device, to be n times as high as the resolution of the three-dimensional image display device, wherein n≧1; after making the horizontal resolution n times as high as the resolution of the three-dimensional image display device, obtaining the multi-view images by shifting a sampling position to perform sampling on the two-dimensional image in the horizontal direction at every m pixels, wherein m≧1, so as to satisfy the following equation: 
 x:g =( m/k/n )× Pe:Pp, where x represents a distance between a position to display the two-dimensional image and the display face of the three-dimensional image display device, g represents an air-conversion gap between the exit pupils and the two-dimensional image display unit, Pe represents an exit pupil pitch, and Pp represents a pixel pitch; enlarging or reducing the viewpoint images in a longitudinal direction; and rearranging the multi-view images to form the elementary image array according to the positional relationship between the exit pupils and the projecting directions.