1. A texture mapping device comprising: an area information generating unit for generating plural pieces of area information each showing a partial area of a texture image; a polygon information generating unit for generating polygon information including plural pieces of vertex information each including coordinates of a vertex on an output image and texture coordinates brought into correspondence with the vertex, and an area ID for specifying one of said plural pieces of area information; a rasterizing unit for generating pixel information including position coordinates, texture coordinates, and an area ID for every of all pixels located inside a polygon on said output image, said polygon being shown by said polygon information; a texture mapping unit for processing the texture coordinates of said pixel information by using the area information specified by the area ID of said pixel information, and for acquiring a pixel value from said texture image by using said processed texture coordinates and determining a pixel value of a pixel on the output image, the pixel being shown by the position coordinates of said pixel information, by using said pixel value acquired thereby; and an output unit for outputting an output of said texture mapping unit to an image display device, wherein said polygon information generating unit does not hold said area ID which constructs said polygon information as an element of said polygon information directly, but processes each vertex information in such a way that said area ID can be reconstructed from the pixel information inputted to said texture mapping unit, thereby holding said area ID as a part of the vertex information.