1. A texture mapping device comprising: a processor to execute a program; and a memory to store the program which, when executed by the processor, results in performance of steps comprising: generating plural pieces of area information each showing a partial area of a texture image; 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; 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; processing the texture coordinates of said pixel information by using the area information specified by the area ID of said pixel information, and 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 outputting an output of said processing the texture coordinates to an image display device, wherein said polygon information generating does not use 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 processing the texture coordinates, thereby holding said area ID as a part of the vertex information.