limited to that of fig5 in the structure shown in fig8 a representative value of x y corresponding to u v is obtained in each of the tables for representative values of the distance z and a resultant x y is calculated by interpolation processing on the basis of the actually measured distance alternatively a resultant value of x y may be obtained by referring to a three dimensional table for u v z at a calibration stage or by using a transformation expression such as a polynomial to an approximate value of x y for u v z further the coordinate transformation section 106 may be provided with a plurality of lookup tables luts each storing a correspondence between u v and x y for a corresponding preset distance between the image projector 101 and the screen 20 the number of luts is not limited to 3 as described in the present embodiment next a second embodiment of the present invention will be described with reference to fig9 an image projection device 11 according to the second embodiment is not provided with the distance measuring device 106 of the first embodiment but another distance determination means as described below in the second embodiment a controller 104 prepares an appropriate image before screen.