1. A game machine for showing a game screen image showing a picture obtained by viewing, from a predetermined viewpoint, a virtual three dimensional space where a light source and an object are placed, comprising: shadow rendering object placing means for placing a shadow rendering object for rendering a shadow of the object in the virtual three dimensional space, the shadow rendering object divided into a plurality of polygons; permeability determination means for determining permeability of each of vertexes of polygons forming the shadow rendering object, based on a position of the light source, a position of the object, and shape data about the object; and display control means for producing the game screen image based on the permeability determined by the permeability determination means, and displaying, wherein the shadow rendering object placing means includes polygon number control means for controlling a number of the polygons forming the shadow rendering object, based on a distance between the viewpoint and the object, and further wherein the shadow rendering object is planar, and that the plurality of polygons in the planar shadow rendering object is determined by reference to a polygon control table that comprises a first division number in a first axis and a second division number in a second axis, the first division number and the second division number decreasing as said distance increases.