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; 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 polygons forming the shadow rendering object, based on a distance between the viewpoint and the object.