A rapid method for calculating a local eye vector in a fixed point lighting unit. For a given triangle primitive which is to be projected into a given 
viewport in 
screen space coordinates, the local eye vector corresponds to a given 
eye position and a first vertex of the given triangle primitive. (A different local eye vector is calculated for each vertex of the given triangle primitive). The method first comprises generating a view vector matrix which corresponds to the given 
eye position and corner coordinates of the given 
viewport, where the corner coordinates are expressed in 
screen space coordinates. The view vector matrix is 
usable to map 
screen space coordinates to an eye vector space which corresponds to the given 
viewport. The method next includes receiving a first set of coordinates (in screen space) which correspond to the first vertex. The first set of coordinates are then scaled to a 
numeric range which is representable by the fixed point lighting unit. Next, the first set of coordinates are transformed using the view vector matrix, which produces a non-normalized local eye vector within the eye vector space for the given viewport. The non-normalized local eye vector is normalized to form a normalized local eye vector. The normalized local eye vector is then 
usable to perform subsequent lighting computations such as computation of 
specular reflection values for infinite light sources, producing more realistic lighting effects than if an infinite eye vector were used. These more realistic lighting effects do not come at decreased performance, however, as the local eye vector may be calculated rapidly using this method.