Unreliability of Information about Far Objects

In the case that an object in sight is a ball or a player, the value of distance to the object is quantized in the following manner:

d' = (3.15)

where d and d' are the exact distance and quantized distance respectively, and

= (3.16)

This means that players can not know the exact positions of very far objects. For example, when distance is about 100.0 the maximum noise is about 10.0, while when distance is less than 10.0 the noise is less than 1.0. In the case of flags and lines, the distance value is quantized in the following manner.

d' = (3.17)