The approximation of a line drawing using the sequence of curve points found using any of the three quantization schemes described above can be coded using at most 8 bits per line segment. This is because for any curve point the next curve point in the sequence can be in at most eight directions as shown in the figure below.
Each line segment in the approximation is given a code according to the eight directions the segment can take, giving rise to a chain code representation for each line drawing. Each of the three quantization schemes desribed yield the chain codes shown in the next figure.
The different quantization schemes often yield very different chain codes for the same line drawing. One of the factors in which the schemes differ is the number of diagonal line segments they contain. It can be readily seen that the square quantization does not give any diagonal segments (assuming that the line drawing never passes through the intersection of two mesh lines), whereas they do occur in circular and grid-intersect quantizations. According to Freeman, diagonal elements should occur half the time for random configurations for a good or close approximation.