Figure 3.

Regular and Grid-based sampling methods where d is the actual distance and m is the measured distance. (left) For regular subdivision, the worst-case error in the distance estimate <a onClick="popup('http://www.biomedcentral.com/1471-2105/13/S8/S7/mathml/M27','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2105/13/S8/S7/mathml/M27">View MathML</a> as d → 0. (right) Grid-based subdivision improves the worst case error while forcing E → 0 as d → 0. The difference in error becomes even more significant when scaled by the nonlinear metric function (Equation 3).

Mayerich et al. BMC Bioinformatics 2012 13(Suppl 8):S7   doi:10.1186/1471-2105-13-S8-S7