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 $E\to \frac{\epsilon \sigma }{2}$ 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).