Figure 2

Expected resolutions of ChopSticks and threshold-based RP methods. The expected resolution of our method ($E\left[{\Delta }_b^{\prime }\right|b,c]$) is shown by a thick red line, that of threshold-based RP methods (E[Δ _b |b,c]) is shown by a thin solid black line, and that of threshold-based RP methods with double coverage (E[Δ _b |b,2c]) is shown by a dashed black line. The difference between $E\left[{\Delta }_b^{\prime }\right|b,c]$ and E[Δ _b |b,2c] is also shown by a dotted blue line. As the coverage goes away from zero, the resolution obtained by our method quickly outperforms that of normal RP methods. It is also clear that the resolution of our method is very close to that of threshold-based RP methods with double coverage. The difference approaches zero when coverage approaches zero or infinity, as indicated by the blue dotted line. E[Δ _b |b,c], $E\left[{\Delta }_b^{\prime }\right|b,c]$, and E[Δ _b |b,2c] are given by Equations (2), (3), and (5), respectively. In this figure, d=200 and r=100.