Table 1.

Statistics for the simulated alignment of 500 randomly rotated particles of each of 500 randomly generated configurations with four clusters per particle

Noise, Å	% correctly matched	% mistakenly matched	Median angular error for correct matches, °	% deformed particles excluded (45° domain shift)
0	100.0	0.00	0.00	99.9
1	96.2	0.04	0.25	99.2
2	91.8	0.26	0.50	98.3
3	85.6	0.73	0.75	97.3
4	81.5	1.10	0.99	96.0
5	75.6	1.91	1.26	94.6
6	70.6	2.47	1.49	93.1
7	64.2	3.29	1.73	91.4

In cases where the absolute value of β was over 81° (see Appendix for the definition of α, β, and γ), α and γ were either added or subtracted before calculating an error, because as β approaches 90° or −90° only the sum or difference of these angles is geometrically relevant, respectively.