Minimum Energy (ME)
Interpolation points on the Sphere S2

Notation, and comparisons of different point sets.

The Points data files each have four columns corresponding to the x, y, and z coordinates of the points,
plus a fourth column giving the weight for that point in the quadrature rule.

Caveat: All point sets are only approximate local optimizers of their respective criteria.

Minimum Energy (ME) points

n dn Points Images
(JPEG)
h ||Ln|| lmin lavg lmax R log det G || G-1 ||1
PE
1
4
me01.0004
me01_0004
1.231
2.00
0.318
0.318
0.318
2.00
-4.58
3.14
3.67
2
9
me02.0009
 me02_0009
0.806
3.19
0.4l39
0.716
0.895
3.83
-3.22
2.56
25.76
3
16
me03.0016
me03_0016
0.580
3.67
0.7l08
1.273
1.809
5.36
3.23
1.89
92.91
4
25
me04.0025
me04_0025
0.522
5.60
0.629
1.989
3.155
8.90
15.81
2.36
243.81
5
36
me05.0036
me05_0036
0.412
7.59
0.463
2.865
5.129
14.93
35.43
2.73
529.12
6
49
me06.0049
me06_0049
0.349
7.39
0.l545
3.899
6.962
18.73
63.31
3.05
1011.56
7
64
me07.0064
me07_0064
0.304
12.54
0.251
5.093
9.854
36.02
98.90
5.55
1765.90
8
81
me08.0081
me08_0091
0.272
12.92
0.371
6.446
12.427
37.50
143.21
4.80
2878.52
9
100
me09.0100
me09_0100
0.244
9.96
1.042
7.958
14.645
27.63
199.89
1.82
4448.35
10
121
me10.0121
me10_0121
0.340
161.81
0.0026
9.629
19.314
670.74
253.86
749.32
6588.88
11
144
me11.0144
me11_0144
0.208
373.87
0.00062
11.459
22.855
1625.81
330.33
3021.25
9414.50
12
169
me12.0169
me12_0169
0.183
1504.78
0.00005
13.449
26.864
6652.99
409.47
42945.49
13068.21
13
196
me13.0196
me13_0196
0.172
422.10
0.00069
15.597
31.261
2106.57
503.49
3227.22
17693.65
14
225
me14.0225
me14_0225
0.164
172.57
0.0062
17.905
35.792
803.42
616.74
375.29
23449.75
15
256
me15.0256
me15_0256
0.156
267.06
0.0035
20.372
40.729
1228.36
728.37
653.82
30507.21
16
289
me16.0289
me16_0289
0.144
162.13
0.0099
22.998
45.864
818.77
863.06
252.48
39048.32
17
324
me17.0324
me17_0324
0.142
1968.00
0.000071
25.783
51.570
10855.44
989.23
31143.84
49268.71
18
361
me18.0361
me18_0361
0.138
2101.60
0.000042
28.727
57.375
15698.31
1154.63
58146.73
61373.90
19
400
me19.0400
me19_0400
0.126
1138.44
0.00039
31.831
63.668
5745.22
1318.69
6849.10
75583.70
20
441
me20.0441
me20_441
0.119
29565.16
0.000001
35.094
70.220
174470.38
1496.98
5118424.42
92127.42
21
484
me21.0484
me21_0484
0.115
793.14
0.00094
38.515
77.104
4445.17
1693.98
3385.83
111249.01
22
529
me22.0529
me22_0529
0.108
1569.28
0.00023
42.096
84.126
9906.68
1891.69
12812.09
133202.03
23
576
me23.0576
me23_0576
0.104
1369.47
0.00053
45.837
91.775
7064.97
2112.62
4809.79
158254.33
24
625
me24.0625
me24_0625
0.103
5106.09
0.000032
49.736
99.518
30964.70
2331.58
88255.91
186684.72
25
676
me25.0676
me25_0676
0.097
2109.76
0.00024
53.794
107.758
12252.43
2568.31
11743.32
218782.28
26
729
me26.0729
me26_0729
0.094
9615.69
0.000015
58.012
116.184
53517.20
2800.63
201669.75
254850.25
27
784
me27.0784
me27_0784
0.090
20224.51
0.000003
62.389
124.835
133698.72
3113.54
1165768.32
295205.32
28
841
me28.0841
me28_0841
0.085
878.43
0.0020
66.925
133.874
5318.04
3406.69
1342.66
340171.66
29
900
me29.0900
me29_0900
0.084
2127.35
0.00026
71.620
143.403
15642.14
3701.63
11790.83
390087.64

Rob Womersley, School of Mathematics, UNSW. Last updated 3-Nov-1999