README
1 SPHERE_LEBEDEV_RULE
2Quadrature Rules for the Sphere
3
4SPHERE_LEBEDEV_RULE is a dataset directory which contains files
5defining Lebedev rules on the unit sphere, which can be used for
6quadrature, and have a known precision.
7
8A Lebedev rule of precision p can be used to correctly integrate any
9polynomial for which the highest degree term xiyjzk satisfies i+j+k <=
10p.
11
12The approximation to the integral of f(x) has the form Integral
13f(x,y,z) = 4 * pi * sum ( 1 <= i < n ) wi * f(xi,yi,zi) where
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15 xi = cos ( thetai ) * sin ( phii )
16 yi = sin ( thetai ) * sin ( phii )
17 zi = cos ( phii )
18
19
20The data file for an n point rule includes n lines, where the i-th
21line lists the values of
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23 thetai phii wi
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25
26The angles are measured in degrees, and chosen so that:
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28 - 180 <= thetai <= + 180
29 0 <= phii <= + 180
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31
32and the weights wi should sum to 1.
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34Licensing:
35
36The computer code and data files described and made available on this
37web page are distributed under the GNU LGPL license.
38
39Downloaded from:
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41http://people.sc.fsu.edu/~jburkardt/datasets/sphere_lebedev_rule/sphere_lebedev_rule.html
42