Weights for Numerical Integration on the Sphere

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Adam 2013-3-5

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https://ww2.mathworks.cn/matlabcentral/answers/65872-weights-for-numerical-integration-on-the-sphere

Hi, I'm just dealing with numerical integration (quadrature) on the sphere. I know positions of nodes but don't know how to compute integration weights that should ensure correct integration of all spherical harmonics functions up to given order.

Thank you fo your answers. Adam

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Youssef Khmou 2013-3-5

hi, correct integration means the result can not exceed 4/3piR^3 ? and weights based on nodes's distances from (0,0,0) ?

Adam 2013-3-5

hi, the correct integration means that it provides exact numerical integration of product of spherical harmonics up to a given sum of orders. When the integration in Eq.(1) is approximated by the sum in eq.(2) <https://www.dropbox.com/s/4iiv991xzm9ktln/pic.png?m> where \Omega is (theta,phi) and j=1,... is the number of points sampling the sphere surface. Thanks

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