Numerical integration over a hemisphere
I am trying to solve the following problem:
A function is given on the surface of a unity hemisphere, and I need to find an efficient way to numerically integrate it over the surface.
I started with an equidistant approach (both angles of the spherical coordinates subdivided into constant intervals). This gives good results but needs a large amount of computations.
In the internet, I found an alternative (Gaussian) approach with equidistant points, but only for integration over spheres, not over hemispheres. This approach can be found here: Integration nodes for the sphere
Can somebody help me on doing the numerical integration over the hemisphere? Any help is appreciated!