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So, this post talks about cosine weighted hemisphere sampling.

Really its simple.

There are 2 ways to do this, both are outlined in Philip Dutre’s “Total Compedium”

Way #1
– generate points on the disk
– project points upward

Way #2
– Use these explicit formulae.

//generate 2 random floats, each between 0 and 1
RANDOM_NUMBER_1 = randFloat() ; 
RANDOM_NUMBER_2 = randFloat() ; 

PHI(aziumthal angle) = 2*PI*RANDOM_NUMBER_1 ;
THETA (elevation angle) = acos( sqrt( RANDOM_NUMBER_2 ) ) ;

That’s it! This is what you get:

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