This comprehensive post outlines over twenty various methods for uniformly random sampling from the surface of a $d$-dimensional sphere or the interior of a $d$-dimensional ball. Methods range from intuitive to mathematically sophisticated approaches, with some being particularly efficient for lower dimensions. The author emphasizes the importance of code complexity and time efficiency when choosing a method. Surprisingly, some techniques that seem unrelated can produce the same result. Notably, a method based on dropped coordinates showcases a unique and magical way to achieve uniform sampling in lower dimensions. Uniform random sampling terminology and widely applicable methods are thoroughly explained, offering valuable insights for researchers and practitioners.
https://extremelearning.com.au/how-to-generate-uniformly-random-points-on-n-spheres-and-n-balls/