The purpose of this interactive demonstration is the visualization of different mappings of the random variables u and v in range [0.0, 1.0], which have a uniform distribution, to the polar angle θ (theta) and azimuthal angle ϕ (phi) of a spherical coordinate system. For a hemisphere, ϕ should be in range [0,2π] and θ in range [0,π/2].

Presets:

Mapping:

Here are some notes on how to compute the mappings that are provided by the presets: importance sampling notes

This website is a part of the Graphics Programming lecture at the University of Marburg. Importance sampling of a hemisphere is often used for photorealistic rendering (ray-tracing).