Visualization of the rejection sampling method. An arbitrary probability density function P(θ, φ) is shown in blue, and the ceiling value υ_cei1 is in yellow. An angle pair (θ, φ) is accepted if a third (0, υ_cei1) is smaller than P(θ, φ). For two-angle pairs, the segments in green and red visualize the ζ value leading to acceptance or rejection, respectively. The case where the green line is longer has a higher chance of being selected than the other case where the green line is shorter. For the selected case of the longer green line, P(θ, φ) becomes much larger than in the other case, as is expected.