"Hot spots" of directions appear because the more your spacecraft pitches "up" or "down", the less contribution yaw changes make on the final result. At the ext

"Hot spots" of directions appear because the more your spacecraft pitches "up" or "down", the less contribution yaw changes make on the final result. At the extremes, the entire range of yaw values is effectively wasted on rolling: https://en.wikipedia.org/wiki/Gimbal_lock#In_three_dimensions https://en.wikipedia.org/wiki/Gimbal_lock#In_three_dimension... gattr suggests in another comment to look for clues around global illumination methods on how to solve this problem; his reference has the equations for picking polar coordinates from two random numbers generated from a [0..1] uniform distribution in section IV. B.