The Sample Sphere VOP gives ways to sample either the interior or surface of the unit circle (2D), sphere (3D), or hypersphere (4D), either uniformly, optionally within some angle of a particular direction, or biased toward that direction. The sample is determined by 1, 2, 3, or 4 Uniform Sample values, (depending on how many are needed to parameterize the sample space), between 0 and 1.

In the Orientation Quaternion (4D Direction) case, in order to make generating orientation quaternions within a certain angle of the specified orientation easier, the Maximum Angle from Direction parameter is a quaternion rotation angle, instead of the Euclidean angle in the 4D hypersphere, which would be half as large, and quite confusing.

The Bias Toward Direction, if non-zero, is applied to the axial Uniform Sample component:

u = 1-pow(1-u, 1/(1+powerbias));

Where u is the axial component (the first component for 3D and 4D), and powerbias is the bias.