sample_hemisphere

vector  sample_hemisphere(vector2 u)

vector  sample_hemisphere(vector center, vector2 u)

vector  sample_hemisphere(float bias, vector2 u)

vector  sample_hemisphere(vector center, float bias, vector2 u)

center

Direction in the center of the hemisphere. This does not need to be normalized. If not specified, the center direction is (1,0,0), along the x-axis.

bias

Bias toward the center direction, between -1 and infinity, with 0 being unbiased, -1 forcing all points to the horizon, and infinity forcing all points to center. When supplied, u.y is simply replaced with 1-pow(1-u.y, 1.0/(bias+1.0)). To get a bias similar to this when using the more general sample_direction_cone, sample_sphere_cone, and related functions, apply the same change to u.x before calling those functions.

u

Pair of numbers between 0 and 1.

Returns a unit vector, i.e. a vector of length 1, based on u. Given uniform random u pairs of values in [0,1), if bias is 0, the returned unit vectors will be uniform random and continuous with respect to u on the surface of the unit hemisphere centered at center. If bias is greater than zero, the unit vectors will be smoothly biased toward center. If bias is between -1 and 0, the unit vectors will be biased away from center, toward the horizon.