sample_cauchy

float  sample_cauchy(float u)

float  sample_cauchy(float scale, float u)

vector2  sample_cauchy(float scale, vector2 u)

float  sample_cauchy(float origscale, float minvalue, float maxvalue, float u)

<vector> sample_cauchy(<vector>u)

Sample multivariate Cauchy distributions with median 0 and scale 1. The distribution of these vectors is forced to be isotropic, i.e. rotating the distribution won’t change it, which can be useful in simulations. This wouldn’t be the case if one generated components of the vectors as independent samples of the univariate Cauchy distribution.

u

A number, or multiple numbers, in the range [0,1).

scale

The scale of the distribution, or 1 if not specified. This is the difference between the 50th percentile and the 75th percentile.

origscale

The scale the distribution would have, were it not for minvalue and maxvalue, limiting the range.

minvalue,maxvalue

When given, instead of sampling the full Cauchy distribution, the distribution with its range limited to [minvalue,maxvalue] will be sampled.

Returns

Monotonically increasing value with respect to u.

Samples the Cauchy distribution with median zero and the specified scale, optionally with a minvalue and maxvalue. Given uniform random u values in [0,1), this will return Cauchy distributed random numbers.

Note that without limits, the Cauchy distribution has no defined mean or variance, which can cause statistical problems if not dealt with carefully.

To add a maximum distance from the origin, while keeping the distribution isotropic, use:

!vex
sample_cauchy(1,0,maxdist,u.x) * sample_direction_uniform(set(u.y,u.z))

The 2D Cauchy distribution is the distribution of photons hitting a plane, coming from a point light that is distance scale from the plane.