[jira] [Created] (RNG-131) TriangleSampler: Sample uniformly within a triangle

["Alex Herbert (Jira)" <ji...@apache.org>]

Alex Herbert created RNG-131:
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             Summary: TriangleSampler: Sample uniformly within a triangle
                 Key: RNG-131
                 URL: https://issues.apache.org/jira/browse/RNG-131
             Project: Commons RNG
          Issue Type: New Feature
          Components: sampling
    Affects Versions: 1.4
            Reporter: Alex Herbert


Create a sampler to sample uniformly within a triangle:
{code:java}
public abstract class TriangleSampler implements 
        SharedStateSampler<TriangleSampler> {
    public static TriangleSampler of(double[] a,
                                     double[] b,
                                     double[] c,
                                     UniformRandomProvider rng);
}
{code}
Sampling of a point p can be performed within a triangle with vertices a, b, c using:
{noformat}
v = b - a
w = c - a

p = a + s * v + t * w

with s and t uniform deviates in [0, 1] and s + t <= 1

Note: When s + t > 1 then transform s = 1 - s and t = 1 - t.{noformat}
This algorithm is described in:
 Turk, G. Generating random points in triangles. Glassner, A. S. (ed) (1990).
 Graphic Gems, Academic Press, pp. 24-28.

The method is applicable to any number of dimensions for the vertices. The triangle defines the 2D Euclidean space (plane) for sampling.



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