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

["Gilles Sadowski (Jira)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/RNG-131?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17332054#comment-17332054 ] 

Gilles Sadowski commented on RNG-131:
-------------------------------------

Regarding the introduction of the {{Coordinates}} class: Is it safe enough to {{requireFinite}} (there are subtractions, linear combinations)?

> 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
>            Priority: Minor
>          Time Spent: 40m
>  Remaining Estimate: 0h
>
> 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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