[RNG-131] TriangleSampler: Sample uniformly within a triangle

• Type: New Feature
• Status: Closed
• Priority: Minor
• Resolution: Implemented
• Affects Version/s: 1.4
• Fix Version/s: 1.4
• Component/s: sampling
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 23/Apr/21 21:23
• Updated: 13/Sep/21 10:41
• Resolved: 29/Apr/21 12:31

Description

Create a sampler to sample uniformly within a triangle:

public abstract class TriangleSampler implements 
        SharedStateSampler<TriangleSampler> {
    public static TriangleSampler of(double[] a,
                                     double[] b,
                                     double[] c,
                                     UniformRandomProvider rng);
}

Sampling of a point p can be performed within a triangle with vertices a, b, c using:

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.

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.

Issue Links

• is a child of: RNG-132 Package rng.sampling.shape for sampling coordinates from shapes