Triangulate a set of points with a concave domain

Question

Setup

Given some set of nodes within a convex hull, assume the domain contains one or more concave areas:

where blue dots are points, and the black li

Answer 1

Since my question is seeming to continue to get a decent amount of activity, I wanted to follow up with the application that I'm currently using.

Assuming that you have your boundary defined, you can use a ray casting algorithm to determine whether or not the polygon is inside the domain.

To do this:

1. Take the centroid of each polygon as C_i = (x_i,y_i).
2. Then, imagine a line L = [C_i,(+inf,y_i)]: that is, a line that spans east past the end of your domain.
3. For each boundary segment s_i in boundary S, check for intersections with L. If yes, add +1 to an internal counter intersection_count; else, add nothing.

4. After the count of all intersections between L and s_i for i=1..N are calculated:

   if intersection_count % 2 == 0:
       return True # triangle outside convex hull
   else:
       return False # triangle inside convex hull
   

If your boundary is not explicitly defined, I find it helpful to 'map' the shape onto an boolean array and use a neighbor tracing algorithm to define it. Note that this approach assumes a solid domain and you will need to use a more complex algorithm for domains with 'holes' in them.