Determine ordering of polygon 3D

Question

I have a list of vertices 3D, creating a polygon. I need to triangulate it and i use the cutting ears algorithm. My polygons are non-convex, so i need to find the concave angles in the polygon. I also dont know wich orientation are my polygons ( clockwise or counter clocwise)

Could anyone help me how to determine if is clockwise or counter clockwise

Thank you

Answer 1

It's probably simplest to project the polygon into a convenient plane (say z=0) and then use a method like reinier's.

1) Set all z=0. This won't change the answer.

2) Use a method like reinier's or this one to determine whether the polygon is clockwise or counterclockwise, and therefore whether the cross products "should be" +z or -z.

3) Any vertex with a cross product that points in the "wrong" direction is concave.

Answer 2

use the cross product

ordering of polygon