Question

I want to sort a vector of points in clockwise order to form a polygon but I need the proper center to do so. I have tried the averages method, but a few of the points did not sort correctly at all. What is the correct way to find the center that will work when sorting points in a clockwise manner?

It is failing on the concave parts

Thanks

Here is a picture:

The green circle is the center.

It should look more like this:

Answer 1

The notion of “sorting in clockwise order” is not well-defined if you don’t have a pre-defined center point.

If all you have is just a bunch of points that you need to sort and you don’t know the center in advance, then the problem does not generally have a single solution. The problem has many alternative solutions, each of which will give you a different polygon as the result.

Moreover, finding a center that would allow you to re-create the original polygon by CW (or CCW) sorting is only possible for a special class of polygons: so called star-shaped polygons. The main property of star-shaped polygon is that it is possible to find a point inside the polygon from which the entire interior of the polygon is “observable” (I hope it is clear without definition what “observable” means).

If your polygon is not star-shaped, then such center point simply does not exist. And, for this reason, it is not possible to re-create the original polygon by CW sorting.

Your cow contour in the picture is obviously not a star-shaped polygon, which means that you will never be able to re-create the original cow contour by sorting the points around some center, any center. There’s no “correct way”. It is not possible.