Understanding K-Convexity: Visualization and Intuitive Explanation

[Constantinos]

Hey!

Can anyone help me with visualizing this concept or explaining it in more intuitive terms?

:

thanks!

 

[chiro]

Hey Constantinos.

This PDF describes the visual intuition for K-Convex polygons with the following:

Clearly, a polygon P is k-convex if every line segment with endpoints in P crosses at most 2(k − 1) edges of P.

I'm going to make a guess and say that this holds for a general continuous object in n-dimensions if the following holds where the edges just translate into n-dimensional surface itself.

Hopefully the PDF might help you out.