# Find an edge that is completely visible from point outside a polygon (Convex Hull)

I want to implement algorithms from this paper:

In particular, I am currently dealing with the one in section 2.2.1. In page 4 (first paragraph), one algorithm step is as follows:

Find an edge $(v_k, v_{k+1})$ of $P_i$ ($P_i$ is a convex hull) that is completely visible from $s_i$ ($s_i$ is a point outside the convex hull).

My question is, how can I find a completely visible edge of a convex hull, that is completely visible from a point outside the convex hull?

• If the two ends of an edge is visible, the the whole edge is visible. To check if $v_k$ is visible from $s_i$, you need to check if line segment $s_iv_k$ intersects with any of the edges (other than $v_kv_{k+1}$. – Helium Jul 15 '18 at 17:42