Suppose I have a discrete set of points $S \subset \mathbb{R}^{3}$ and I am given the points which belong to the convex hull of S, $CH(S)$. Without loss of generality, let us assume that I project the points of $CH(S)$ onto the $yz$ plane.
How would I go about finding the points which belong to the convex hull of the projection $CH(S)$ in the $yz$ plane?
Edit: My hope is to find a procedure which is $O(n)$, where n is the number of points in $CH(S)$.
Since there are simple and fast algorithms for finding the convex hull in 2D, I think that the easiest way is just to project the vertices of the 3D convex hull and find the 2D convex hull of the projected points.
Alternatively, I think that the edges of the projected convex hull are the projections of the edges in the 3D convex hull that have one adjacent face pointing in the positive $x$ direction and the other face pointing in the negative $x$ direction, that is, the silhouette edges with respect to the $x$ axis, assuming the faces are oriented consistently.