A $2D$ polygon of n edges and vertices is projected onto the XY plane. The vertices and edges are connected forming a watertight convex polyhedron (truncated prism-ish? except angled top face) with $N + 2$ faces, lets call this polyhedron $P$.
I also have m number of 3D points in $x,y,z$. It is given that these points all fall within the volume of $P$, this is checked by getting the signed cross product from the point to each plane.
The $2D$ polygon and its projection now transform (translate, reflect or rotate but retain shape) and form a new Polyhedron ($P'$) with the same guarantee that $m$ points (same coordinates) all fall within the new volume as well.
I am trying to find a way to determine which polygon covers the points better. My question is, what is a good way to define "cover better". If I were to try and define it I'd say "having the shortest single distance from each point to a plane being as equal as possible and maximized"?
I have also thought about the following ways to define/calculate "cover better":
Compare the average, median and standard deviation for individual and summed distance values from each point m to each face that makes P and P'.
Have the distance from a point to each plane be as equal as possible.
Create a line $L$ from the centroid of the $2D$ polygon and its projection and compare the average, median and standard deviation for individual and summed distance values from each point $m$ to each $L$ that makes $P$ and $P'$.
Conceptual question to see what some people might think is a better way to define "covers" the points better.
Illustrations below to hopefully make things clearer with $n$$=4$ and $m$$=2$:
