So I have a point cloud, a set $\mathcal{P}$ of points in 3D space. Each $i$-th point $p_i\in\mathcal{P}$ has a mass $m(p_i)$, which is a prime number. Some points can have equal masses.
Now let's define a bisecting plane $\alpha$. This plane has the property that it contains the origin (or, equivalently, that its normal vector $\bf\hat n$ bound at the origin). A general bisecting plane $\alpha$ splits the point cloud into two sub-sets of points: $\mathcal{R}$ and $\mathcal{L}$.
The measure $W[\mathcal{P}] = \prod_{p\in\mathcal{P}}m(p)$ is the weight of a set.
Given these definitions my question is:
Is there a way to find the plane $\alpha'$ for which the magnitude of the differences of the weights at each side, denoted $\Delta[\mathcal{R},\mathcal{L}] = |W[\mathcal{R}]-W[\mathcal{L}]|$, is as large as possible for a given point cloud $\mathcal{P}$?
I am trying to use that measure as a begining for the treatment of chirality in point clouds such as these. I am currently numerically optimizing these normal vectors using a quasi-newton algorithm but that approach was the fastest one I could code with the time I was given. Now that I have more room to maneuver I was trying to figure out a more direct way, but so far to no avail, I have no idea how do I even start trying to figure that one.