Let's start in 3D. Suppose $A\subset \Bbb R^3$ is a finite collection of points, the so-called minimum zone flatness is the minimised distance between two parallel planes that "sandwich" $A$ in between. And the minimum zone is the region sandwiched by such two planes.
This article proposes a highly efficient algorithm to accomplish the task of finding the minimum zone and minimum zone flatness for large datasets. In the introduction part, the author says
Flatness is one of the most fundamental geometric forms that are used in manufacturing to measure the quality of a machined surface.
Beyond this, however, I cannot think of any other situations in which finding the minimum zone of a dataset may be useful. And if we extend the task to higher dimensions ($\Bbb R^k, k\ge 4$), then I'm unable to imagine a single usage of finding such a minimum zone. Interestingly, though, finding the minimum zone seems to be an "opposite" task of finding the "maximum zone" formed by two separating planes in support vector machine. But I don't see any way to relate it to SVM.
Could anybody enlighten me? Thanks!