Imagine a 2D space in which are samples. Each sample belongs to a class and there are two classes "true" and "false".
In this problem, we know that these two classes are separable by one or multiple line segments. Given are all the points that are close to the border, the question is now if we can find the line segments that can cleanly separate the classes.
As seen in this picture, there are two line segments that are able to divide these points like this:
The two classes are now cleanly divided by two line segments
My task now is to find an efficient way to do this, and also find a way to do this in 3D. For example, consider this 3D space with points: 3D plot
We can now imagine 3 plane segments that cleanly divide the points like in the 2D example.
So my question comes down to how we do this in 3D? Can we find the equations for the plane segments that divide our sample space?
Generally speaking this is the Support Vector Machine problem, which is a very vast field of mathematics relying on a strong linear algebra foundation.
To find a plane in $\mathbb{R}^3$, you could specify $3$ distinct points $\vec{a}, \vec{b}, \vec{c}$ and solve $$ (\vec{r}-\vec{a}) \cdot[(\vec{b}-\vec{a}) \times(\vec{c}-\vec{a})]=0 $$
The set of all vectors $\vec{r}$ that satisfy the equation defines the plane. If this is unfamiliar you will need to study some linear algebra to solve your problem.