Convex Hull given set of planes.

83 Views Asked by At

If I have some finite amount of planes, for example

\begin{equation} z_1=2x, \\ z_2=2y, \\ z_3=3+x+y, \\ z_4= 2+x, \\ z_5=2+y \\ z_6 =3 \end{equation}

And I wish to find the convex hull in order to project it onto the $xy$-plane, what is the best way to go about it?

Is it the convex hull of the intersection points that I would be taking?

Would I then just draw, in $\mathbb{R}^3$, a corresponding triangulation for every triple of intersection points? Then project each edge of the triangulations onto the $xy$-plane?

I don't necessarily need the heavy duty math, though it would be interesting.

I'm trying to decipher some min-plus Tropical Geometry, namely tropical polynomials in $\mathbb{R}^2$.