Let a convex bounded polytope be given by an intersection of half planes: $Ax \leq b$. Let $z=Cx$ be a vector (in my case $z$ is 2-dimensional, while $x$ has a higher dimension). How can I compute $D$ and $e$ such that $Dz \leq e$ is a projection of $Ax \leq b$ into the $z$-space.
Theorem 3 in this paper gives you the algorithm for your case (projection onto a plane). For general dimension the problem is NP-hard.