Faster box approximation of VPolytope

[schillic]

The box approximation from a vertex representation can be computed more efficiently than evaluating the support function in all 2n directions on all m vertices. The idea is to create the box incrementally: Start with the first vertex and then extend the bounds for each new vertex.

low = copy(vertices[1])
high = copy(vertices[1])
for v in vertices[2:m]
    for i in 1:n
        if v[i] < high[i]
            high[i] = v[i]
        elseif v[i] > low[i]
            low[i] = v[i]
        end
    end
end
return Hyperrectangle(low=low, high=high)

The crucial part is the elseif: If a vertex extends the upper bound in dimension i, it cannot extend the lower bound in the same dimension.

In fact, this idea generalizes to parallelotopes with fixed directions.