  We obtain new presentations for the imprimitive complex reflection groups of
type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams
for these presentations are proposed. The presentations have much in common
with Coxeter presentations of real reflection groups. They are positive and
homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms
correspond to group automorphisms. The new presentation shows how the braid
group $B(de,e,r)$ is a semidirect product of the braid group of affine type
$\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $B(de,e,r)$ are
visualized as geometric braids on $r+1$ strings whose first string is pure and
whose winding number is a multiple of $e$. We classify periodic elements, and
show that the roots are unique up to conjugacy and that the braid group
$B(de,e,r)$ is strongly translation discrete.
