A rectangle-of-influence (RI) drawing is a straight-line drawing where for every edge $(u,v)$ the minimum axis-aligned rectangle containing $u$ and $v$ contains no other points. We show how to create RI-triangulations (i.e., triangulations that are RI-drawings) for any point set. Moreover, by using the $L^\infty$-Delaunay-triangulations, we show that we can flip from any RI-triangulation to any other while maintaining RI-triangulations.