  We investigate the study of smooth irreducible rational curves in $Y_s^r$, a
general blowup of $\mathbb{P}^r$ at $s$ general points, whose normal bundle
splits as a direct sum of line bundles all of degree $i$, for $i \in
\{-1,0,1\}$: we call these $(i)$-curves. We systematically exploit the theory
of Coxeter groups applied to the Chow space of curves in $Y_s^r$, which
provides us with a useful bilinear form that helps to expose properties of
$(i)$-curves. We are particularly interested in the orbits of lines (through
$1-i$ points) under the Weyl group of standard Cremona transformations (all of
which are $(i)$-curves): we call these $(i)$-Weyl lines. We prove various
theorems related to understanding when an $(i)$-curve is an $(i)$-Weyl line,
via numerical criteria expressed in terms of the bilinear form. We obtain
stronger results for $r=3$, where we prove a Noether-type inequality that gives
a sharp criterion.
