Here's the algorithm Wikipedia gives for double-and-add point multiplication:
N ← P Q ← 0 for i from 0 to m do if d[i] = 1 then Q ← point_add(Q, N) N ← point_double(N) return Q
$P$ is an $(x, y)$ coordinate and so it seems reasonable to assume that $0$ is a $(0, 0)$ coordinate but there's no guarantee that $(0, 0)$ will even be on the curve, which would thus skew the whole thing.
Indeed, it seems to me that $Q$ is probably better represented as $\infty$ due to the
P + ∞ = P identity?
I suppose one could assume that $0$ and $\infty$ are the same thing, but that wouldn't work if $(0, 0)$ were an actual point on the curve.