In this paper we propose an RNG-based heuristic for curve reconstruction. Given a set of n sample points S, we first construct a Relative Neighbourhood Graph on S, which is shown to contain all edges joining adjacent points on the unknown curve for an \in -sample with \in \lt 1/5. Next, we use a heuristic to remove non-adjacent edges. It is extremely simple and works remarkably well for sample points drawn from a large variety of curves.