We present a novel algorithm to reconstruct curves with self-intersections and multiple parts from unorganized strip-shaped points,which may have different local shape scales and sampling densities.We first extract an initial curve,a graph composed of polylines,to model the different structures of the points.Then a least-squares optimization is used to improve the geometric approximation.The initial curve is extracted in three steps:anisotropic farthest point sampling with an adaptable sphere,graph construction followed by non-linear region identification,and edge refinement.Our algorithm produces faithful results for points sampled from non-simple curves without pre-segmenting them.Experiments on many simulated and real data demonstrate the efficiency of our method,and more faithful curves are reconstructed compared to other existing methods.