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.