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The shape reconstruction problem is one of important and most applied problems in many branches of computer science. In this paper a new method is introduced which a graph as output and work on boundary samples as input, in the plan. The proposed method starts reconstruction from the random polygon production on input points and by calculating the Euclidean distance between points, it produces a set of new points. By adding produced points to the initial points and implementation of algorithm on a set of final point, this approach performs the shape reconstruction process. This method reduces reconstruction error compared to the initial shape and improves the process of shape reconstruction.