Modelling a geometric surface or contour surface is a modern field involving a wide range of topics such as mathematics, computer science, engineering design. The main task in modelling a geometric surface is to approximation the shape of the contour surface of a 3D solid object the most efficient way. In this paper we will give a method to optimize the geometric model, by defining a local sampling of the mesh, based on k-means method and minimization of the Hausdorff measure with an homologous model.
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