Mesh surface smoothing is an important process in the optimization of three-dimensional models, especially in the context of simulations and computer graphics. In this thesis, we present and analyze a method for smoothing hexahedral meshes, based on the use of a mathematical algorithm called the Lasserre hierarchy. We test the method on two different models, using various sizes and intensities of Gaussian noise. We assess smoothness by comparing the visual characteristics of the models and the numerical values of the Jacobian determinants of the hexahedra. This allows us to determine the level of mesh deformation at which smoothing is still successful.
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