How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?

Growing of 3D model products and its applications in mobile devices and multimedia tools increases demands to establish an effective approach for representing and compressing of these models. In this paper, we propose an algorithm to simplify a complex 3D mesh and reduce the number of vertices by re-sampling the mesh based on the Nyquist theorem in order to find the sufficient number of samples that is necessary to save the quality of the reconstructed mesh, precisely. To achieve the optimum number of samples in the simplified mesh, both maximum curvature (C-max) and minimum curvature (C-min) in the original mesh are employed for adaptive sampling in different directions. Since the samples are adaptively taken regarding the curvature variations in both directions of maximum and minimum curvatures, the least number of vertices is obtained to represent the model. Hence, the method not only simplifies the complex mesh, but also preserves fine scale features in the mesh. The proposed method is applied to different complex mesh surfaces. The experimental results demonstrate that our proposed framework can represent a mesh surface with the least number of samples besides preserving important features in the surface.