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Mesh segmentation and partitioning of 3D models have always been significant as one of the most structural tools used in many applications of CAD and computer graphics. One of the most versatile of these algorithms, which is capable of optimum segmentation of model, is the iterative algorithm. It is a parametric method based on Lloyd algorithm, which segments the model in an optimized way by plotting the voronoi diagram through the points cloud data. The main disadvantage of this method, which confines its application, is the time-consuming problem. In this paper, employing the nature of fuzzy segmentation, a solution has been proposed to specify the number of regions required for model’s partitioning and to carry out the nonparametric segmentation with no need for user’s initial settings. Additionally, utilizing the approximate voronoi diagram and fuzzy regions construction, a novel method for obtaining the optimized segmentation in a shorter time interval in comparison with other iterative algorithms has been presented. The proposed method has been implemented in a standard model for validation. It has been observed that the obtained results have remarkable improvements relative to the results from the iterative algorithm, which demonstrates the efficiency of this method in segmentation of 3D models.

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One important problem investigated in reverse engineering (RE) field is finding the best surface to approximate point cloud data. Swept surface is a surface type that in addition to various applications in CAD/CAM software, satisfies the whole standards required for use in RE software. The most important problem in utilization of swept surfaces for RE purposes is the finding of the areas belonging to it out of point cloud data. Through an algorithm presented in this paper, a method has been introduced to find these areas automatically. Currently, this process is performed by user intervention. In this paper, using kinematic surface formulation and slippable motion concept, a general method to find swept surfaces with any arbitrary central curve and profile is introduced. To this end, point cloud data are processed regarding slippable motion criterion using iterative segmentation algorithm, then by presenting an effective algorithm and employing the concept of hierarchical classification and drawing the dual graph, swept-surface-related areas are found. The introduced method is implemented in several models with different conditions for validation. It is observed that the results have good agreement with real model condition, showing the efficiency of this method in finding the swept surface.