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Discrete curvature approximations and segmentation of polyhedral surfaces

机译:多面体表面的离散曲率近似和分段

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摘要

The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches.The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process.The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluationof curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces.
机译:对数字化数据进行分割以将自由形式的曲面划分为小块是执行对象逆向工程过程所需的关键步骤之一。为此,引入了离散曲率近似作为分割过程的基础,该过程导致将数字化数据分解为有助于构造参数化曲面补丁的区域。建议的方法依赖于对象的多面体表示从数字化数据输入构建。然后,说明了降噪,边缘交换技术和适用的重划方案如何可以参与不同的准备阶段,以提供突出显示分割过程有用特征的几何形状。分割过程是在多面体上评估的离散曲率的各种近似值下进行的在准备阶段生产。提出的分割过程涉及两个阶段:特征多边形线的识别和对面片构建过程有用的多面区域的识别。离散曲率准则适用于每个阶段,引入了曲率不变评估的概念以生成在等效网格上恒定的准则。提供了分割过程的描述以及自由形式对象表面的结果示例。

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