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A Novel Volume Constrained Smoothing Method for Meshes

机译：一种新的网格体积约束平滑方法

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摘要

In general, mesh smoothing is performed by minimizing the discrete energy function for the surface. One of the major problems in mesh smoothing is to prevent the mesh from shrinking. In this paper, we propose a novel volume constraint to address the shrinking problem in mesh smoothing. Our key observation is that the mesh can be efficiently smoothed patch by patch in a signal processing manner, and then a local volume preserving constraint can be easily imposed to the energy minimization problem associated with the small patch, called the smoothing stencil, so as to effectively avoid the mesh shrinkage. In our implementation, the smoothing stencil is the 1-ring neighboring region of an edge or a triangle. And the constrained minimization problem is solved by a 2-step approximation method for efficiency. A series of examples demonstrate that the proposed smoothing method can be applied to remove noise from a mesh or remove rough detail from an original mesh to generate a smooth model in object reconstruction and geometry modeling.
机译：通常，通过使表面的离散能量函数最小化来执行网格平滑。网格平滑的主要问题之一是防止网格收缩。在本文中，我们提出了一种新颖的体积约束来解决网格平滑中的收缩问题。我们的主要观察结果是，网格可以通过信号处理方式高效地逐块地平滑斑块，然后可以轻松地对与小块斑块相关的能量最小化问题施加局部体积保留约束，从而称为平滑模版。有效避免网孔收缩。在我们的实现中，平滑模板是边缘或三角形的1环相邻区域。并通过两步逼近方法解决了约束最小化问题。一系列示例表明，所提出的平滑方法可以应用于从网格中去除噪声或从原始网格中去除粗糙细节，从而在对象重建和几何建模中生成平滑模型。

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