Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation

Sun, Shichao; Zhang, Minglei; Gou, Zhihong

doi:10.1155/2015/435648

Cited by 6 publications

(11 citation statements)

References 29 publications

(50 reference statements)

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“…This viewpoint focuses on each element shape instead of the central point position of its ring. SSO [18] is also an element transformation method, which optimizes mesh quality with the assistance of the height of element.…”

Section: Related Workmentioning

confidence: 99%

Mesh smoothing algorithm based on exterior angles split

et al. 2020

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Since meshes of poor quality give rise to low accuracy in finite element analysis and kinds of inconveniences in many other applications, mesh smoothing is widely used as an essential technique for the improvement of mesh quality. With respect to this issue, the main contribution of this paper is that a novel mesh smoothing method based on an exterior-angle-split process is proposed. The proposed method contains three main stages: the first stage is independent element geometric transformation performed by exterior-angle-split operations, treating elements unconnected; the second stage is to offset scaling and displacement induced by element transformation; the third stage is to determine the final positions of nodes with a weighted strategy. Theoretical proof describes the regularity of this method and many numerical experiments illustrate its convergence. Not only is this method applicable for triangular mesh, but also can be naturally extended to arbitrary polygonal surface mesh. Quality improvements of demonstrations on triangular and quadrilateral meshes show the effectiveness of this method.

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Section: Related Workmentioning

confidence: 99%

Mesh smoothing algorithm based on exterior angles split

et al. 2020

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“…The element geometric transformation for smoothing triangular and quadrilateral meshes has been introduced by Sun et al in Reference [30]. It is based on transforming elements by a specially designed two-step stretching and shrinking operation (SSO).…”

Section: Basic Geometric Transformationmentioning

confidence: 99%

“…The purpose of stretching operation is to regularize the element, while the shrinking operation is performed to preserve the element size. The stretching operation proposed by Sun et al [30] is shown in Figure 1 for a triangular and a quadrilateral element. The element geometric transformation operation proposed by Sun et al [30] is mainly used for mesh smoothing, and the regularizing effect for arbitrary triangular and quadrilateral elements remains to be proved in their paper.…”

Section: Basic Geometric Transformationmentioning

confidence: 99%

“…The stretching operation proposed by Sun et al [30] is shown in Figure 1 for a triangular and a quadrilateral element. The element geometric transformation operation proposed by Sun et al [30] is mainly used for mesh smoothing, and the regularizing effect for arbitrary triangular and quadrilateral elements remains to be proved in their paper. In this subsection, the element geometric transformation operation will be generalized for polygonal elements with an arbitrary number of nodes, which may even be inverted.…”

Section: Basic Geometric Transformationmentioning

confidence: 99%

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Simultaneous Smoothing and Untangling of 2D Meshes Based on Explicit Element Geometric Transformation and Element Stitching

2020

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Mesh quality can affect both the accuracy and efficiency of numerical solutions. This paper first proposes a geometry-based smoothing and untangling method for 2D meshes based on explicit element geometric transformation and element stitching. A new explicit element geometric transformation (EEGT) operation for polygonal elements is firstly presented. The transformation, if applied iteratively to an arbitrary polygon (even inverted), will improve its regularity and quality. Then a well-designed element stitching scheme is introduced, which is achieved by carefully choosing appropriate element weights to average the temporary nodes obtained by the above individual element transformation. Based on the explicit element geometric transformation and element stitching, a new mesh smoothing and untangling approach for 2D meshes is proposed. The proper choice of averaging weights for element stitching ensures that the elements can be transitioned smoothly and uniformly throughout the calculation domain. Numerical results show that the proposed method is able to produce high-quality meshes with no inverted elements for highly tangled meshes. Besides, the inherent regularity and fine-grained parallelism make it suitable for implementation on Graphic Processor Unit (GPU).

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“…Relevant indicator values were recorded during the process of surface reconstruction to assess IPSR and PSR, including triangular facets, size, reconstruction time, average frames per second (FPS), and occupied CPU percentage [38]. The specific values of these metrics are listed in Table 5, while four histograms of the triangular facets, size, reconstruction time, and average FPS are shown in Figure 14.…”

Section: Online Surface Reconstruction Experimentsmentioning

confidence: 99%

A Lightweight Surface Reconstruction Method for Online 3D Scanning Point Cloud Data Oriented toward 3D Printing

Sheng

Zhao

Yin

et al. 2018

Mathematical Problems in Engineering

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The existing surface reconstruction algorithms currently reconstruct large amounts of mesh data. Consequently, many of these algorithms cannot meet the efficiency requirements of real-time data transmission in a web environment. This paper proposes a lightweight surface reconstruction method for online 3D scanned point cloud data oriented toward 3D printing. The proposed online lightweight surface reconstruction algorithm is composed of a point cloud update algorithm (PCU), a rapid iterative closest point algorithm (RICP), and an improved Poisson surface reconstruction algorithm (IPSR). The generated lightweight point cloud data are pretreated using an updating and rapid registration method. The Poisson surface reconstruction is also accomplished by a pretreatment to recompute the point cloud normal vectors; this approach is based on a least squares method, and the postprocessing of the PDE patch generation was based on biharmonic-like fourth-order PDEs, which effectively reduces the amount of reconstructed mesh data and improves the efficiency of the algorithm. This method was verified using an online personalized customization system that was developed with WebGL and oriented toward 3D printing. The experimental results indicate that this method can generate a lightweight 3D scanning mesh rapidly and efficiently in a web environment.

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Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation

Cited by 6 publications

References 29 publications

Mesh smoothing algorithm based on exterior angles split

Mesh smoothing algorithm based on exterior angles split

Simultaneous Smoothing and Untangling of 2D Meshes Based on Explicit Element Geometric Transformation and Element Stitching

A Lightweight Surface Reconstruction Method for Online 3D Scanning Point Cloud Data Oriented toward 3D Printing

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