Статті в журналах: "MESH POINTS"

1

Gao, Ying, Rui Zhao Wang, and Jue Yuan. "Interest Points Guided Mesh Simplification." Applied Mechanics and Materials 263-266 (December 2012): 2320–23. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.2320.

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Based on interest point detection, a feature preserving mesh simplification algorithm is proposed. The Harris operator values of all vertices in the mesh were computed firstly. On the base of Garland’s simplification algorithm, we combine the Harris operator value with quadric error metric and change the order of edge collapsing in the simplification. The experimental results show that the proposed algorithm is effective and feature preserving.

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2

JIAO, Xue, Huixin ZHANG, and Tieru WU. "Mesh segmentation guided by seed points." Journal of Advanced Mechanical Design, Systems, and Manufacturing 9, no. 4 (2015): JAMDSM0051. http://dx.doi.org/10.1299/jamdsm.2015jamdsm0051.

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3

Sun, Yan, Xuelin Deng, Liangli He, and Haiyan Yao. "Regularization Method for Discrete Mesh Points." Journal of Computer-Aided Design & Computer Graphics 34, no. 05 (May 1, 2022): 804–10. http://dx.doi.org/10.3724/sp.j.1089.2022.19003.

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4

Medimegh, Nassima, Samir Belaid, Mohamed Atri, and Naoufel Werghi. "3D mesh watermarking using salient points." Multimedia Tools and Applications 77, no. 24 (June 18, 2018): 32287–309. http://dx.doi.org/10.1007/s11042-018-6252-6.

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5

Lei, Humin, Tao Liu, Deng Li, Jikun Ye, and Lei Shao. "Adaptive Mesh Iteration Method for Trajectory Optimization Based on Hermite-Pseudospectral Direct Transcription." Mathematical Problems in Engineering 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/2184658.

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An adaptive mesh iteration method based on Hermite-Pseudospectral is described for trajectory optimization. The method uses the Legendre-Gauss-Lobatto points as interpolation points; then the state equations are approximated by Hermite interpolating polynomials. The method allows for changes in both number of mesh points and the number of mesh intervals and produces significantly smaller mesh sizes with a higher accuracy tolerance solution. The derived relative error estimate is then used to trade the number of mesh points with the number of mesh intervals. The adaptive mesh iteration method is applied successfully to the examples of trajectory optimization of Maneuverable Reentry Research Vehicle, and the simulation experiment results show that the adaptive mesh iteration method has many advantages.

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6

Liu, Yong-Jin, and Matthew Ming-Fai Yuen. "Optimized triangle mesh reconstruction from unstructured points." Visual Computer 19, no. 1 (March 1, 2003): 23–37. http://dx.doi.org/10.1007/s00371-002-0162-2.

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7

Ejlali, Nastaran, and Seyed Mohammad Hosseini. "Adaptive control parameterization method by density functions for optimal control problems." IMA Journal of Mathematical Control and Information 37, no. 2 (April 1, 2019): 497–512. http://dx.doi.org/10.1093/imamci/dnz010.

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Abstract This paper proposes an efficient adaptive control parameterization method for solving optimal control problems. In this method, mesh density functions are used to generate mesh points. In the first step, the problem is solved by control parameterization on uniform mesh points. Then at each step, the approximate control obtained from the previous step is applied to construct a mesh density function, and consequently a new adapted set of mesh points. Several numerical examples are included to demonstrate that the adaptive control parameterization method is more accurate than a uniform control parameterization one.

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8

Oh, Sahuck. "A New Mesh Moving Technique for a Fluid–Structure Interaction Problem Using Mesh Deformation Energy Minimization." International Journal of Computational Methods 18, no. 01 (July 19, 2019): 1950039. http://dx.doi.org/10.1142/s0219876219500397.

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When mesh boundaries move in a simulation because of the motion of a target object such as translation, rotation, and oscillation, the mesh should be regenerated to the points it will obey the locations of its new boundaries. Because recreating new mesh from the beginning is a time-consuming task, new mesh is usually created by deforming an initial mesh, which is called the mesh moving method (or mesh deformation method). In this paper, we present a new mesh moving method that produces a higher quality deformed mesh than the current mesh moving methods. In the proposed method, the deformation of mesh is evaluated by two energy quantities that are related to (i) the distortion of mesh that is invariant to translation, rotation, and size changes of the elements of the mesh and (ii) the deformation of mesh calculated using elements’ size based on stiffened-linear elasticity equations. The total deformation energy of mesh is defined as a weighted sum of these two quantities. Because there is no need to pre-fix the locations of the outer boundary points for most mesh moving problems, we use new constraints, allowing the outer boundary points to move along tangential directions in the proposed method. The deformed mesh is computed by calculating the positions of the mesh points where the total deformation energy of the mesh is minimized. For test purposes, the proposed method is applied to 2D triangular meshes and a 3D tetrahedral mesh, where the meshes are deformed by the motions of the target objects such as translation, rotation, and deformation. When the quality of the deformed meshes computed with the proposed method are compared with the ones computed with current mesh moving methods, the meshes from the proposed method are shown to be better than the other meshes.

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9

EZAWA, Yoshitaka. "Automatic mesh generation by automatic generating internal points." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 755–56. http://dx.doi.org/10.1299/jsmecmd.2003.16.755.

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10

Remski, Joan. "Mesh Spacing Estimates and Efficiency Considerations for Moving Mesh Systems." Numerical Mathematics: Theory, Methods and Applications 9, no. 3 (July 20, 2016): 432–50. http://dx.doi.org/10.4208/nmtma.2016.m1508.

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AbstractAdaptive numerical methods for solving partial differential equations (PDEs) that control the movement of grid points are called moving mesh methods. In this paper, these methods are examined in the case where a separate PDE, that depends on a monitor function, controls the behavior of the mesh. This results in a system of PDEs: one controlling the mesh and another solving the physical problem that is of interest. For a class of monitor functions resembling the arc length monitor, a trade off between computational efficiency in solving the moving mesh system and the accuracy level of the solution to the physical PDE is demonstrated. This accuracy is measured in the density of mesh points in the desired portion of the domain where the function has steep gradient. The balance of computational efficiency versus accuracy is illustrated numerically with both the arc length monitor and a monitor that minimizes certain interpolation errors. Physical solutions with steep gradients in small portions of their domain are considered for both the analysis and the computations.

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11

Ha, Yujin, Jung-Ho Park, and Seung-Hyun Yoon. "Geodesic Hermite Spline Curve on Triangular Meshes." Symmetry 13, no. 10 (October 14, 2021): 1936. http://dx.doi.org/10.3390/sym13101936.

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Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing C1 piecewise cubic curves on a triangular mesh M while interpolating the given mesh points is presented. The conventional Hermite interpolation method is extended such that the generated curve lies on M. For this, a geodesic vector is defined as a straightest geodesic with symmetric property on edge intersections and mesh vertices, and the related geodesic operations between points and vectors on M are defined. By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh. The method follows the basic steps of the conventional Hermite interpolation process, except that the operations between the points and vectors are replaced with the geodesic. The effectiveness of the method is demonstrated by designing several sophisticated curves on triangular meshes and applying them to various applications, such as mesh-cutting, segmentation, and simulation.

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12

RAMASWAMI, SUNEETA, MARCELO SIQUEIRA, TESSA SUNDARAM, JEAN GALLIER, and JAMES GEE. "CONSTRAINED QUADRILATERAL MESHES OF BOUNDED SIZE." International Journal of Computational Geometry & Applications 15, no. 01 (February 2005): 55–98. http://dx.doi.org/10.1142/s0218195905001609.

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We introduce a new algorithm to convert triangular meshes of polygonal regions, with or without holes, into strictly convex quadrilateral meshes of small bounded size. Our algorithm includes all vertices of the triangular mesh in the quadrilateral mesh, but may add extra vertices (called Steiner points). We show that if the input triangular mesh has t triangles, our algorithm produces a mesh with at most [Formula: see text] quadrilaterals by adding at most t+2 Steiner points, one of which may be placed outside the triangular mesh domain. We also describe an extension of our algorithm to convert constrained triangular meshes into constrained quadrilateral ones. We show that if the input constrained triangular mesh has t triangles and its dual graph has h connected components, the resulting constrained quadrilateral mesh has at most [Formula: see text] quadrilaterals and at most t+3h Steiner points, one of which may be placed outside the triangular mesh domain. Examples of meshes generated by our algorithm, and an evaluation of the quality of these meshes with respect to a quadrilateral shape quality criterion are presented as well.

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13

Yang, Ren Zi, and Hong Sen Yan. "The Structure Principle of Knowledge Mesh and its Application." Advanced Materials Research 433-440 (January 2012): 4428–33. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.4428.

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Aiming at the rationality of new knowledge mesh, which is obtained from the self-reconfiguration of knowledgeable manufacturing systems, the inherent structure principle of the knowledge mesh is studied. Firstly, the sets of the knowledge points are classified by the equivalent relations, and the function topological space is constructed. The relationships between the sets of the knowledge points and the function topological space are established by the real set. In the function topological space, the conclusions of the base are given, which show the essential mapping relationships of the knowledge mesh, the topological space and the base. After knowing the principle, the structure of the knowledge mesh is reduced by using the equivalent relations, the base and the basic knowledge points. The completeness of the complex relationships in the knowledge mesh is studied by the transitive closure. These conclusions can reduce the structure and enhance the rationality of the knowledge mesh. Finally the given example shows that these theories are effective.

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14

Tyranowski, Tomasz M., and Mathieu Desbrun. "R-Adaptive Multisymplectic and Variational Integrators." Mathematics 7, no. 7 (July 18, 2019): 642. http://dx.doi.org/10.3390/math7070642.

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Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this paper, we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations, and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. Numerical results for the Sine–Gordon equation are also presented.

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15

Iwamoto, Masatami, and Chuzo Iwamoto. "Application of Finite Difference Method to Arbitrary Mesh Points." IEEJ Transactions on Fundamentals and Materials 120, no. 2 (2000): 116–21. http://dx.doi.org/10.1541/ieejfms1990.120.2_116.

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16

Bourquat, Pierre, David Coeurjolly, Guillaume Damiand, and Florent Dupont. "Hierarchical mesh-to-points as-rigid-as-possible registration." Computers & Graphics 102 (February 2022): 320–28. http://dx.doi.org/10.1016/j.cag.2021.10.016.

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17

Dimov, I., and O. Tonev. "Random walk on distant mesh points Monte Carlo methods." Journal of Statistical Physics 70, no. 5-6 (March 1993): 1333–42. http://dx.doi.org/10.1007/bf01049435.

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18

SUZUKI, Hiromasa, Yasuyuki KANDORI, Takashi KANAI, and Fumihiko KIMURA. "Triangular Mesh Reconstruction from Measured Data Points (1st Report)." Journal of the Japan Society for Precision Engineering 64, no. 9 (1998): 1314–19. http://dx.doi.org/10.2493/jjspe.64.1314.

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19

KANDORI, Yasuyuki, Hiromasa SUZUKI, Takashi KANAI, and Fumihiko KIMURA. "Triangular Mesh Reconstruction from Measured Data Points (2nd Report)." Journal of the Japan Society for Precision Engineering 64, no. 10 (1998): 1461–66. http://dx.doi.org/10.2493/jjspe.64.1461.

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20

Stys, Tadeusz. "A finite-difference scheme overconvergent at certain mesh points." Journal of Computational and Applied Mathematics 42, no. 2 (October 1992): 233–43. http://dx.doi.org/10.1016/0377-0427(92)90077-b.

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21

Zhang, Zhimin, and Runchang Lin. "Ultraconvergence of ZZ patch recovery at mesh symmetry points." Numerische Mathematik 95, no. 4 (October 1, 2003): 781–801. http://dx.doi.org/10.1007/s00211-003-0457-x.

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22

CLARKSON, KENNETH L., DAVID EPPSTEIN, GARY L. MILLER, CARL STURTIVANT, and SHANG-HUA TENG. "APPROXIMATING CENTER POINTS WITH ITERATIVE RADON POINTS." International Journal of Computational Geometry & Applications 06, no. 03 (September 1996): 357–77. http://dx.doi.org/10.1142/s021819599600023x.

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We give a practical and provably good Monte Carlo algorithm for approximating center points. Let P be a set of n points in Rd. A point c∈Rd is a β-center point of P if every closed halfspace containing c contains at least βn points of P. Every point set has a 1/(d+1)-center point; our algorithm finds an Ω(1/d2)-center point with high probability. Our algorithm has a small constant factor and is the first approximate center point algorithm whose complexity is subexponential in d. Moreover, it can be optimally parallelized to require O( log 2d log log n) time. Our algorithm has been used in mesh partitioning methods and can be used in the construction of high breakdown estimators for multivariate datasets in statistics. It has the potential to improve results in practice for constructing weak ∊-nets. We derive a variant of our algorithm whose time bound is fully polynomial in d and linear in n, and show how to combine our approach with previous techniques to compute high quality center points more quickly.

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23

Springel, Volker. "Moving-mesh hydrodynamics with the AREPO code." Proceedings of the International Astronomical Union 6, S270 (May 2010): 203–6. http://dx.doi.org/10.1017/s1743921311000378.

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AbstractAt present, hydrodynamical simulations in computational star formation are either carried out with Eulerian mesh-based approaches or with the Lagrangian smoothed particle hydrodynamics (SPH) technique. Both methods differ in their strengths and weaknesses, as well as in their error properties. It would be highly desirable to find an intermediate discretization scheme that combines the accuracy advantage of mesh-based methods with the automatic adaptivity and Galilean invariance of SPH. Here we briefly describe the novel AREPO code which achieves these goals based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. A particularly powerful feature is that the mesh-generating points can in principle be moved arbitrarily. If they are given the velocity of the local flow, an accurate Lagrangian formulation of continuum hydrodynamics is obtained that features a very low numerical diffusivity and is free of mesh distortion problems. If the points are kept fixed, the scheme is equivalent to a Eulerian code on a structured mesh. The new AREPO code appears especially well suited for problems such as gravitational fragmentation or compressible turbulence.

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24

Jiang, Hong Fei. "Triangle Interpolation on Discrete Point Set." Applied Mechanics and Materials 580-583 (July 2014): 2872–75. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2872.

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An algorithm for triangle interpolation on discrete points is presented in the paper. It creates a square mesh which covers all the discrete points, then puts the points into the mesh and records the relationship between grids and points. When interpolating elevation of an interpolation point, it can fast find the discrete points which are near the interpolation point and these discrete points can be used to create a special triangle which contains the interpolation point. The elevation of the interpolation point can be obtained from the triangle. The method has the advantage of fast speed, high precision and needing less memory.

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25

Li, Ningbo, Humin Lei, Lei Shao, Tao Liu, and Bin Wang. "Trajectory Optimization Based on Multi-Interval Mesh Refinement Method." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/8521368.

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In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

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26

Sun, Xiaopeng, J. Pan, and Xiaopeng Wei. "3D mesh skeleton extraction using prominent segmentation." Computer Science and Information Systems 7, no. 1 (2010): 63–74. http://dx.doi.org/10.2298/csis1001063s.

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Skeleton of 3D mesh is a fundamental shape feature, and is useful for shape description and other many applications in 3D Digital Geometry Processing. This paper presents a novel skeleton extraction algorithm based on feature point and core extraction by the Multidimensional scaling (MDS) transformation. The algorithm first straights the folded prominent branch up, as well as the prominent shape feature points of mesh are computed, a meaningful segmentation is applied under the direction of feature points. The Node-ring of all segmented components is defined by discrete geodesic path on mesh surface, and then the skeleton of every segmented component is defined as the link of the Node-ring's center. As to the core component without prominent feature points, principal curve is used to fit its skeleton. Our algorithm is simple, and invariant both to the pose of the mesh and to the different proportions of model's components.

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27

Ma, Xinwu, and Lu Sun. "An automatic approach to constrained quadrilateral mesh generation." Engineering Computations 37, no. 3 (November 7, 2019): 929–51. http://dx.doi.org/10.1108/ec-03-2019-0114.

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Purpose Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly. Design/methodology/approach This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation. Findings An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach. Originality/value An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.

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Liao, Haixiang, and Xiang Gao. "Parallel Efficient Mesh Deformation Method Based On Support Vector Regression." Applied Science and Innovative Research 4, no. 4 (November 27, 2020): p54. http://dx.doi.org/10.22158/asir.v4n4p54.

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Mesh deformation method is widely used in unsteady numerical simulations involving moving boundaries. This kind of method redistributes the position of grid points in accordance with the movement of the computational domain without changing their connectivity relations. In this paper, we present a parallel mesh deformation method based on the support vector machine regression (SVR). In each time step, the proposed method first trains three SVRs by the coordinates of the boundary points and their known displacements in each direction, and then predicts the displacements of the internal points using the SVRs. After deforming the mesh, the dual-time step flow solver is used to solve the governing equations. To ensure the consistency of the method running in parallel, the training part of the method is executed with all global boundary points in each decomposed domain. Therefore, each CPU needs to maintain a copy of the entire boundary points via a point-to-point communication. The internal evaluation of the method is predicted separately in each decomposed domain without any data dependency. An oscillatory and transient pitching airfoil case is simulated to demonstrate the applicability of the proposed mesh deformation method, and its parallel efficiency is over 60% with 64 cores.

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Jiang, Juan Fen, Yue Qi Zhong, and Qiu Ping Zhang. "Three-Dimensional Garment Surface Reconstruction Based on Ball-Pivoting Algorithm." Advanced Materials Research 821-822 (September 2013): 765–68. http://dx.doi.org/10.4028/www.scientific.net/amr.821-822.765.

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After 3D garment surface resampling, the topological graph of the resampling points should be reconstructed, that is a new triangular mesh can be generated. We exploit automatic method to generate topology of the mesh with total number of resampling points. In our approach, based and ball-pivoting algorithm based surface reconstruction techniques are introduced respectively, has an accurate shape approximated the original resampling points cloud, but exists large unwanted components. The ball-pivoting algorithm is selected to reconstruct the topological graph, as the principle is simple, the ball with given radius can pivot along an existing edge to touch another point to shape a new triangle. Eventually the 3D garment surface mesh reconstructed by the ball-pivoting algorithm has regular and uniform visual effect.

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30

Zhang, Shujun. "An Adaptive Progressive Mesh Reconstruction Algorithm for Spatial Discrete Points." Procedia Engineering 29 (2012): 589–96. http://dx.doi.org/10.1016/j.proeng.2012.01.009.

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31

Niu, Jianping, Juanmian Lei, and Jiandong He. "Radial basis function mesh deformation based on dynamic control points." Aerospace Science and Technology 64 (May 2017): 122–32. http://dx.doi.org/10.1016/j.ast.2017.01.022.

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32

Tsai, F., H. Chang, and Y. W. Lin. "COMBINING 3D VOLUME AND MESH MODELS FOR REPRESENTING COMPLICATED HERITAGE BUILDINGS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W5 (August 21, 2017): 673–77. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w5-673-2017.

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This study developed a simple but effective strategy to combine 3D volume and mesh models for representing complicated heritage buildings and structures. The idea is to seamlessly integrate 3D parametric or polyhedral models and mesh-based digital surfaces to generate a hybrid 3D model that can take advantages of both modeling methods. The proposed hybrid model generation framework is separated into three phases. Firstly, after acquiring or generating 3D point clouds of the target, these 3D points are partitioned into different groups. Secondly, a parametric or polyhedral model of each group is generated based on plane and surface fitting algorithms to represent the basic structure of that region. A “bare-bones” model of the target can subsequently be constructed by connecting all 3D volume element models. In the third phase, the constructed bare-bones model is used as a mask to remove points enclosed by the bare-bones model from the original point clouds. The remaining points are then connected to form 3D surface mesh patches. The boundary points of each surface patch are identified and these boundary points are projected onto the surfaces of the bare-bones model. Finally, new meshes are created to connect the projected points and original mesh boundaries to integrate the mesh surfaces with the 3D volume model. The proposed method was applied to an open-source point cloud data set and point clouds of a local historical structure. Preliminary results indicated that the reconstructed hybrid models using the proposed method can retain both fundamental 3D volume characteristics and accurate geometric appearance with fine details. The reconstructed hybrid models can also be used to represent targets in different levels of detail according to user and system requirements in different applications.

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Chen, Zhong, Zhiwei Hou, Mujian Xia, and Yuegang Xing. "Adaptive Surface Mesh Reconstruction for Computed Tomography Images." Journal of Medical Imaging and Health Informatics 9, no. 6 (August 1, 2019): 1086–94. http://dx.doi.org/10.1166/jmihi.2019.2710.

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In medical applications, it is important to reconstruct surface meshes from Computed Tomography (CT) images. Surface mesh reconstruction of biological tissues actually suffers from staircase artifacts, due to anisotropic CT data. To solve this problem, this paper proposes an adaptive surface mesh reconstruction method. We convert the contour pixels of medical image to contour points and exploit the adaptive spherical cover to produce an approximating surface based on the contour points. Due to the reconstruction quality depending on the accurate normal estimation, computing the normal vectors from the negative gradient based on 3D binary volume data instead of classical principal component analysis (PCA), and then covering contour points by adaptive spheres, linking the auxiliary points in the spheres for reconstructing adaptive triangular meshes. The presented method has been used in CT images of the first cervical vertebrae (C1), scapula, as well as the third lumbar vertebrae (L3) and the results are analyzed regarding their smoothness, accuracy and mesh quality. The results show that our method can reconstruct smooth, accurate and high-quality adaptive surface meshes.

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34

Shi, Lina, Dehui Kong, Shaofan Wang, and Baocai Yin. "Adaptive Geometry Images for Remeshing." International Journal of Digital Multimedia Broadcasting 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2724184.

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Geometry images are a kind of completely regular remeshing methods for mesh representation. Traditional geometry images have difficulties in achieving optimal reconstruction errors and preserving manually selected geometric details, due to the limitations of parametrization methods. To solve two issues, we propose two adaptive geometry images for remeshing triangular meshes. The first scheme produces geometry images with the minimum Hausdorff error by finding the optimization direction for sampling points based on the Hausdorff distance between the original mesh and the reconstructed mesh. The second scheme produces geometry images with higher reconstruction precision over the manually selected region-of-interest of the input mesh, by increasing the number of sampling points over the region-of-interest. Experimental results show that both schemes give promising results compared with traditional parametrization-based geometry images.

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Shahan, Charles P., Nathaniel N. Stoikes, Esra Roan, James Tatum, David L. Webb, and Guy R. Voeller. "Biomechanical and Histologic Evaluation of LifeMesh™: A Novel Self-Fixating Mesh Adhesive." American Surgeon 84, no. 4 (April 2018): 520–25. http://dx.doi.org/10.1177/000313481808400424.

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Mesh fixation with the use of adhesives results in an immediate and total surface area adhesion of the mesh, removing the need for penetrating fixation points. The purpose of this study was to evaluate LifeMesh™, a prototype mesh adhesive technology which coats polypropylene mesh. The strength of the interface between mesh and tissue, inflammatory responses, and histology were measured at varying time points in a swine model, and these results were compared with sutures. Twenty Mongrel swine underwent implantation of LifeMesh™ and one piece of bare polypropylene mesh secured with suture (control). One additional piece of either LifeMesh™ or control was used for histopathologic evaluation. The implants were retrieved at 3, 7, and 14 days. Only 3- and 7-day specimens underwent lap shear testing. On Day 3, LifeMesh™ samples showed considerably less contraction than sutured samples. The interfacial strength of Day 3 LifeMesh™ samples was similar to that of sutured samples. At seven days, LifeMesh™ samples continued to show significantly less contraction than sutured samples. The strength of fixation at seven days was greater in the control samples. The histologic findings were similar in LifeMesh™ and control samples. LifeMesh™ showed significantly less contraction than sutured samples at all measured time points. Although fixation strength was similar at three days, the interfacial strength of LifeMesh™ remained unchanged, whereas sutured controls increased by day 7. With histologic equivalence, considerably less contraction, and similar early fixation strength, LifeMesh™ is a viable mesh fixation technology.

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Md. Masum Murshed, Md. Morshed Bin Shiraj, Md. Safik Ullah, Md. Mizanur Rahman, and Md. Manik Hossain. "On the Approximation of the Bay of Bengal Domain to be Compatible for the Implementation of Finite Element Method." World Journal of Advanced Engineering Technology and Sciences 9, no. 1 (June 30, 2023): 290–95. http://dx.doi.org/10.30574/wjaets.2023.9.1.0170.

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In this study, the Bay of Bengal domain has been approximated using triangular mesh so that the finite element method (FEM) can be employed on it. The area between 15º N and 23º N Latitudes and 85º E and 95º E Longitudes is considered as the physical domain. A MATLAB routine and the cubic spline interpolation have been used to extract the coordinates of the points on the boundary of the whole domain and the points on the boundary of the islands from a colour image of the domain. A C++ routine is used to generate an edp file for triangular mesh using the extracted coordinates. Then FreeFem++ is used to create triangular mesh for the whole domain from the generated edp file. All the major islands are also incorporated in the final mesh. The obtained triangular mesh can be used to develop a storm surge prediction model for the Bay of Bengal region implementing FEM.

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Chen, Shao Ke, and Hui Qun Chen. "Triangulation Method of 3D Scattered Data Points Based on CAD Model." Applied Mechanics and Materials 52-54 (March 2011): 139–43. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.139.

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A new method of triangulation for large scale scattered 3D points is proposed. This method is based on the available CAD model, with the thought of DC(divide and conquer).Alignment between the data and the CAD model, registration which establishes correspondence between the data points and those on the CAD trimmed NURBS surface entities;2D-Delaunay triangulation, performed on the corresponding points in the parametric domains(u, v)of each entity, application of the connectivity structure to the 3D data points for each mesh patch; Elimination of redundant triangles of each 3D mesh patch and stitching of patches together. Unlike many other methods, it is not constrained by certain types of measurement distribution or object shape. The experimental results testify that the approach is feasible and efficient.

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38

Stachó, László L. "A Simple Affine-Invariant Spline Interpolation over Triangular Meshes." Mathematics 10, no. 5 (February 28, 2022): 776. http://dx.doi.org/10.3390/math10050776.

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Given a triangular mesh, we obtain an orthogonality-free analogue of the classical local Zlámal–Ženišek spline procedure with simple explicit affine-invariant formulas in terms of the normalized barycentric coordinates of the mesh triangles. Our input involves first-order data at mesh points, and instead of adjusting normal derivatives at the side middle points, we constructed the elementary splines by adjusting the Fréchet derivatives at three given directions along the edges with the result of bivariate polynomials of degree five. By replacing the real line R with a generic field K, our results admit a natural interpretation with possible independent interest, and the proofs are short enough for graduate courses.

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39

Grzeczkowicz, G., and B. Vallet. "SEMANTIC SEGMENTATION OF URBAN TEXTURED MESHES THROUGH POINT SAMPLING." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2022 (May 17, 2022): 177–84. http://dx.doi.org/10.5194/isprs-annals-v-2-2022-177-2022.

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Abstract. Textured meshes are becoming an increasingly popular representation combining the 3D geometry and radiometry of real scenes. However, semantic segmentation algorithms for urban mesh have been little investigated and do not exploit all radiometric information. To address this problem, we adopt an approach consisting in sampling a point cloud from the textured mesh, then using a point cloud semantic segmentation algorithm on this cloud, and finally using the obtained semantic to segment the initial mesh. In this paper, we study the influence of different parameters such as the sampling method, the density of the extracted cloud, the features selected (color, normal, elevation) as well as the number of points used at each training period. Our result outperforms the state-of-the-art on the SUM dataset, earning about 4 points in OA and 18 points in mIoU.

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40

Long, Jianbo, and Colin G. Farquharson. "On the forward modelling of three-dimensional magnetotelluric data using a radial-basis-function-based mesh-free method." Geophysical Journal International 219, no. 1 (July 5, 2019): 394–416. http://dx.doi.org/10.1093/gji/ggz306.

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SUMMARY The investigation of using a novel radial-basis-function-based mesh-free method for forward modelling magnetotelluric data is presented. The mesh-free method, which can be termed as radial-basis-function-based finite difference (RBF-FD), uses only a cloud of unconnected points to obtain the numerical solution throughout the computational domain. Unlike mesh-based numerical methods (e.g. grid-based finite difference, finite volume and finite element), the mesh-free method has the unique feature that the discretization of the conductivity model can be decoupled from the discretization used for numerical computation, thus avoiding traditional expensive mesh generation and allowing complicated geometries of the model be easily represented. To accelerate the computation, unstructured point discretization with local refinements is employed. Maxwell’s equations in the frequency domain are re-formulated using $\mathbf {A}$-ψ potentials in conjunction with the Coulomb gauge condition, and are solved numerically with a direct solver to obtain magnetotelluric responses. A major obstacle in applying common mesh-free methods in modelling geophysical electromagnetic data is that they are incapable of reproducing discontinuous fields such as the discontinuous electric field over conductivity jumps, causing spurious solutions. The occurrence of spurious, or non-physical, solutions when applying standard mesh-free methods is removed here by proposing a novel mixed scheme of the RBF-FD and a Galerkin-type weak-form treatment in discretizing the equations. The RBF-FD is applied to the points in uniform conductivity regions, whereas the weak-form treatment is introduced to points located on the interfaces separating different homogeneous conductivity regions. The effectiveness of the proposed mesh-free method is validated with two numerical examples of modelling the magnetotelluric responses over 3-D conductivity models.

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Kim, A. Ram, Shawn Keshmiri, Weizhang Huang, and Gonzalo Garcia. "Guidance of Multi-Agent Fixed-Wing Aircraft Using a Moving Mesh Method." Unmanned Systems 04, no. 03 (July 2016): 227–44. http://dx.doi.org/10.1142/s2301385016500084.

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This paper presents a novel guidance logic for multi-agent fixed-wing unmanned aerial systems using a moving mesh method. The moving mesh method is originally designed for use in the adaptive numerical solution of partial differential equations, where a high proportion of mesh points are placed in the regions of large solution variations and few points in the rest of the domain. In this work, the positions of the aircraft are considered as mesh nodes connected to form a triangular mesh in two spatial dimensions. The outer aircraft positions are planned with the reference point algorithm. This logic provides the outer agents moving point positions that are relative to a virtual point position with the desired heading angle and velocity. The inner agents, or interior mesh nodes, are moved with a moving mesh technique to keep the whole mesh as uniform as possible. The moving mesh technique has built-in mechanisms to keep the mesh as uniform as possible and prevent nodes from crossing over or tangling. This property can be seen as an automatic internal collision avoidance mechanism. It also has explicit formulas for nodal velocities, making the technique easy to implement on computer. The mesh nodes are replaced by unmanned aerial systems with nonlinear six degrees of freedom dynamics. The centralized moving mesh guidance is complimented by a decentralized nonlinear predictive controller to control each aircraft. To validate flexibility and coherency of agents and formation, the moving point concept is used in the simulation to follow an arbitrary, linear, sinewave-like, or curvature shaped flight segments. Robustness of the algorithm is also verified where agents were affected by external wind.

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Voutchkov, Ivan, Andy Keane, Shahrokh Shahpar, and Ron Bates. "(Re-) Meshing using interpolative mapping and control point optimization." Journal of Computational Design and Engineering 5, no. 3 (December 15, 2017): 305–18. http://dx.doi.org/10.1016/j.jcde.2017.12.003.

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Abstract This work proposes a simple and fast approach for re-meshing the surfaces of smooth-featured geometries prior to CFD analysis. The aim is to improve mesh quality and thus the convergence and accuracy of the CFD analysis. The method is based on constructing an interpolant based on the geometry shape and then mapping a regular rectangular grid to the shape of the original geometry using that interpolant. Depending on the selected interpolation algorithm the process takes from less than a second to several minutes. The main interpolant discussed in this article is a Radial Basis Function with cubic spline basis, however other algorithms are also compared. The mesh can be optimized further using active (flexible) control points and optimization algorithms. A range of objective functions are discussed and demonstrated. The difference between re-interpolated and original meshes produces a metric function which is indicative of the mesh quality. It is shown that the method works for flat 2D surfaces, 3D surfaces and volumes. Highlights RBF Map is created between key points on an arbitrary shape and an ideal equivalent. The rest of the points are recreated using reverse transformation to the original. Control points are automatically selected based on k-mean clustering. Optimization of the control points position based on desired mesh quality metrics. The method is shown to work both on 2D and 3D shapes as well as 3D surfaces.

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Ding, Li, Tongqing Guo, and Zhiliang Lu. "A Hybrid Method for Dynamic Mesh Generation Based on Radial Basis Functions and Delaunay Graph Mapping." Advances in Applied Mathematics and Mechanics 7, no. 3 (May 28, 2015): 338–56. http://dx.doi.org/10.4208/aamm.2014.m614.

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AbstractAiming at complex configuration and large deformation, an efficient hybrid method for dynamic mesh generation is presented in this paper, which is based on Radial Basis Functions (RBFs) and Delaunay graph mapping. Based on the computational mesh, a set of very coarse grid named as background grid is generated firstly, and then the computational mesh can be located at the background grid by Delaunay graph mapping technique. After that, the RBFs method is applied to deform the background grid by choosing partial mesh points on the boundary as the control points. Finally, Delaunay graph mapping method is used to relocate the computational mesh by employing area or volume weight coefficients. By applying different dynamic mesh methods to a moving NACA0012 airfoil, it can be found that the RBFs-Delaunay graph mapping hybrid method is as accurate as RBFs and is as efficient as Delaunay graph mapping technique. Numerical results show that the dynamic meshes for all test cases including one two-dimensional (2D) and two three-dimensional (3D) problems with different complexities, can be generated in an accurate and efficient manner by using the present hybrid method.

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44

Cao, Zhi-Wei, Zhi-Fan Liu, Zhi-Feng Liu, and Xiao-Hong Wang. "A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/8379609.

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Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.

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45

Palma, Stella S. A., and Raquel Gonçalves. "Tomographic images of tree trunks generated using ultrasound and post-processed images: Influence of the number of measurement points." BioResources 17, no. 4 (October 14, 2022): 6638–55. http://dx.doi.org/10.15376/biores.17.4.6638-6655.

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Tomography is a technique increasingly used in tree inspections. This technique can be performed in two stages: field testing and postimage processing. To feed the tomographic image construction software, it is necessary to adopt a measurement grid composed of points positioned on the perimeter of the stem. The images are generated through spatial interpolation algorithms. From a theoretical point of view, more measurement points taken in the perimeter of the stem result in better interpolation results. However, an increase in the number of mesh points causes a substantial increase in field work and image processing time. The general objective of this study was to verify the influence of the number of measurement points of the diffraction mesh on the ultrasound tomography results. For this purpose, ten simulated discs were used, all 500 mm in diameter and with different defects in terms of size, position, and geometry. In each of the discs, diffraction grids were simulated with 6, 8, 10, 12, and 14 measurement points in the contour. The results showed that a favorable combination of accuracy and a minimization of effort can be achieved with diffraction mesh with number of measurement points calculated as five times the perimeter of the trunk in meters.

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46

Ozendi, M., D. Akca, and H. Topan. "STOCHASTIC SURFACE MESH RECONSTRUCTION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2 (May 30, 2018): 805–12. http://dx.doi.org/10.5194/isprs-archives-xlii-2-805-2018.

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A generic and practical methodology is presented for 3D surface mesh reconstruction from the terrestrial laser scanner (TLS) derived point clouds. It has two main steps. The first step deals with developing an anisotropic point error model, which is capable of computing the theoretical precisions of 3D coordinates of each individual point in the point cloud. The magnitude and direction of the errors are represented in the form of error ellipsoids. The following second step is focused on the stochastic surface mesh reconstruction. It exploits the previously determined error ellipsoids by computing a point-wise quality measure, which takes into account the semi-diagonal axis length of the error ellipsoid. The points only with the least errors are used in the surface triangulation. The remaining ones are automatically discarded.

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MA, ZHIHUA, and HONGQUAN CHEN. "SIMULATIONS OF TRANSONIC INVISCID FLOWS OVER AIRFOILS USING MESHFREE ADAPTIVE ALGORITHM." Modern Physics Letters B 19, no. 28n29 (December 20, 2005): 1491–94. http://dx.doi.org/10.1142/s0217984905009730.

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A new mesh free algorithm, which is both solution and geometry adaptive, is introduced and described in this paper to capture the physical features of inviscid flows modeled by the Euler equations. Only clouds of points instead of grids are distributed over the computational domain and the spatial derivatives of the Euler equations are estimated using a weighted least-square curve fit on local clouds of points. The adaptive approach is compared to traditional global refinement techniques using structured grids. In this procedure, unnecessary "grid" points in adjacent area are prevented from being generated by using mesh free local clouds refinement techniques. These techniques operate, in particular, in the vicinity of shock influencing regions and near large curvature regions including the boundary surface of the geometry. Several numerical experiments with Euler flow simulation around airfoils at transonic regimes will be presented to illustrate the potential of this methodology in terms of accuracy, efficiency and low computer memory requirement of the mesh free adaptive algorithm.

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Yao, Peng, and Wei Zhang. "Construct 2D Stable and Unstable Manifolds of Nonlinear Maps." Advanced Materials Research 580 (October 2012): 432–36. http://dx.doi.org/10.4028/www.scientific.net/amr.580.432.

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The procedure resolves the insertion of new mesh point, the searching of the image (or pre-image) and computation of the 1D sub-manifolds following the new mesh point tactfully, it does not require the 1D sub-manifolds to be computed from the initial circle and avoids the assembling of mesh points. The performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.

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Juško, Marika, and Igors Ivanovs. "Quality of life after hiatal hernia repair with biosynthetic mesh Phasix^TM." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 76, no. 5-6 (December 1, 2022): 632–35. http://dx.doi.org/10.2478/prolas-2022-0097.

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Abstract Hiatal hernias are one of the most common types of hernia, which are found in 55–60% patients over 50 years, but only 9% are symptomatic. In most cases hiatal hernia manifests with the signs of gastroesophageal reflux disease (GERD) and is managed with lifestyle changes and proton pump inhibitors. In some cases, surgical therapy is indicated. Usually, surgical repair includes cruroplasty and fundoplication; however, the recurrence rate is up to 42%. Mesh reinforcement helps to decrease recurrence rate, but may lead to a development of visceral adhesions, erosions, mesh migration or infection. To avoid these complications, a new completely resorbable mesh PhasixTM is offered in the market. The aim of the study was to evaluate the quality of life (QoL), complications, and patient satisfaction after large hiatal hernia repair with PhasixTM mesh at 1-year follow-up. All the patients were satisfied with the surgery. The median GERD Health Related QoL index was 6.5 points, which is significantly less than before surgery — 29.5 points (p = 0.04). There were no mesh related complications and no clinical data of recurrence. Hiatal hernia repair with slowly resorbable biosynthetic mesh PhasixTM has acceptable results in terms of GERD Health Related QoL, complications and patient satisfaction at one-year follow-up.

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Liu, Yawen, Bingxuan Guo, Xiongwu Xiao, and Wei Qiu. "3D Mesh Pre-Processing Method Based on Feature Point Classification and Anisotropic Vertex Denoising Considering Scene Structure Characteristics." Remote Sensing 13, no. 11 (May 29, 2021): 2145. http://dx.doi.org/10.3390/rs13112145.

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3D mesh denoising plays an important role in 3D model pre-processing and repair. A fundamental challenge in the mesh denoising process is to accurately extract features from the noise and to preserve and restore the scene structure features of the model. In this paper, we propose a novel feature-preserving mesh denoising method, which was based on robust guidance normal estimation, accurate feature point extraction and an anisotropic vertex denoising strategy. The methodology of the proposed approach is as follows: (1) The dual weight function that takes into account the angle characteristics is used to estimate the guidance normals of the surface, which improved the reliability of the joint bilateral filtering algorithm and avoids losing the corner structures; (2) The filtered facet normal is used to classify the feature points based on the normal voting tensor (NVT) method, which raised the accuracy and integrity of feature classification for the noisy model; (3) The anisotropic vertex update strategy is used in triangular mesh denoising: updating the non-feature points with isotropic neighborhood normals, which effectively suppressed the sharp edges from being smoothed; updating the feature points based on local geometric constraints, which preserved and restored the features while avoided sharp pseudo features. The detailed quantitative and qualitative analyses conducted on synthetic and real data show that our method can remove the noise of various mesh models and retain or restore the edge and corner features of the model without generating pseudo features.

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