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mesh parameterization based on one-step inverse forming

COMPUTER-AIDED DESIGN 2010年第7期42卷 633-640页

作者： Li, Baojun Zhang, Xiangkui Zhou, Ping Hu, Ping Dalian Univ Technol Fac Vehicle Engn & Mech Sch Automot Engn Dalian 116024 Peoples R China Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Jilin Univ Coll Automot Engn Changchun 130022 Peoples R China

A novel planar mesh parameterization algorithm via flattening or unfolding is proposed by introducing a so-called one-step inverse approach (IA) based on physical plastic deformation of metal materials. As opposed to methods based on geometric idea, the algorithm is more suitable for CAD models, e.g. rapid prediction of blank shape in sheet metal forming for auto-body panels. Benefiting from proper preprocessing steps, rapid simulation of sheet metal forming and optimal initial solution guess, the proposed algorithm flattens meshes onto a plane with lower area distortion and minimizes the angular distortion. Some numerical examples of results generated by the new parameterization method are provided, and the corresponding analyses are given as well, such as distributions of strain, stress, thickness distribution and formability, etc. (c) 2010 Elsevier Ltd. All rights reserved.

关键词： mesh parameterization Flattening One-step inverse forming Elasto-plastic deformation CAD models

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mesh parameterization based on inverse finite element method: theory and application

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2013年第7期21卷 1169-1182页

作者： Zhu, Xue-Feng Hu, Ping Dalian Univ Technol Sch Automot Engn Dalian 116024 Liaoning Provin Peoples R China

A novel mesh parameterization (MP) method based on inverse finite element method (IFEM), called MP-IFEM, is proposed in this article. Unlike traditional methods, the geometry surface is considered to own real physical properties and can undergo large plastic deformation based on the shell theory. It can be unfolded into a two-dimensional planar domain under a given pressure. This method can quickly obtain a more accurate unfolding surface from an open surface with arbitrary topology meshed by triangular or quadrilateral meshes. MP-IFEM is robust enough to deal with 100,000 elements within about 2min. In order to reduce the folds and to keep global bijectivity, a step by step unfolding technique is also developed for unfolding complex surfaces.

关键词： mesh parameterization inverse finite element method surface parameterization mesh generation surface reconstruction

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mesh parameterization by minimizing the synthesized distortion metric with the coefficient-optimizing algorithm

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IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2006年第1期12卷 83-92页

作者： Yan, JQ Yang, X Shi, PF Zhang, D Shanghai Jiao Tong Univ Inst Image Proc & Pattern Recognit Shanghai 200030 Peoples R China Hong Kong Polytech Univ Ctr Multimedia Signal Proc Dept Comp Kowloon Hong Kong Peoples R China

The parameterization of a 3D mesh into a planar domain requires a distortion metric and a minimizing process. Most previous work has sought to minimize the average area distortion, the average angle distortion, or a combination of these. Typical distortion metrics can reflect the overall performance of parameterizations but discount high local deformations. This affects the performance of postprocessing operations such as uniform remeshing and texture mapping. This paper introduces a new metric that synthesizes the average distortions and the variances of both the area deformations and the angle deformations over an entire mesh. Experiments show that, when compared with previous work, the use of synthesized distortion metric performs satisfactorily in terms of both the average area deformation and the average angle deformation;furthermore, the area and angle deformations are distributed more uniformly. This paper also develops a new iterative process for minimizing the synthesized distortion, the coefficient-optimizing algorithm. At each iteration, rather than updating the positions immediately after the local optimization, the coefficient-optimizing algorithm first update the coefficients for the linear convex combination and then globally updates the positions by solving the Laplace system. The high performance of the coefficient-optimizing algorithm has been demonstrated in many experiments.

关键词： mesh parameterization texture mapping barycentric mapping conformal mapping harmonic mapping

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Conformal mesh parameterization using discrete Calabi flow

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COMPUTER AIDED GEOMETRIC DESIGN 2018年 63卷 96-108页

作者： Zhao, Hui Li, Xuan Ge, Huabin Lei, Na Zhang, Min Wang, Xiaoling Gu, Xianfeng [a]Tsinghua University China [b]Beijing Advanced Innovation Center for Imaging Technology Capital Normal University China [c]Department of Mathematics Beijing Jiaotong University China [d]DUT-RU International School of Information and Software Engineering Dalian University of Technology China [e]Computer Science Department State University of New York at Stony Brook USA [f]Brigham and Women's Hospital Harvard Medical School USA [g]Center of Mathematical Sciences and Applications Harvard University USA [h]Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province China [i]School of Mechanical Engineering University of Science and Technology Beijing China

In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and explicit format. Its corresponding flow is conformal and convergent under certain conditions. Our method is based on the Calabi energy and Calabi flow with solid theoretical and mathematical base. We demonstrate our approach on dozens of models and compare it with other related flow based methods, such as the well-known Ricci flow and conformal equivalence of triangle meshes (CETM). Our experiments show that the performance of our algorithm is comparably the same with other methods. The discrete Calabi flow in our method provides another perspective on conformal flow and conformal parameterization. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Calabi flow mesh parameterization Conformal mapping

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Weighted area/angle distortion minimization for mesh parameterization

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ENGINEERING COMPUTATIONS 2017年第6期34卷 1874-1895页

作者： Mejia, Daniel Acosta, Diego A. Ruiz-Salguero, Oscar Univ EAFIT Lab CAD CAM CAE Medellin Colombia Univ EAFIT Grp Desarrollo & Diseno Proc Medellin Colombia

Purpose - mesh parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions. Design/methodology/approach - A mesh parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0;an affine transform within the plane Z = 0 to glue the triangles back together;and a Levenberg-Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: a with 0 <= alpha <= 1) and angle distortion (weight: 1 - alpha). Findings - The present study parameterization algorithm has linear complexity [O(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. Originality/value - The devised free boundary nonlinear mesh parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterize

关键词： Reverse engineering Sensitivity analysis Complexity analysis Levenberg-Marquardt mesh parameterization Nonlinear optimization

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mesh parameterization using elastic FEM with negative Poisson's ratio material and triangle shape transformation

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COMPUTER-AIDED DESIGN 2023年第1期160卷

作者： Kong, Haijiao Zhang, Zhibing Liu, Yuqi Wang, Zhen Wei, Yang Li, Qiaomin Huazhong Univ Sci & Technol State Key Lab Mat Proc & Die & Mould Technol Wuhan 430074 Peoples R China Wuhan Text Univ Wuhan 430074 Peoples R China

Linear mesh parameterization method with a free boundary is an attractive technology and a ubiquitous tool that is widely used in computer graphics and geometry processing. The existing methods always have the shortcoming of element flipping. In this study, a novel linear mesh parameterization method with a free boundary is proposed based on the linear elastic finite element model of a material with negative Poisson's ratio. With appropriate parameter settings, the method can flatten a 3D mesh without element flipping to the most extent. The proposed method is divided into two steps: (1) each element of the 3D mesh is compressed to the origin point;(2) the degenerated mesh is gradually expanded in a plane under the two forces of equal magnitude and opposite directions based on a finite element model of an elastic membrane material with negative Poisson's ratio. Subsequently, the causes of element flipping are analyzed at internal nodes and boundary nodes. The triangle shape transformation (TST) method is proposed to solve the problem of internal element flipping, and the stiffness enhancement method is presented to overcome the boundary element flipping caused by the severe mutual extrusion of the internal elements near the boundary. Finally, typical examples are tested to verify the effectiveness of the proposed mesh parameterization method. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Negative Poisson's ratio mesh parameterization Free boundary mesh mapping Finite element method

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Enhancing mesh parameterization Efficiency: A Study on Patch Generation Optimization in V-DMC Standard

Enhancing Mesh Parameterization Efficiency: A Study on Patch...

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International Conference on Ubiquitous Communication (Ucom)

作者： Huang, Haidi Sun, Zhe Zou, Wenjie Lv, Zhuoyi Xidian Univ Sch Telecommun Engn Xian Peoples R China Vivo Mobile Commun Co Ltd Beijing Peoples R China

ISBN: (纸本)9798350374223;9798350374216

The emergence of immersive video concepts like the Metaverse has increased the importance of 3D meshes in various fields. Given that 3D mesh compression facilitates storing and transmitting a large amount of data from 3D meshes, it is a crucial aspect of their application. The Moving Picture Experts Group (MPEG) is developing a standard known as Video-based Dynamic mesh Coding (V-DMC), aimed at dynamic meshes with high-precision attribute information. As a type of information representing surface texture or material properties of 3D meshes, the attribute information significantly influences the subjective quality of the 3D model. In the V-DMC framework, the encoding of attribute information involves mesh parameterization, which is used to regenerate texture coordinates. One of the adopted mesh parameterization methods, i.e., OrthoAtlas, has the advantage of low time complexity. In this paper, an optimization scheme is proposed for OrthoAtlas. Specially, considering the issue of inaccurate projection planes for patches, the optimal projection planes are determined by recalculating the normal vectors of the patches. Furthermore, to enhance coding efficiency, it is integrated with rate-distortion optimization to decide whether to merge patches. Experimental results show that the proposed methods can improve the performance in terms of BD-Rate. The proposed methods have been adopted by the V-DMC standard and integrated into the MPEG V-DMC reference software.

关键词： mesh compression mesh parameterization OrthoAtlas attribute V-DMC

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A General Framework for Constrained mesh parameterization 15

A General Framework for Constrained Mesh Parameterization

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31st Spring Conference on Computer Graphics

作者： Vaitkus, Marton Varady, Tamas Budapest Univ Technol & Econ Budapest Hungary

ISBN: (纸本)9781450336932

Parameterizing or flattening a triangle mesh is necessary for many applications in computer graphics and geometry. While mesh parameterization is a very popular research topic, the vast majority of the literature is focused on minimizing distortion or satisfying constraints related to certain applications such as texturing or quadrilateral remeshing. Certain downstream applications require adherence to more general, geometric constraints - possibly at the cost of higher distortion. These geometric constraints include requirements such as certain vertices lie on some line or circle, or a planar curve or developable region keeps its shape during parameterization. We present a framework for enforcing such constraints, motivated by the As-Rigid-As-Possible parameterization method, and demonstrate its effectiveness through several examples.

关键词： mesh parameterization geometric constraints vector field geometry processing

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Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional

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COMPUTER AIDED GEOMETRIC DESIGN 2023年第1期105卷

作者： Weill-Duflos, Colin Coeurjolly, David de Goes, Fernando Lachaud, Jacques-Olivier Univ Grenoble Alpes Univ Savoie Mont Blanc CNRS LAMA F-73000 Chambery France Univ Lyon CNRS INSA Lyon UCBLLIRISUMR5205 Villeurbanne France Pixar Animat Studios Emeryville CA USA

UV mapping is a classical problem in computer graphics aiming at computing a planar parameterization of the input mesh with the lowest possible distortion while minimizing the seams length. Recent works propose optimization methods for solving these two joint problems at the same time with variational models, but they tend to be slower than other cutting methods. We present a new variational approach for this problem inspired by the Ambrosio-Tortorelli functional, which is easier to optimize than already existing methods. This functional has widely been used in image and geometry processing for anisotropic denoising and segmentation applications. The key feature of this functional is to model both regions where smoothing is applied, and the loci of discontinuities corresponding to the cuts. Our approach relies on this principle to model both the low distortion objective of the UV map, and the minimization of the seams length (sequences of mesh edges). Our method significantly reduces the distortion in a faster way than state-of-the art methods, with comparable seam quality. We also demonstrate the versatility of the approach when external constraints on the parameterization are provided (packing constraints, seam visibility). & COPY;2023 Elsevier B.V. All rights reserved.

关键词： mesh parameterization UV mapping Variational model Ambrosio-Tortorelli functional Joint distortion and cut

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MDSSN: An end-to-end deep network on triangle mesh parameterization

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KNOWLEDGE-BASED SYSTEMS 2024年 284卷

作者： Hu, Ruihan Tang, Zhi-Ri Yang, Rui Wang, Zhongjie Harbin Inst Technol Fac Comp Harbin Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Guangdong Inst Intelligent Mfg Guangdong Key Lab Modern Control Technol Guangzhou Peoples R China

mesh data plays a crucial role in a wide range of applications worldwide within the field of 3D computer vision. In contrast to traditional Euclidean space arrangements, meshes encompass spatial information, including edges, faces, angles, and graph structures that embed face information within the mesh data. Nevertheless, conventional deep learning frameworks such as convolutional neural networks (CNNs) have struggled to achieve significant advancements in handling meshes. This paper proposes a simple mesh computation framework called mesh Decomposition Second-order Sobolev Network (MDSSN) to model triangle meshes and represent their shape. The construction of face-based Riemannian and edge-based Riemannian graphs is motivated by the remarkable representation capabilities of edges and faces in mesh data, achieved through a graph composition mechanism. Furthermore, we design end-to-end operators, including the Sobolev-filter block, pooling, and unpooling blocks, which draw inspiration from traditional deep learning frameworks for modeling the mesh structure. Importantly, the design of the mesh-filter block incorporates the second-order Sobolev metric. To address common challenges in mesh classification and segmentation tasks, we have designed dedicated classification and segmentation modules. We utilize a joint loss function that integrates losses from adjacent faces and categories. We evaluate the performance of the MDSSN in mesh classification and segmentation tasks, focusing on its ability to represent 3D shapes. Experimental results demonstrate that MDSSN achieves superior performance compared to other state-of-the-art approaches.

关键词： Graph composition Ssecond-order Sobolev End -to -end learning mesh parameterization

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