Volume-Enhanced Compatible Remeshing of 3D Models

Yang, Yang; Fu, Xiao‐Ming; Chai, Shuangming; Xiao, Shi-Wei; Liu, Ligang

doi:10.1109/tvcg.2018.2861396

Cited by 15 publications

(8 citation statements)

References 48 publications

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“…• Block coordinate descent method [72] updates one block of variables each time. • Monotone preconditioned conjugate gradient method [73] monotonically and efficiently reduces the objective function. The block coordinate descent method is a local method.…”

Section: Penalty-based Methodsmentioning

confidence: 99%

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Inversion-free geometric mapping construction: A survey

Zhao

et al. 2021

Comp. Visual Media

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A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

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Section: Penalty-based Methodsmentioning

confidence: 99%

“…Here, we focus on bijective inter-surface mappings that provide one-to-one correspondences between two shapes. Besides, inter-surface mappings can be used to generate compatible meshes that possess the same connectivity structures [73,93,94].…”

Section: Bijective Inter-surface Mappingsmentioning

confidence: 99%

Inversion-free geometric mapping construction: A survey

Zhao

et al. 2021

Comp. Visual Media

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“…Bottom: If there are some missed landmarks, the distortion is large. The manually selected landmarks are provided by [55].…”

Section: Isotropic Remeshingmentioning

confidence: 99%

Voting for Distortion Points in Geometric Processing

Chai

Liu

2021

IEEE Trans. Visual. Comput. Graphics

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Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of these vertices is non-trivial. We call these vertices distortion points. We present a novel and automatic method to detect distortion points using a voting strategy. Our method integrates two components: candidate generation and candidate voting. Given a closed triangular mesh, we generate candidate distortion points by executing a three-step procedure repeatedly: (1) randomly cut an input to a disk topology; (2) compute a low conformal distortion parameterization; and (3) detect the distortion points. Finally, we count the candidate points and generate the final distortion points by voting. We demonstrate that our algorithm succeeds when employed on various closed meshes with a genus of zero or higher. The distortion points generated by our method are utilized in three applications, including planar parameterization, semi-automatic landmark correspondence, and isotropic remeshing. Compared to other state-of-the-art methods, our method demonstrates stronger practical robustness in distortion point detection.

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“…Another class of remeshing methods deals with compatible meshing. Such methods remesh multiple shapes to generate common connectivity among them [Yang et al 2018[Yang et al , 2020. These methods generally aim to produce meshes of regular connectivity and minimal polygon count that fit both shapes to facilitate applications like morphing or attribute mapping; however, they discard the original mesh connectivity, in contrast to the goal of our work.…”

Section: Related Work 21 Remeshingmentioning

confidence: 99%

Mesh Draping: Parametrization-Free Neural Mesh Transfer

Hertz¹,

Perel²,

Giryes³

et al. 2021

Preprint

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Despite recent advances in geometric modeling, 3D mesh modeling still involves a considerable amount of manual labor by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one shape to another. The method drapes the source mesh over the target geometry and at the same time seeks to preserve the carefully designed characteristics of the source mesh. At its core, our method deforms the source mesh using progressive positional encoding. We show that by leveraging gradually increasing frequencies to guide the neural optimization, we are able to achieve stable and high quality mesh transfer. Our approach is simple and requires little user guidance, compared to contemporary surface mapping techniques which rely on parametrization or careful manual tuning. Most importantly, Mesh Draping is a parameterization-free method, and thus applicable to a variety of target shape representations, including point clouds, polygon soups, and non-manifold meshes. We demonstrate that the transferred meshing remains faithful to the source mesh design characteristics, and at the same time fits the target geometry well.

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Volume-Enhanced Compatible Remeshing of 3D Models

Cited by 15 publications

References 48 publications

Inversion-free geometric mapping construction: A survey

Inversion-free geometric mapping construction: A survey

Voting for Distortion Points in Geometric Processing

Mesh Draping: Parametrization-Free Neural Mesh Transfer

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