Robust edge-preserving surface mesh polycube deformation

Zhao, Hui; Lei, Na; Li, Xuan; Zeng, Peng; Xu, Ke; Gu, Xianfeng

doi:10.1007/s41095-017-0100-x

Cited by 13 publications

(11 citation statements)

References 27 publications

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“…Axis-alignment is an important property for many geometry processing tasks, such as [Muntoni et al 2018;Stein et al 2019]. Especially, this concept is one of the main instruments in the construction of polycube maps [Tarini et al 2004], including defining polycube segmentations [Fu et al 2016;Livesu et al 2013;Zhao et al 2018] and the cost function for polycube deformations [Gregson et al 2011;. Although polycube methods can obtain cubic geometry, they fail to preserve detail ( Fig.…”

Section: Related Workmentioning

confidence: 99%

Cubic stylization

Liu

Jacobson

2019

ACM Trans. Graph.

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Fig. 1. Cubic stylization deforms a given 3D shape into the style of a cube while maintaining textures and geometric features. This can be used as a non-realistic modeling tool for creating stylized 3D virtual world. We obtain 3D assets from sketchfab.com by smeerws and Jesús Orgaz licensed under CC BY 4.0.We present a 3D stylization algorithm that can turn an input shape into the style of a cube while maintaining the content of the original shape. The key insight is that cubic style sculptures can be captured by the as-rigidas-possible energy with an ℓ 1 -regularization on rotated surface normals.Minimizing this energy naturally leads to a detail-preserving, cubic geometry. Our optimization can be solved efficiently without any mesh surgery. Our method serves as a non-realistic modeling tool where one can incorporate many artistic controls to create stylized geometries.

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Section: Related Workmentioning

confidence: 99%

Cubic stylization

Liu

Jacobson

2019

ACM Trans. Graph.

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“…the union of a set of cubes, to define the connectivity of the final mesh. In contrast with spatial partitioning, these methods strive to deform the surface, usually filled with tetrahedra, to generate an axis‐aligned polycube [GSZ11, LVS*13, HJS*14, FXBH16, FBL16, LLWQ13, ZLL*18]. After the deformation, the polycube (which is a hex mesh by definition) is optionally subdivided and then mapped to the interior with the inverse of the deformation applied to the surface.…”

Section: Related Workmentioning

confidence: 99%

Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Computer Graphics Forum

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We propose an octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user‐controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self‐intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly‐lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open‐source implementation will be made available online to foster further research in this direction.

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“…The deformation based approaches in [GSZ11; HJS∗ 14; FBL16] obtain polycube meshes by minimizing an energy. Given a surface and a valid polycube topology , Zhao et al [ZLL∗ 18] propose a novel method to deform a mesh into its polycube mesh by rotating face normals. The algorithm in [GSZ11] uses a rotation‐driven method to align each surface normal to one direction of (± X , ± Y , ± Z ) gradually; then a position‐driven deformation is used to enforce the planarity and straightness.…”

Section: Related Workmentioning

confidence: 99%

Polycube Shape Space

Zhao

Wang

et al. 2019

Computer Graphics Forum

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There are many methods proposed for generating polycube polyhedrons, but it lacks the study about the possibility of generating polycube polyhedrons. In this paper, we prove a theorem for characterizing the necessary condition for the skeleton graph of a polycube polyhedron, by which Steinitz's theorem for convex polyhedra and Eppstein's theorem for simple orthogonal polyhedra are generalized to polycube polyhedra of any genus and with non‐simply connected faces. Based on our theorem, we present a faster linear algorithm to determine the dimensions of the polycube shape space for a valid graph, for all its possible polycube polyhedrons. We also propose a quadratic optimization method to generate embedding polycube polyhedrons with interactive assistance. Finally, we provide a graph‐based framework for polycube mesh generation, quadrangulation, and all‐hex meshing to demonstrate the utility and applicability of our approach.

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Robust edge-preserving surface mesh polycube deformation

Cited by 13 publications

References 27 publications

Cubic stylization

Cubic stylization

Feature Preserving Octree‐Based Hexahedral Meshing

Polycube Shape Space

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