A divide-and-conquer approach for automatic polycube map construction

He, Ying; Wang, Hongyu; Fu, Chi‐Wing; Qin, Hong

doi:10.1016/j.cag.2009.03.024

Cited by 84 publications

(96 citation statements)

References 15 publications

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“…The main problem of this approach is the construction of the poly-cube that approximates the initial geometry, since it has a great impact on the quality of the final mesh. Several techniques have been proposed in [94][95][96].…”

Section: Feature-based Methodsmentioning

confidence: 99%

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Ramos¹,

Ruiz‐Gironés²,

Navarro³

2014

Comp. Tech. Rev.

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Discretization techniques such the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in applied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to generate. However, in many applications such as boundary layers in computational fluid dynamics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.

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Section: Feature-based Methodsmentioning

confidence: 99%

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Ramos¹,

Ruiz‐Gironés²,

Navarro³

2014

Comp. Tech. Rev.

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“…[7,[16][17][18]. The authors use a segmentation method to patch the input mesh, then use box-primitives to approximate it coarsely in Ref.…”

Section: Related Workmentioning

confidence: 99%

“…[18] applies distance-based, divide-and-conquer algorithms to build the polycube, while the one in Ref. [16] generates over-refined polycubes and is sensitive to off-axis features. The algorithms in Refs.…”

Section: Related Workmentioning

confidence: 99%

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Robust edge-preserving surface mesh polycube deformation

Zhao

Lei

et al. 2018

Comp. Visual Media

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Polycube construction and deformation are essential problems in computer graphics.In this paper, we present a robust, simple, efficient, and automatic algorithm to deform the meshes of arbitrary shapes into polycube form. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserving, and works on surface meshes with or without boundaries. Our algorithm outperforms previous ones with respect to speed, robustness, and efficiency. Our method is simple to implement. To demonstrate the robustness and effectivity of our method, we have applied it to hundreds of models of varying complexity and topology. We demonstrate that our method compares favorably to other state-of-the-art polycube deformation methods.

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“…Polycubes serve as nice parametric domains because they approximate well the geometry of the model and possess great regularity. A polycube mapping can be constructed either manually [18], [19], [20] or automatically [21], [22]. Based upon specially designed surface parameterization, Wang et al [19] build manifold bivariate T-spline over a polycube that can handle models with arbitrary topology.…”

Section: Related Workmentioning

confidence: 99%

Restricted Trivariate Polycube Splines for Volumetric Data Modeling

Wang

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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Abstract-This paper presents a volumetric modeling framework to construct a novel spline scheme called restricted trivariate polycube splines (RTP-splines). The RTP-spline aims to generalize both trivariate T -splines and tensor-product B-splines; it uses solid polycube structure as underlying parametric domains and strictly bounds blending functions within such domains. We construct volumetric RTP-splines in a top-down fashion in four steps: 1) Extending the polycube domain to its bounding volume via space filling; 2) building the B-spline volume over the extended domain with restricted boundaries; 3) inserting duplicate knots by adding anchor points and performing local refinement; and 4) removing exterior cells and anchors. Besides local refinement inherited from general Tsplines, the RTP-splines have a few attractive properties as follows: 1) They naturally model solid objects with complicated topologies/ bifurcations using a one-piece continuous representation without domain trimming/patching/merging. 2) They have guaranteed semistandardness so that the functions and derivatives evaluation is very efficient. 3) Their restricted support regions of blending functions prevent control points from influencing other nearby domain regions that stay opposite to the immediate boundaries. These features are highly desirable for certain applications such as isogeometric analysis. We conduct extensive experiments on converting complicated solid models into RTP-splines, and demonstrate the proposed spline to be a powerful and promising tool for volumetric modeling and other scientific/engineering applications where data sets with multiattributes are prevalent.

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A divide-and-conquer approach for automatic polycube map construction

Cited by 84 publications

References 15 publications

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Robust edge-preserving surface mesh polycube deformation

Restricted Trivariate Polycube Splines for Volumetric Data Modeling

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