A Surface Remeshing Approach

Aubry, Romain; Houzeaux, Guillaume; Vázquez, Mariano

doi:10.2514/6.2010-161

Cited by 8 publications

(8 citation statements)

References 48 publications

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“…As a large disparity of sizing values may be present in space, an adaptive procedure will be more amenable to control the sizing scale. In this work, an adaptive Cartesian mesh has been implemented [1,4] in an unstructured manner, where each cell knows its neighbors. This allows fast and easy propagation algorithms inside the Cartesian mesh as well as extremely fast interpolation if spatial locality is exploited.…”

Section: Edge Sourcementioning

confidence: 99%

Linear Sources for Mesh Generation

Aubry¹,

Karamete²,

Mestreau³

et al. 2013

SIAM J. Sci. Comput.

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Sources offer a convenient way to prescribe a size distribution in space. For each newly created mesh point, the mesh generator queries the local size distribution, either to create a new point or element, depending on the underlying mesh generation method, to smooth the mesh, or to get a local relevant length scale. Sources may have different shapes such as points, edges, triangles, or boxes. They provide the size distribution given some user defined parameters and the distance of a point location to the source. Traditionally, the source strength is considered as constant. In this work, extensions to linear sources in space are proposed. It is shown that in the case of curvature refined mesh generation, substantial savings may occur due to the much better approximation of the curvature variation for a simple modification of traditional sources. Even though curvature refinement is the main application of this work, improvements through linear sources are relevant to other contexts such as user defined sources. The technique is very general as it deals with a fundamental aspect of mesh generation and can be easily incorporated into an existing mesh generator with traditional sources. Thorough details of source approximations and source filtering are provided. Relations with lower envelopes are highlighted. Practical examples illustrate the accuracy and efficiency of the method.

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Section: Edge Sourcementioning

confidence: 99%

Linear Sources for Mesh Generation

Aubry¹,

Karamete²,

Mestreau³

et al. 2013

SIAM J. Sci. Comput.

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“…4,8,21 In an engineering context, reparametrization is often used to remesh a poor initial triangular surface mesh. 7,16,18 An obvious advantage compared to a remesher working directly in the three dimensional surface, 1,9,14 is provided by the fact that, once a parametrization has been sought, the two dimensional remesher does not have to deal with possibly ill-defined projections on the surface, while being faster due to the reduced dimension of the problem. However, mapping distortion has to be taken into account, and quality may therefore suffer.…”

Section: Introductionmentioning

confidence: 99%

Geodesics-based surface reparametrization

Aubry

Karamete

Mestreau

et al. 2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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An algorithm is presented to obtain a parametrization from a three dimensional surface described as a set of triangular faces, possibly originating from different geometric patches. It is considered as an extension of the unfolding algorithm presented by Sorkine et al. 23 In the aforementioned work, triangles are unfolded on the plane by solid rotations until some criterion stops the progression, creating numerous patches. In this work, a unique patch is sought. A general backbone of the algorithm is provided by considering the geodesic polar map in order to get a bijective mapping. As the original method, arbitrary genus can be handled as well as free boundary. An emphasis is put on trying to minimize discontinuities in the parametrization. Details of the algorithm are presented as well as timings and numerical examples, in order to show the capabilities of this new version.

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“…From a visibility standpoint, this normal is optimal by construction. For discrete remeshings, this provides a robust criterion to evaluate possible surface foldings [15,16]. It would therefore have been more appropriate to call it the 'most visible' normal.…”

Section: Introductionmentioning

confidence: 99%