Mesh Enhancement - Selected Elliptic Methods, Foundations and Applications

Hansen, Glen; Douglass, R.W.; Żardecki, A.

doi:10.1142/9781860946813

Cited by 18 publications

(21 citation statements)

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“…In earlier variational grid generation approaches, suitable user-specified weights were needed to ensure grid quality. While, in principle, grid quality should be considered in connection to a given physical problem of interest [55], there are case studies in the literature which are so ill-posed that they produce poor-quality grids for most applications and mesh generators of interest. (See e.g.…”

Section: Discussionmentioning

confidence: 99%

An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge–Kantorovich optimization

Delzanno

Chacòn

Finn

et al. 2008

Journal of Computational Physics

143

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Section: Discussionmentioning

confidence: 99%

An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge–Kantorovich optimization

Delzanno

Chacòn

Finn

et al. 2008

Journal of Computational Physics

143

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“…When the models are reconstructed with the MC algorithm, triangle or mesh smoothing methods can be used to smooth the surface models. The Laplacian smoothing algorithm [29], which is an iterative algorithm, was used to smooth the triangle surfaces. The principle of this algorithm is that the position of a vertex is replaced with the average of the positions of adjacent vertices.…”

Section: Smoothingmentioning

confidence: 99%

Constructing three-dimensional detachable and composable computer models of the head and neck

Min

Dai

Zheng

et al. 2015

Australas Phys Eng Sci Med

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The head and neck region has a complex spatial and topological structure, three-dimensional (3D) computer model of the region can be used in anatomical education, radiotherapy planning and surgical training. However, most of the current models only consist of a few parts of the head and neck, and the 3D models are not detachable and composable. In this study, a high-resolution 3D detachable and composable model of the head and neck was constructed based on computed tomography (CT) serial images. First, fine CT serial images of the head and neck were obtained. Then, a color lookup table was created for 58 structures, which was used to create anatomical atlases of the head and neck. Then, surface and volume rendering methods were used to reconstruct 3D models of the head and neck. Smoothing and polygon reduction steps were added to improve 3D rendering effects. 3D computer models of the head and neck, including the sinus, pharynx, vasculature, nervous system, endocrine system and glands, muscles, bones and skin, were reconstructed. The models consisted of 58 anatomical detachable and composable structures and each structure can be displayed individually or together with other structures.

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“…As such, the proposed approach is conceptually similar to an approach advanced by Liseikin [4], who writes the Beltrami equations employing a metric tensor derived from a monitor surface. Unlike Liseikin, the coarse-graining procedure, in which the average node positions are used to estimate the target metric tensor [5], is used on unstructured surface meshes.…”

Section: Introductionmentioning

confidence: 99%

Unstructured surface mesh adaptation using the Laplace–Beltrami target metric approach

Hansen

Żardecki

2007

Journal of Computational Physics

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Mesh Enhancement - Selected Elliptic Methods, Foundations and Applications

Cited by 18 publications

References 0 publications

An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge–Kantorovich optimization

An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge–Kantorovich optimization

Constructing three-dimensional detachable and composable computer models of the head and neck

Unstructured surface mesh adaptation using the Laplace–Beltrami target metric approach

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