Adaptive triangular element generation and optimization-based smoothing, Part 1: On the plane

Lee, M. C.; Joun, Man Soo

doi:10.1016/j.advengsoft.2006.11.004

Cited by 10 publications

(10 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the companion paper [1], the mesh density specifying schemes together with the time-effective virtual grid method are presented with emphasis on their extensibility to three-dimensional application and their capability of describing continuous mesh density functions. In the schemes, the user-specified mesh density is identified by the combination of the primitive mesh density functions defined by the density specifying geometries such as sphere, cylinder and pipe.…”

Section: Minimization Of Geometrical Error Due To Curvaturementioning

confidence: 99%

“…where Q i denotes the normalized quality [1] and the primed values are for the edge swapped meshes. Eq.…”

Section: Local Transformation Schemes For Surface Triangulationmentioning

confidence: 99%

“…In this study, the face splitting scheme, the edge splitting scheme and the edge collapsing scheme employed for generating triangular elements on the plane in the companion paper [1] are adopted without any modification for generating triangular elements on the surface. On the contrary, the edge swapping scheme is modified in order to reflect the three-dimensional situations.…”

Section: Local Transformation Schemes For Surface Triangulationmentioning

confidence: 99%

“…In this paper, the approach to adaptive triangular element generation and optimization-based smoothing on the plane, presented in the companion paper [1], is extended to triangulation of the three-dimensional surface.…”

Section: Introductionmentioning

confidence: 99%

“…In the companion paper [1], a systematic approach to optimization-based triangular element generation on the plane is presented. In the approach, the input geometry of an initially rough triangular element is gradually improved until an optimal mesh is achieved.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Adaptive triangular element generation and optimization-based smoothing: Part 2. On the surface

Lee¹,

Joun²

2008

Advances in Engineering Software

Self Cite

View full text Add to dashboard Cite

A general and systematic approach to adaptive triangular element generation and optimization-based smoothing on the surface is presented in this paper. The approach starts from a rough triangular mesh that needs to be remeshed in order to meet the desired mesh density. Various local transformation processes including edge and face splitting, edge collapsing and edge swapping are employed for enhancement of mesh quality as well as for generation of new triangular elements from the rough triangular elements. An edge swapping scheme is proposed, which satisfy both of the Delaunay criterion and topological consistency. To reduce the geometrical error that is inevitable in remeshing, curvature of the surface is not only considered in determining the mesh density distribution but the characteristic edges and the triangular elements are also interpolated by the third-order chord-length spline curves and the bi-cubic Bezier patches, respectively. The nodal points of the generated mesh are smoothed by the physically-based smoothing scheme and then optimally placed by the optimization-based smoothing scheme. Through various application examples, the characteristics and effects of the presented approaches are quantitatively investigated.

show abstract

Section: Minimization Of Geometrical Error Due To Curvaturementioning

confidence: 99%

“…where Q i denotes the normalized quality [1] and the primed values are for the edge swapped meshes. Eq.…”

Section: Local Transformation Schemes For Surface Triangulationmentioning

confidence: 99%

Section: Local Transformation Schemes For Surface Triangulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%