A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
The NURBS book
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design
Adaptive triangulation of evolving, closed, or open surfaces by the advancing-front method
Journal of Computational Physics
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Topology-reducing surface simplification using a discrete solid representation
ACM Transactions on Graphics (TOG)
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Surface Modeling for CAD - Cam
Surface Modeling for CAD - Cam
Computer Aided Geometric Design
Journal of Computational Physics
Finite Element Mesh Generation
Finite Element Mesh Generation
Adaptive triangular element generation and optimization-based smoothing, Part 1: On the plane
Advances in Engineering Software
The Gaussian and mean curvature criteria for curvature continuity between surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Adaptive triangular element generation and optimization-based smoothing, Part 1: On the plane
Advances in Engineering Software
Three-dimensional simulation of forging using tetrahedral and hexahedral elements
Finite Elements in Analysis and Design
| Hi-index | 0.00 |
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.