Simplification of tetrahedral meshes with error bounds

Author

Trotts, Lssac J. ; Hamann, Bernd ; Joy, Kenneth I.

Author_Institution

Dept. of Comput. Sci., California Univ., Davis, CA, USA

Volume

5

Issue

3

fYear

1999

Firstpage

224

Lastpage

237

Abstract

Presents a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate scalar-valued function at different levels of detail. Starting with an initial, high-resolution triangulation of a 3D region, we construct coarser representation levels by collapsing edges of the mesh. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Error bounds are stored for individual tetrahedra and are updated as the mesh is simplified. Two algorithms are presented that simplify the mesh within prescribed error bounds. Each algorithm treats simplification on the mesh boundary. The result is a hierarchical data description that is suited for the efficient visualization of large data sets at varying levels of detail

Keywords

data description; data structures; data visualisation; error analysis; function approximation; mesh generation; splines (mathematics); 3D region; error bound updating; hierarchical data description; hierarchical representation; high-resolution triangulation; large data set visualization; level of detail; linear spline function; mesh edge collapsing; multi-resolution method; multiple mesh levels; representation levels; scattered data; spline coefficients; tetrahedral mesh simplification; trivariate scalar-valued function approximation; vertices; Acoustic scattering; Chemicals; Computer errors; Data mining; Data visualization; Error correction; Large-scale systems; Legged locomotion; Spline; Surface contamination;

fLanguage

English

Journal_Title

Visualization and Computer Graphics, IEEE Transactions on

Publisher

ieee

ISSN

1077-2626

Type

jour

DOI

10.1109/2945.795214

Filename

795214