Simplification of Tetrahedral Meshes

title="Simplification of Tetrahedral Meshes",
booktitle="Proceedings of IEEE Visualization '98",
author="Isaac J. Trotts AND Bernd Hamann AND Ken Joy AND David F. Wiley ",
keywords="Approximation; hierarchical representation; mesh generation; multiresolution method; scattered data; spline; triangulation; visualization.",
location="Research Triangle Park, North Carolina",
eventtime="October 18--23, 1998",
abstract="We present a method for the construction of multiple levels of tetrahedral meshes approximating a trivariate function at different levels of detail. Starting with an initial, high-resolution triangulation of a three-dimensional region, we construct coarser representation levels by collapsing tetrahedra. Each triangulation defines a linear spline function, where the function values associated with the vertices are the spline coefficients. Based on predicted errors, we collapse tetrahedron in the grid that do not cause the maximum error to exceed a use-specified threshold. Bounds are stored for individual tetrahedra and are updated as the mesh is simplified. We continue the simplification process until a certain error is reached. The result is a hierarchical data description suited for the efficient visualization of large data sets at varying levels of detail.",
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