Simplification of Tetrahedral Meshes with Error Bounds

We present a method for multiple levels of tetrahedral meshes approximating a trivariate scalar-valued function at different levels of detail. Starting with an itital, high-resolution triangulation of three-dimensional 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 simplification on the mesh boundary. The result is a hierarchical data description suited for efficient visualization of large data sets at varying levels of detail