Simplification of tetrahedral meshes with error bounds

We present 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 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 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 suited for efficient visualization of large data sets at varying levels of detail.