Extracting Boolean isosurfaces from tetrahedral meshes

Surfaces separating the inside from the outside of most solid objects of interest are piecewise smooth: they can be decomposed into smooth surface patches meeting along smooth boundary curves called creases. Normal vectors are discontinuous across creases, and creases join at their ends forming corners. Rather than identifying sharp features in an isosurface with additional Hermite data or detecting large changes in surface normals (see [Ju et al. 2002] and references within), we consider the Constructive Solid Geometry (CSG) representation of surfaces as boundaries of regularized Boolean combinations of half spaces. But here each half space is defined by one piecewise linear implicit function inequality. The Boolean Isosurface Algorithm for tetrahedral meshes (TBIso) outlined in this sketch extends the classical isosurface algorithms for tetrahedral grids from smooth implicit surfaces to volumetric sampled CSG surfaces in such a way that the feature lines are identified and extracted as poly-line networks. These feature lines and corners can be preserved during subsequent smoothing and simplification.