Robust computation of implicit surface networks for piecewise linear functions

Implicit surface networks, such as arrangements of implicit surfaces and materials interfaces, are used for modeling piecewise smooth or partitioned shapes. However, accurate numerically robust algorithms discretizing either structure on a grid still lacking. We present unified approach computing both types networks linear functions defined tetrahedral grid. Both guaranteed to produce correct combinatorial any number functions. Our main contribution is an exact efficient method partitioning tetrahedron using the level sets by barycentric interpolation. To further improve performance, we designed look-up tables speed up processing tetrahedra involving few introduced algorithm identifying nested 3D regions.