  From a scalar field defined at the corner of a cube, an isosurface can be
extracted using the Marching Cube algorithm. The isosurface separates the cell
into two or more partial cells. A similar situation arises when an material
interface in the Front Tracking method cuts through the computational cells. A
popular method to calculate the volumes of the partial cells is to first
partition the cells into tetrahedra and then sum together the volumes of the
tetrahedra for the corresponding partial cells. In this paper, the divergence
theorem is used to calculate the volumes of the partial cells generated by the
Marching Cubes algorithm. This method is both more robust and efficient
compared with the tetrahedralization approach.
