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The interval volume is a generalization of the isosurface commonly associated with the marching cubes algorithm. Based upon samples at the locations of a 3D rectilinear grid, the algorithm produces a triangular approximation to the surface defined by F(x,y,z)=c. The interval volume is defined by α≤F(x,y,z)≤β. The authors describe an algorithm for computing a tetrahedrization of a polyhedral approximation to the interval volume.