The VOFI (Volume Of Fluid Initializer) library has been developed to initialize the volume fraction field determined by implicitly-defined interfaces. The major conceptual changes in the numerical algorithms of the library are discussed and a few new features, including the computation of the reference phase centroid and of the interface length/area, are presented and applied to grid cells that are cuboids. Several numerical tests are considered to demonstrate both the accuracy of the new features, as the grid resolution and the number of integration points are varied, and the considerably improved efficiency of the library with respect to its previous version. A few of these tests are also included in the software distribution written in C, examples of C++ and Fortran interfaces are also provided.