The software package includes FORTRAN routines with improved accuracy and computational efficiency, along with added capabilities, to perform analytic and geometric operations involving intersections between half-spaces or hyperplanes and 2- or 3- polytopes (polygons or polyhedra, either convex or non-convex) that typically arise in advanced volume of fluid (VOF) methods on arbitrary grids. To show the new capabilities and performance improvements, the proposed tools have been included in a PLIC (piecewise linear interface calculation) reconstruction method (the conservative level contour interface reconstruction, CLCIR, method) and two advection methods: a fluid-volume intersection advection (FVIA) method (the edge-matched flux polyhedron advection, EMFPA, method) and a new wetted-area time-integration advection (WATIA) method. A test program has been implemented to deform a spherical fluid body under a prescribed velocity field using the different reconstruction and advection methods on several structured and unstructured grids.