Abstract: A method of local reconstructing a grid containing a plurality of adjoining tetrahedrals wherein spheres cannot be constructed around each tetrahedral without including a vertex of another tetrahedral into a grid containing the tetrahedrals wherein spheres can be constructed around each tetrahedral without including a vertex of another tetrahedral. In the method, a face which adjoins two of the tetrahedrals is removed, thereby defining a hexahedron. If four vertices of the hexahedron are not on the same plane, an edge is constructed from a vertex of one tetrahedral to a vertex of another tetrahedral, such that three faces are defined inside the hexahedron, and such that the hexahedron is divided into three tetrahedrals, wherein spheres can be constructed around each tetrahedral without including a vertex of another tetrahedral. If four vertices of the hexahedron are on the same plane, a modified approach is used.