The creation of local clusters in arbitrarily given grids

A method is presented to smoothly insert pointwise clusters into any given grid regardless of its origin, its topology, or its dimensionality. The process amounts to a local movement of the given coordinate curves or surfaces to more highly resolve an object. The object about which clustering is created can be a point, a curve, a surface, or segments of a curve or surface. The basic clustering capability is established by forming a grid operator for a single cluster. With a view toward multiple clusters being created about various objects, the basic operator is seen as an elementary operator. An algorithm is presented to execute the general elementary operation in three dimensions. In FORTRAN, this assumes the form of a subroutine which is fully operational and is presented to serve as a basic model for any such elementary clustering operation.