

   PPaaiirrss OObbjjeecctt

        pairs(point.obj,num.lags=10,type='isotropic', theta=0, dtheta=5, maxdist)

   AArrgguummeennttss::

   point.obj: a point object generated by `point()'

   num.lags: the number of lags into which to divide the pairs
             of points in the pairs object. The lags are all of
             equal size.

       type: either ` object. If `'anisotropic'', then the
             arguments `theta' and `dtheta' are used to deter
             mine which pairs of points to include.

      theta: an angle, measured in degrees from the horizontal
             x axis, that determines pairs of points to be
             included in the `pairs' object (see Notes below).

     dtheta: a tolerance angle, around `theta', measured in
             degrees that determines pairs of points to be
             included in the `pairs' object (see Notes below).

    maxdist: the distance beyond which not to consider pairs of
             points. A large number of spatial locations can
             cause the `pairs' function to consume a consider
             able amount of computation time. In most cases,
             spatial dependence can be adaquately characterized
             without examining the entire spaital extent of the
             data set.

   DDeessccrriippttiioonn::

        Create a pairs object from a point object.

        A pairs object contains information defining pairs of
        points contained in a point object. A pairs object is a
        list containing five vectors: `from', `to', `lags',
        `dist', and `bins'. The length of each of these vectors
        (except `bins') is equal to the number of pairs of
        points being represented, say k. The vectors `from' and
        `to' contain pointers into the vectors of a point
        object, pointing to each member of the pair of points
        (e.g., from[k] points to si and to[k] points to sj).
        The vector `dist' contains the distance between the
        pairs of points. The vector `lags' contains the lag
        number to which each pair of points has been assigned.
        The vector `bins' contains the spatial midpoint between
        each lag and is used for plotting.

   VVaalluuee::

        A `pairs' object:

       from: vector of indices into the point object for "from"
             point

         to: vector of indices into the point object for "to"
             point

       lags: vector of spatial lags of each pair

       dist: vector of distances between each pair

       bins: vector of spatial midpoints of each lag (used for
             plotting)

   NNoottee::

        When creating an anisotropic pairs object, the assump
        tion is that the direction, as well as the distance,
        between pairs of points is important in describing the
        variation. Using the theta and dtheta arguments, pairs
        of points that meet direction requirements can be
        selected. A pair of points will be included when the
        angle between the positive x axis and the vector formed
        by the pair of points falls within the tolerance angle
        given by (theta-dtheta,theta+dtheta)

   RReeffeerreenncceess::

        http://www.gis.iastate.edu/SGeoStat/homepage.html

   SSeeee AAllssoo::

        `point'

   EExxaammpplleess::

        maas.pairs   <- pairs(maas.pts,num.lags=10,maxdist=2000)
        maas.pairs25 <- pairs(maas.pts,num.lags=10,type='anisotropic',
                              theta=25,maxdist=500)

