NAME

       CSVORO - calculate Voronoi polygons for data on a sphere.

SYNOPSIS

       CALL CSVORO (NPTS, RLATI, RLONI, NI, NF, IWK, RWK,
                    NC, RLATO, RLONO, RC,
                    NCA, NUMV, NV, IER)

DESCRIPTION

       NPTS        (integer,input) The number of input data points (NPTS > 3).

       RLATI       (real,  input)  An array containing the latitudes of the input data, expressed
                   in degrees.  The first three points must not be collinear  (lie  on  a  common
                   great circle).

       RLONI       (real,  input) An array containing the longitudes of the input data, expressed
                   in degrees.

       NI          (integer, input) The index of the input  coordinate  for  which  you  want  to
                   determine the Voronoi polygon (1 .LE. NI .LE. NPTS).

       NF          (integer,  input)  Flag  indicating  if  this  is  the first call to CSVORO to
                   retrieve Voronoi polygons for this dataset (1=yes, 0=no).  Calls subsequent to
                   the first call for a given dataset are much faster than the first call.

       IWK         (integer, input) Integer work space dimensioned for 27*NPTS.

       RWK         (double  precision, input) A work space dimensioned for 9*NPTS.  Note that RWK
                   must be typed DOUBLE PRECISION.

       NC          (integer, input) The maximum size of the output arrays RLATO, RLONO,  and  RC.
                   NC should be 2*NPTS.

       RLATO       (real,  output) The latitudes for the vertices of the Voronoi polygons.  These
                   are circumcenters of circles passing through  the  Delaunay  triangles.  If  a
                   coordinate  is  a  boundary  point,  then  the circle may pass through certain
                   "pseudo points" that have been added to  the  original  dataset  in  order  to
                   complete the Voronoi polygon.

       RLONO       (real, output) The longitudes for the vertices of the Voronoi polygons.

       RC          (real,  output)  Array  containing  circumradii (arc lengths in degrees of the
                   angle between a circumcenter and its associated triangle vertices).

       NCA         (integer, output) The actual number of circumcenters  returned  in  RLATO  and
                   RLONO.  This  number may be larger than NPTS if the input dataset has boundary
                   points since certain "pseudo points" may  have  been  added  to  the  original
                   dataset in order to complete the Voronoi polygon set.

       NUMV        (integer,  output) The number of vertices in the Voronoi polygon enclosing the
                   coordinate (RLATI(NI),RLONI(NI)).

       NV          (integer, output) An array (dimensioned for NPTS) containing NUMV indices  for
                   the  Voronoi  polygon  enclosing  the  coordinate  (RLATI(NI),RLONI(NI)).  The
                   indices returned in this array refer to the  coordinates  returned  in  RLATO,
                   RLONO,  and RC. For example, if the integer "J" is an element of the NV array,
                   then  (RLATO(J),RLONO(J))  is  a  vertex  of  the  Voronoi  polygon  enclosing
                   (RLATI(NI),RLONI(NI)).  The indices in NV list out the vertices of the Voronoi
                   polygon in counter-clockwise order.

       IER         (integer, output) An error return value.  If IER is returned  as  0,  then  no
                   errors  were  detected.  If  IER  is  non-zero, then refer to the man page for
                   cssgrid_errors for details.

USAGE

       CSVORO is called if  you  want  to  determine  the  Voronoi  polygons  for  data  randomly
       positioned  on  a  sphere.  Each  call  to  CSVORO calculates the vertices for the Voronoi
       polygon surrounding a specified input point.

ACCESS

       To use CSVORO, load the NCAR Graphics library ngmath.

SEE ALSO

       css_overview, csstri, cssgrid.

       Complete documentation for Cssgrid is available at URL
       http://ngwww.ucar.edu/ngdoc/ng/ngmath/cssgrid/csshome.html

COPYRIGHT

       Copyright (C) 2000
       University Corporation for Atmospheric Research

       The use of this Software is governed by a License Agreement.