 
 This package computes and plots the Dirichlet (Voronoi) tesselation
 and the Delaunay triangulation of a set of of data points and
 possibly a superimposed ``grid'' of dummy points.

 The tesselation is constructed with respect to the whole plane
 by suspending it from ideal points at infinity.

 ORIGINALLY PROGRAMMED BY: Rolf Turner in 1987/88, while with the
 Division of Mathematics and Statistics, CSIRO, Sydney, Australia.
 Re-programmed by Rolf Turner to adapt the implementation from a
 stand-alone Fortran program to an S function, while visiting the
 University of Western Australia, May 1995.  Further revised
 December 1996, October 1998, April 1999, and February 2002.
 Adapted to an R package 21 February 2002.

 This R package continues to be revised and updated from time to time.

 Current address of the author:

		Department of Statistics
                University of Auckland
                Private Bag 92019
                Auckland 1142
                New Zealand
 Email:
                r.turner@auckland.ac.nz

 The author gratefully acknowledges the contributions, assistance,
 and guidance of Mark Berman, of D.M.S., CSIRO, in collaboration with
 whom this project was originally undertaken.  The author also
 acknowledges much useful advice from Adrian Baddeley, formerly of
 D.M.S. CSIRO (now Professor of Statistics at Curtin University in
 Western Australia).  Daryl Tingley of the Department of Mathematics
 and Statistics, University of New Brunswick provided some helpful
 insight.  Special thanks are extended to Alan Johnson, of the Alaska
 Fisheries Science Centre, who supplied two data sets which were
 extremely valuable in tracking down some errors in the code.

 Don MacQueen, of Lawrence Livermore National Lab, wrote an Splus
 driver function for the old stand-alone version of this software.
 That driver, which was available on Statlib, is now deprecated in
 favour of this current package.  Don also collaborated in the
 preparation of this current package.

 Bill Dunlap of MathSoft Inc. tracked down a bug which was making
 the deldir() function crash on some systems, and pointed out some
 other improvements to be made.

 Berwin Turlach of the Department of Maths and Stats at the
 University of Western Australia pointed out a bug in the procedure
 for eliminating duplicated points.

 Many others have contributed to the package over the years by
 pointing out bugs and suggesting fixes.  Most of these contributors
 are acknowledged in the ChangeLog and possibly in the help files.
 I apologise to those whom I have overlooked or neglected to include.
 It's just ineptitude, not malice!

 The Fortran code contained in the src directory, is ponderous
 --- it was automatically generated from Ratfor code.  This code
 can be found in the directory inst/ratfor.  The Ratfor code
 was pretty ponderous to start with.   It is quite possibly very
 kludgy as well --- i.e. a good programmer could make it ***much***
 more efficient I'm sure.  It contains all sorts of checking for
 anomalous situations most of which probably can/will never occur.
 These checks basically reflect my pessimism and fervent belief in
 Murphy's Law.

 The program  was also designed with a particular application
 in mind, in which Mark Berman and I wished to superimpose a
 grid of dummy points onto the actual data points which we were
 triangulating.  This fact adds slightly to the complication of
 the code.

                       *****************************

 Here follows a brief description of the package:

 (1) The function deldir computes the Delaunay Triangulation (and
 hence the Dirichlet Tesselation) of a planar point set according to
 the second (iterative) algorithm of Lee and Schacter, International
 Journal of Computer and Information Sciences, Vol. 9, No. 3, 1980,
 pages 219 to 242.

 The tesselation/triangulation is made to be

             **** with respect to the whole plane ****

 by `suspending' it from `ideal' points (-Inf,-Inf), (Inf,-Inf)
 (Inf,Inf), and (-Inf,Inf).

 (2) The tesselation/triangulation is also enclosed in a finite
 rectangle with corners

          (xmin,ymax) * ------------------------ * (xmax,ymax)
                      |                          |
                      |                          |
                      |                          |
                      |                          |
                      |                          |
          (xmin,ymin) * ------------------------ * (xmax,ymin)

 The boundaries of this rectangle truncate some Dirichlet tiles, in
 particular any infinite ones. This rectangle is referred to
 elsewhere as `the' rectangular window.
               ===
