 Version 0.0-9 (??? 2 June 2009)

 Added a new function tile.centroids() --- which does the obvious.
 Motivated by an inquiry from Leandro Moreira.

 Version 0.0-8 (4 April 2009)

 Removed the labels from the x and y vectors in the tile descriptions
 produced by tile.list.  These labels (which were the row numbers in
 the dirsgs data frame returned by deldir()) served no useful purpose
 and were potentially confusing.

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

 Versions 0.0-2 through 0.0-7 were not tracked here. :-( Simply forgot
 about doing this.  I thouroughly *intend* [ :-) ] to get the archives
 from CRAN and try to document the changes.  Recent ones involved
 fixing bugs in and adding features to the tile.list() and
 plot.tile.list() functions.

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

 Version 0.0-1 (21 February 2002)
 This version is simply an adaptation of the Splus version
 of the package to R.

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

 Version date: 14 February 2002.
 This version supercedes the version dated 24 April 1999.

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

 The changes from the version dated 24 April 1999 to the
 version dated 14 February 2002 were:

	A bug in the procedure for eliminating duplicated points was
	fixed.  Thanks go to Dr. Berwin Turlach of the Department of
	Maths and Stats at the University of Western Australia, for
	spotting this bug.

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

 The changes from the version dated 26 October 1998 to the
 version dated 24 April 1999 were:

	(1) The function mipd(), stored in mipd.sf, and the
	corresponding Fortran subroutine mipd, stored in mipd.r, have
	been replaced by mnnd() in mnnd.sf and mnnd in mnnd.r.  The
	function mipd calculated the mean interpoint distance, to be
	used in constructing dummy point structures of a certain
	type.  After some reflection it became apparent that the mean
	interpoint distance was much too large for the intended
	purpose, and that a more appropriate value was the ``mean
	nearest neighbour distance'' which is calculated by the new
	function.  This new value is now used in constructing dummy
	point structures.

	Note that the operative result is that the resulting dummy
	point structures contain many more points than before.  The
	old value caused large numbers of the dummy points to fall
	outside the data window and therefore to be clipped.

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

 The changes from the version dated 6 December 1996 to the
 version dated 26 October 1998 were:

	(1) A ratfor/Fortran routine named ``inside'' has been
	renamed ``dldins'' to avoid conflict with a name built in to
	some versions of Splus.

	(2) Some minor corrections have been made to dangerous
	infelicities in a piece of the ratfor/Fortran code.

	(3) The dynamic loading procedure has been changed to use
	dyn.load.shared so that the package is easily usable on
	IRIX systems as well as under SunOS/Solaris.

	(4) The package has been adjusted slightly so that it
	can easily be installed as a section of a library.  In
	particular, the dynamic loading is now done by the
	.First.lib() function rather than from within deldir()
	itself; reference to an environment variable DYN_LOAD_LIB
	is no longer needed.

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

 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.

 Current address of the author:
		Department of Mathematics and Statistics,
                University of New Brunswick,
                P.O. Box 4400, Fredericton, New Brunswick,
                Canada E3B 5A3
 Email:
		rolf@math.unb.ca

 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 the University of
 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.

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

 The man directory, contains, in addition to the R documentation
 files deldir.Rd and plot.deldir.Rd:

	(a) This READ_ME file.
	(b) A file err.list, containing a list of meanings of possible
	    error numbers which could be returned.  NONE of these
	    errors should ever actually happen except for errors 4, 14,
	    and 15.  These relate to insufficient dimensioning, and
	    if they occur, the driver increases the dimensions and
	    tries again (informing you of this fact).
	(c) A file ex.out containing a printout of the object returned
	    by running the example given in the help file for deldir.

 The src directory contains many, many *.f (Fortran) files, which
 get compiled and dynamically loaded.

 The Fortran code is ponderous --- it was automatically generated
 from Ratfor code, which was pretty ponderous to start with.   It is
 quite possibly very kludgy aw well --- i.e. a good programmer could
 make it ***much*** more efficient I'm sure.  It contains all sorts
 of checking for anomalous situations 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 we 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.
               ===

 (2) The function plot.deldir is a method for plot.  I.e. it may be
 invoked simply by typing ``plot(x)'' provided that ``x'' is an
 object of class ``deldir'' (as produced by the function deldir).
 The plot (by default) consists of the edges of the Delaunay
 triangles (solid lines) and the edges of the Dirichlet tiles (dotted
 lines).  By default the real data points are indicated by circles,
 and the dummy points are indicated by triangles.
