%\VignetteIndexEntry{Combining Spatial Data}
%\VignetteDepends{}
%\VignetteKeywords{spatial}
%\VignettePackage{maptools}
\documentclass[a4paper,10pt]{article} 
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
%\usepackage[dvips]{graphicx,color}
\usepackage{times}
\usepackage{hyperref}
\usepackage{natbib}
\usepackage[english]{babel}
\usepackage{xspace}

\usepackage{Sweave}
\usepackage{mathptm}
\usepackage{natbib}

\setkeys{Gin}{width=0.95\textwidth}
\newcommand{\strong}[1]{{\normalfont\fontseries{b}\selectfont #1}}
\let\pkg=\strong
\RequirePackage{alltt}
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\newenvironment{smallexample}{\begin{alltt}\small}{\end{alltt}}
\newcommand{\code}[1]{\texttt{\small #1}}
\def\RR{\textsf{R}\xspace}
\def\SP{\texttt{S-PLUS}\xspace}
\def\SS{\texttt{S}\xspace}
%#Sweave("combine_maptools.Rnw", keep.source=FALSE)
\SweaveOpts{keep.source=FALSE}


\title{Combining Spatial Data} 
\author{Roger Bivand} 

\begin{document} 

\maketitle 

<<echo=FALSE>>= 
owidth <- getOption("width")
options("width"=90)
.PngNo <- 0
@

<<label=afig,echo=FALSE,eval=FALSE>>= 
.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-", .PngNo, ".pdf", sep="")
pdf(file=file, width = 6.5, height = 3.5, pointsize = 12, bg = "white")
opar <- par(mar=c(3,3,1,1)+0.1)
@
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.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-", .PngNo, ".pdf", sep="")
pdf(file=file, width = 6.5, height = 3.5, pointsize = 12, bg = "white")
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pdf(file=file, width = 6.5, height = 5, pointsize = 12, bg = "white")
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.PngNo <- .PngNo + 1; file <- paste("Fig-bitmap-", .PngNo, ".pdf", sep="")
pdf(file=file, width = 6.5, height = 5, pointsize = 12, bg = "white")
opar <- par(mar=c(3,3,1,1)+0.1)
@

<<label=zfig,echo=FALSE,eval=FALSE>>=
par(opar)
dev.null <- dev.off()
cat("\\includegraphics[width=0.95\\textwidth]{", file, "}\n\n", sep="")
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<<label=zfigl,echo=FALSE,eval=FALSE>>=
dev.null <- dev.off()
cat("\\includegraphics[width=0.95\\textwidth]{", file, "}\n\n", sep="")
@

\section{Introduction}

%FIXME

\section{Checking Topologies}

In this vignette, we look at a practical example
involving the cleaning of spatial objects originally read into \RR from
shapefiles published by the US Census. We then aggregate them up
to metropolitan areas using a text table also from the US Census.

The data in this case are for polygons representing county
boundaries in 1990 of North Carolina, South Carolina, and
Virginia, as shown in Fig.\,\ref{fig:poly3a}. The attribute data
for each polygon are the standard polygon identifiers, state and
county identifiers, and county names. All the spatial objects
have the same number of columns of attribute data of the same
types and with the same names. The files are provided without
coordinate reference systems as shapefiles; the metadata are used
for choosing the \code{CRS} values.

\begin{footnotesize}
<<echo=TRUE,eval=TRUE,keep.source=FALSE>>= 
owd <- getwd()
setwd(system.file("shapes", package="maptools"))
library(maptools)
nc90 <- readShapeSpatial("co37_d90")
proj4string(nc90) <- CRS("+proj=longlat +datum=NAD27")
sc90 <- readShapeSpatial("co45_d90")
proj4string(sc90) <- CRS("+proj=longlat +datum=NAD27")
va90 <- readShapeSpatial("co51_d90")
proj4string(va90) <- CRS("+proj=longlat +datum=NAD27")
setwd(owd)
@
\end{footnotesize}

\begin{figure}[htb]
\centering
<<echo=FALSE,results=tex>>= 
<<bfig>>
oopar <- par(mar=c(3,2,1,1)+0.1)
plot(va90, xlim=c(-85,-75), ylim=c(32,40), axes=TRUE, border="grey10")
plot(nc90, add=TRUE, border="grey40")
plot(sc90, add=TRUE, border="grey70")
par(oopar)
<<zfig>>
@
\caption{The
three states plotted from input spatial objects using different
grey colours for county boundaries} 
\label{fig:poly3a}
\end{figure}

\noindent
As read in, shapefiles usually have the polygon IDs set to the external
file feature sequence number from zero to one less than the number
of features. In our case, wanting to combine three states, we
need to change the ID values so that they are unique across the study
area. We can use the FIPS code (Federal Information Processing Standards
Publication 6-4), which is simply the two-digit state FIPS code placed in
front of the three-digit within-state FIPS county code, ending up with
a five-digit string uniquely identifying each county. We can also drop
the first four attribute data columns, two of which (area and perimeter)
are misleading for objects in geographical coordinates, and the other two
are internal ID values from the software used to generate the shapefiles,
replicating the original feature IDs. We can start with the data set of
South Carolina (\code{sc90}):

\begin{footnotesize}
<<echo=TRUE,results=hide,keep.source=FALSE>>= 
library(maptools)
@
<<echo=TRUE,keep.source=FALSE>>= 
names(sc90)
sc90a <- spChFIDs(sc90, paste(sc90$ST, sc90$CO, sep=""))
sc90a <- sc90a[,-(1:4)]
names(sc90a)
@
<<echo=TRUE,results=hide,keep.source=FALSE>>=
proj4string(sc90a) <- CRS(proj4string(sc90a))
@
\end{footnotesize}


\subsection{Dissolving Polygons}

When we try the same sequence of commands for North Carolina, we run
into difficulties:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
names(nc90)
@
<<echo=TRUE,eval=FALSE,keep.source=FALSE>>= 
nc90a <- spChFIDs(nc90, paste(nc90$ST, nc90$CO, sep=""))
@
<<echo=FALSE,eval=TRUE,results=hide>>= 
try1 <- try(spChFIDs(nc90, paste(nc90$ST, nc90$CO, sep="")))
@
<<eval=TRUE,echo=FALSE>>= 
cat(try1)
@
\end{footnotesize}

\noindent
Tabulating the frequencies of polygons per unique county ID, we can see
that 98 of North Carolina's counties are represented by single polygons,
while one has two polygons, and one (on the coast) has four.

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
table(table(paste(nc90$ST, nc90$CO, sep="")))
@
\end{footnotesize}

\noindent
One reason for spatial data being structured in this way is that it
is following the OpenGIS$^{\mbox{\scriptsize\textregistered}}$\footnote{See \url{http://www.opengeospatial.org/}.}
Simple Features Specification,
\label{OpenGIS_SFS}
which allows polygons to have one and only one external boundary
ring, and an unlimited number of internal boundaries -- holes.
This means that multiple external boundaries -- such as a county
made up of several islands -- are represented as multiple
polygons. In the specification, they are linked to attribute data
through a look-up table pointing to the appropriate attribute
data row.

We need to restructure the \code{SpatialPolygons} object such that the
\code{Polygon} objects belonging to each county belong to the same
\code{Polygons} object. To do this, we use a function\footnote{This
function requires that the \pkg{rgeos} package is also installed.} in
the \pkg{maptools} package also used for dissolving or merging polygons,
but which can be used here to re-package the original features, so that
each \code{Polygons} object corresponds to one and only one county:

\begin{footnotesize}
<<echo=TRUE,results=hide,keep.source=FALSE>>= 
nc90a <- unionSpatialPolygons(nc90, IDs=paste(nc90$ST, nc90$CO, sep=""))
@
\end{footnotesize}

\noindent The function uses the IDs argument to set the ID slots
of the output \code{SpatialPolygons} object. Having sorted out
the polygons, we need to remove the duplicate rows from the data
frame and put the pieces back together again:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
nc90_df <- as(nc90, "data.frame")[!duplicated(nc90$CO),-(1:4)]
row.names(nc90_df) <- paste(nc90_df$ST, nc90_df$CO, sep="")
nc90b <- SpatialPolygonsDataFrame(nc90a, nc90_df)
@
\end{footnotesize}

\subsection{Checking Hole Status}

Looking again at Fig.\,\ref{fig:poly3a}, we can see that while
neither North Carolina nor South Carolina has included boroughs
within counties, these are frequently found in Virginia. While
data read from external sources are expected to be structured
correctly, with the including polygon having an outer edge and an
inner hole, into which the outer edge of the included borough
fits, we can also
check and correct the settings of the hole slot in \code{Polygon}
objects. The \code{checkPolygonsHoles} function takes a
\code{Polygons} object as its argument, and, if multiple
\code{Polygon} objects belong to it, checks them for hole status
using functions from the \pkg{rgeos} package:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
va90a <- spChFIDs(va90, paste(va90$ST, va90$CO, sep=""))
va90a <- va90a[,-(1:4)]
va90_pl <- slot(va90a, "polygons")
va90_pla <- lapply(va90_pl, checkPolygonsHoles)
p4sva <- CRS(proj4string(va90a))
vaSP <- SpatialPolygons(va90_pla, proj4string=p4sva)
va90b <- SpatialPolygonsDataFrame(vaSP, data=as(va90a, "data.frame"))
@
\end{footnotesize}

\noindent
Here we have changed the \code{Polygons} ID values as before, and then
processed each \code{Polygons} object in turn for internal consistency, finally
re-assembling the cleaned object. So we now have three spatial objects
with mutually unique IDs, and with data slots containing data frames
with the same numbers and kinds of columns with the same names.


\section{Combining Spatial Data}

It is quite often desirable to combine spatial data of the same kind,
in addition to combining positional data of different kinds as discussed
earlier in this chapter. There are functions \code{rbind} and \code{cbind}
in \RR for combining objects by rows or columns, and \code{rbind} methods
for \code{SpatialPixels} and \code{SpatialPixelsDataFrame} objects, as
well as a \code{cbind} method for \code{SpatialGridDataFrame} objects
are included in \pkg{sp}. In addition, methods with slightly different
names to carry out similar operations are included in the \pkg{maptools}
package.

\subsection{Combining Positional Data}

The \code{spRbind} method combines positional data, such as two
\code{SpatialPoints} objects or two \code{SpatialPointsDataFrame}
objects with matching column names and types in their data slots.
The method is also implemented for \code{SpatialLines} and
\code{SpatialPolygons} objects and their \code{*DataFrame}
extensions. The methods do not check for duplication or
overlapping of the spatial objects being combined, but do reject
attempts to combine objects that would have resulted in
non-unique IDs.

Because the methods only take two arguments, combining more than two
involves repeating calls to the method:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
nc_sc_va90 <- spRbind(spRbind(nc90b, sc90a), va90b)
FIPS <- row.names(nc_sc_va90)
str(FIPS)
length(slot(nc_sc_va90, "polygons"))
@
\end{footnotesize}

\subsection{Combining Attribute Data}
\label{spCbind:here}

Here, as very often found in practice, we need to combine data
for the same spatial objects from different sources, where one
data source includes the geometries and an identifying index
variable, and other data sources include the same index variable
with additional variables. They often include more observations
than our geometries, sometimes have no data for some of our
geometries, and not are infrequently sorted in a different
order. The data cleaning involved in getting ready for analysis
is a little more tedious with spatial data, as we see, but
does not differ in principle from steps taken with non-spatial
data.

The text file provided by the US Census tabulating which counties
belonged to each metropolitan area in 1990 has a header, which
has already been omitted, a footer with formatting information,
and many blank columns. We remove the footer and the blank
columns first, and go on to remove rows with no data -- the
metropolitan areas are separated in the file by empty lines. The
required rows and column numbers were found by inspecting the
file before reading it into \RR:

\begin{footnotesize}
<<echo=TRUE,eval=TRUE,keep.source=FALSE>>= 
t1 <- read.fwf(system.file("share/90mfips.txt", package="maptools"), skip=21,
 widths=c(4,4,4,4,2,6,2,3,3,1,7,5,3,51), colClasses = "character")
@
<<echo=TRUE,keep.source=FALSE>>= 
t2 <- t1[1:2004,c(1,7,8,14)]
t3 <- t2[complete.cases(t2),]
cnty1 <- t3[t3$V7 != "  ",]
ma1 <- t3[t3$V7 == "  ",c(1,4)]
cnty2 <- cnty1[which(!is.na(match(cnty1$V7, c("37", "45", "51")))),]
cnty2$FIPS <- paste(cnty2$V7, cnty2$V8, sep="")
@
\end{footnotesize}

\noindent We next break out an object with metro IDs, state and
county IDs, and county names (\code{cnty1}), and an object with
metro IDs and metro names (\code{ma1}). From there, we subset the
counties to the three states, and add the FIPS string for each
county, to make it possible to combine the new data concerning
metro area membership to our combined county map. We create an
object (\code{MA\_FIPS}) of county metro IDs by matching the
\code{cnty2} FIPS IDs with those of the counties on the map, and
then retrieving the metro area names from \code{ma1}. These two
variables are then made into a data frame, the appropriate row
names inserted and combined with the county map, with method
\code{spCbind}. At last we are ready to dissolve the counties
belonging to metro areas and to discard those not belonging to
metro areas, using \code{unionSpatialPolygons}:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
MA_FIPS <- cnty2$V1[match(FIPS, cnty2$FIPS)]
MA <- ma1$V14[match(MA_FIPS, ma1$V1)]
MA_df <- data.frame(MA_FIPS=MA_FIPS, MA=MA, row.names=FIPS)
nc_sc_va90a <- spCbind(nc_sc_va90, MA_df)
ncscva_MA <- unionSpatialPolygons(nc_sc_va90a, nc_sc_va90a$MA_FIPS)
@
\end{footnotesize}

\begin{figure}[htb]
\centering
<<echo=FALSE,results=tex>>= 
<<bfig>>
oopar <- par(mar=c(3,2,1,1)+0.1)
plot(nc_sc_va90, border="grey", axes=TRUE)
plot(ncscva_MA, lwd=2, add=TRUE)
text(coordinates(ncscva_MA), labels=row.names(ncscva_MA), cex=0.6)
par(oopar)
<<zfig>>
@
\caption{The
three states with county boundaries plotted in grey, and
Metropolitan area boundaries plotted in black; Metro area
standard IDs are shown} 
\label{fig:poly3b}
\end{figure}

Figure~\ref{fig:poly3b} shows the output object plotted on top of
the cleaned input county boundaries. There does appear to be a
problem, however, because one of the output boundaries has no
name -- it is located between 6760 and 5720 in eastern Virginia.
If we do some more matching, to extract the names of the
metropolitan areas, we can display the name of the area with
multiple polygons:

\begin{footnotesize}
<<echo=TRUE,keep.source=FALSE>>= 
np <- sapply(slot(ncscva_MA, "polygons"), function(x) length(slot(x, "Polygons")))
table(np)
MA_fips <- row.names(ncscva_MA)
MA_name <- ma1$V14[match(MA_fips, ma1$V1)]
data.frame(MA_fips, MA_name)[np > 1,]
@
\end{footnotesize}

The Norfolk-Virginia Beach-Newport News, VA MSA is located on both sides
of Hampton Roads, and the label has been positioned at the centre point
of the largest member polygon.

<<echo=FALSE>>= 
options("width"=owidth)
@


\end{document}

