shapefile - Extracting intersection areas in R

I have two polygons. One contains fields(X,Y,Z) and the other contains soil types (A,B,C,D). I want to know what area of every field contains which type of soil. I tried the following:

library(rgdal)
library(rgeos)
Field<-readOGR("./","Field")
Soil<-readOGR("./","Soil")
Results<-gIntersects(Soil,Field,byid=TRUE)
rownames(Results)<-Field@data$FieldName
colnames(Results)<-Soil@data$SoilType

> Results

      A     B     C     D
Z  TRUE FALSE FALSE FALSE
Y FALSE  TRUE  TRUE FALSE
X  TRUE  TRUE  TRUE  TRUE

and achieved good results with it telling me which field contains which soil type. However, how do I get the area instead?

Answer

This method uses the intersect() function from the raster package. The example data I've used aren't ideal (for one thing they're in unprojected coordinates), but I think it gets the idea across.

library(sp)
library(raster)

library(rgdal)
library(rgeos)
library(maptools)

# Example data from raster package
p1 <- shapefile(system.file("external/lux.shp", package="raster"))
# Remove attribute data
p1 <- as(p1, 'SpatialPolygons')
# Add in some fake soil type data
soil <- SpatialPolygonsDataFrame(p1, data.frame(soil=LETTERS[1:12]), match.ID=F)


# Field polygons
p2 <- union(as(extent(6, 6.4, 49.75, 50), 'SpatialPolygons'),
             as(extent(5.8, 6.2, 49.5, 49.7), 'SpatialPolygons'))
field <- SpatialPolygonsDataFrame(p2, data.frame(field=c('x','y')), match.ID=F)
projection(field) <- projection(soil)

# intersect from raster package
pi <- intersect(soil, field)
plot(soil, axes=T); plot(field, add=T); plot(pi, add=T, col='red')


# Extract areas from polygon objects then attach as attribute
pi$area <- area(pi) / 1000000

# For each field, get area per soil type
aggregate(area~field + soil, data=pi, FUN=sum)

Results:

    field soil         area

1      x    A 2.457226e+01
2      x    B 2.095659e+02
3      x    C 5.714943e+00
4      y    C 5.311882e-03
5      x    D 7.620041e+01
6      x    E 3.101547e+01
7      x    F 1.019455e+02
8      x    H 7.106824e-03
9      y    H 2.973232e+00
10     y    I 1.752702e+02

11     y    J 1.886562e+02
12     y    K 1.538229e+02
13     x    L 1.321748e+02
14     y    L 1.182670e+01