# Pycnophylactic Interpolation

### Description

Given a SpatialPolygonsDataFrame and a set of populations for each polygon, compute a population density estimate based on Tobler's pycnophylactic interpolation algorithm. The result is a SpatialGridDataFrame.

### Details

Package: | pycno |

Type: | Package |

Version: | 1.0 |

Date: | 2011-04-15 |

License: | GPL (>=2) |

LazyLoad: | yes |

For use in conjunction with the sp package, computes pycnophylactic surfaces given a SpatialPolygonsDataFrame and a population for each poplygon. A pycnophylactic surface is smooth, but populations allocated to each pixel sum up to the initial polygon counts, when summed over the polygons contained in each pixel.

### Author(s)

Chris Brunsdon

Maintainer: Chris Brunsdon cb179@le.ac.uk

### References

Tobler, W.R. (1979) *Smooth Pycnophylactic Interpolation for Geographical Regions*. Journal of the American Statistical Association, v74(367) pp. 519-530.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# Read in data for North Carolina as a SpatialPolygonsDataFrame
nc.sids <- readShapeSpatial(system.file("shapes/sids.shp", package="maptools")[1],
IDvar="FIPSNO", proj4string=CRS("+proj=longlat +ellps=clrk66"))
# Compute the pycnophylactic surface for 1974 births as a SpatialGridDataFrame
# Note probably shouldn't really base grid cells on Lat/Long coordinates
# This example just serves to illustrate the use of the function
births74 <- pycno(nc.sids,nc.sids$BIR74,0.05, converge=1)
# Draw it
image(births74)
# Overlay North Carolina county boundaries for reference
plot(nc.sids,add=TRUE)
``` |