Given a `SpatialGridDataFrame`

of population estimates and a set of polygons,
compute a population estimate based on Tobler's pycnophylactic interpolation
algorithm for each zone. The result is a vector.

1 | ```
estimate.pycno(sgdf, spdf)
``` |

`sgdf` |
A |

`spdf` |
A |

Takes the estimate of population density for each pixel, checks which polygon each pixel is in, and aggregates them. Accuracy depends on the scale of pixels in the initial interpolation.

A vector in which each each pixel set at the estimated population aggregation to each zone in `spdf`

.

Pycnophylatic interpolation has the property that the sum of the estimated values associated with all of the pixels in any polygon equals the supplied population for that polygon. A further property is that all pixel values are greater than or equal to zero. The method is generally used to obtain pixel-based population estimates when total populations for a set of irregular polygons (eg. counties) are known.

Chris Brunsdon

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# 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 functions
births74 <- pycno(nc.sids,nc.sids$BIR74,0.05,converge=1)
# Create a new 'blocky' set of zones
blocks <- gUnionCascaded(nc.sids,1*(coordinates(nc.sids)[,2] > 36) +
2*(coordinates(nc.sids)[,1] > -80))
# Plot the bloocky zones
plot(blocks)
# Aggregate data to them
estimates <- estimate.pycno(births74,blocks)
# Write the estimates on to the map
text(coordinates(blocks),as.character(estimates))
``` |

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