r - 如何通过简化 R 中的两个 SpatialPolygonsDataFrame 对象来创建新多边形？

Question

说我有两组形状文件覆盖同一区域，并且经常但不总是共享边界，例如美国县和 PUMA。我想定义一个新的多边形比例，它使用 PUMA 和县作为原子构建块，即两者都不能被拆分，但我仍然希望尽可能多的单位。这是一个玩具示例:

library(sp)
# make fake data
# 1) counties:
Cty <- SpatialPolygons(list(
    Polygons(list(Polygon(cbind(x=c(0,2,2,1,0,0),y=c(0,0,2,2,1,0)), hole=FALSE)),"county1"),
    Polygons(list(Polygon(cbind(x=c(2,4,4,3,3,2,2),y=c(0,0,2,2,1,1,0)),hole=FALSE)),"county2"),
    Polygons(list(Polygon(cbind(x=c(4,5,5,4,4),y=c(0,0,3,2,0)),hole=FALSE)),"county3"),
    Polygons(list(Polygon(cbind(x=c(0,1,2,2,0,0),y=c(1,2,2,3,3,1)),hole=FALSE)),"county4"),
    Polygons(list(Polygon(cbind(x=c(2,3,3,4,4,3,3,2,2),y=c(1,1,2,2,3,3,4,4,1)),hole=FALSE)),"county5"),
    Polygons(list(Polygon(cbind(x=c(0,2,2,1,0,0),y=c(3,3,4,5,5,3)),hole=FALSE)),"county6"),
    Polygons(list(Polygon(cbind(x=c(1,2,3,4,1),y=c(5,4,4,5,5)),hole=FALSE)),"county7"),
    Polygons(list(Polygon(cbind(x=c(3,4,4,5,5,4,3,3),y=c(3,3,2,3,5,5,4,3)),hole=FALSE)),"county8")
))

counties <- SpatialPolygonsDataFrame(Cty, data = data.frame(ID=paste0("county",1:8),
            row.names=paste0("county",1:8),
            stringsAsFactors=FALSE)
)
# 2) PUMAs:
Pum <- SpatialPolygons(list(
            Polygons(list(Polygon(cbind(x=c(0,4,4,3,3,2,2,1,0,0),y=c(0,0,2,2,1,1,2,2,1,0)), hole=FALSE)),"puma1"),
            Polygons(list(Polygon(cbind(x=c(4,5,5,4,3,3,4,4),y=c(0,0,5,5,4,3,3,0)),hole=FALSE)),"puma2"),
            Polygons(list(Polygon(cbind(x=c(0,1,2,2,3,3,2,0,0),y=c(1,2,2,1,1,2,3,3,1)),hole=FALSE)),"puma3"),
            Polygons(list(Polygon(cbind(x=c(2,3,4,4,3,3,2,2),y=c(3,2,2,3,3,4,4,3)),hole=FALSE)),"puma4"),
            Polygons(list(Polygon(cbind(x=c(0,1,1,3,4,0,0),y=c(3,3,4,4,5,5,3)),hole=FALSE)),"puma5"),
            Polygons(list(Polygon(cbind(x=c(1,2,2,1,1),y=c(3,3,4,4,3)),hole=FALSE)),"puma6")
    ))
Pumas <- SpatialPolygonsDataFrame(Pum, data = data.frame(ID=paste0("puma",1:6),
            row.names=paste0("puma",1:6),
            stringsAsFactors=FALSE)
)

# desired result:
Cclust <- SpatialPolygons(list(
            Polygons(list(Polygon(cbind(x=c(0,4,4,3,3,2,2,1,0,0),y=c(0,0,2,2,1,1,2,2,1,0)), hole=FALSE)),"ctyclust1"),
            Polygons(list(Polygon(cbind(x=c(4,5,5,4,3,3,4,4),y=c(0,0,5,5,4,3,3,0)),hole=FALSE)),"ctyclust2"),
            Polygons(list(Polygon(cbind(x=c(0,1,2,2,3,3,4,4,3,3,2,2,0,0),y=c(1,2,2,1,1,2,2,3,3,4,4,3,3,1)),hole=FALSE)),"ctyclust3"),
            Polygons(list(Polygon(cbind(x=c(0,2,2,3,4,0,0),y=c(3,3,4,4,5,5,3)),hole=FALSE)),"ctyclust4")
    ))
CtyClusters <- SpatialPolygonsDataFrame(Cclust, data = data.frame(ID = paste0("ctyclust", 1:4),
            row.names = paste0("ctyclust", 1:4),
            stringsAsFactors=FALSE)
)

# take a look
par(mfrow = c(1, 2))
plot(counties, border = gray(.3), lwd = 4)
plot(Pumas, add = TRUE, border = "#EEBB00", lty = 2, lwd = 2)
legend(-.5, -.3, lty = c(1, 2), lwd = c(4, 2), col = c(gray(.3), "#EEBB00"),
    legend = c("county line", "puma line"), xpd = TRUE, bty = "n")
text(coordinates(counties), counties@data$ID,col = gray(.3))
text(coordinates(Pumas), Pumas@data$ID, col = "#EEBB00",cex=1.5)
title("building blocks")
#desired result:
plot(CtyClusters)
title("desired result")
text(-.5, -.5, "maximum units possible,\nwithout breaking either PUMAs or counties",
    xpd = TRUE, pos = 4)

我天真地尝试了 rgeos 包中的许多 g* 函数来实现这一点，但没有取得进展。有没有人知道这个任务的一个很好的功能或很棒的技巧？谢谢!
[我也愿意接受关于更好标题的建议]

Answer 1

我认为您可以通过一组智能的遏制测试来做到这一点。这得到了你的两个部分，简单的配对案例，其中 puma1包含 county1和 county2 , 和 puma2包含 county8和 county3 .

library(rgeos)

## pumas by counties
pbyc <- gContains(Pumas, counties, byid = TRUE)

## row / col pairs of where contains test is TRUE for Pumas
pbyc.pairs <-  cbind(row(pbyc)[pbyc], col(pbyc)[pbyc])

par(mfrow = c(nrow(pbyc.pairs), 1))

for (i in 1:nrow(pbyc.pairs)) {
plot(counties, col = "white")

plot(gUnion(counties[pbyc.pairs[i,1], ], Pumas[pbyc.pairs[i,2], ]), col = "red", add = TRUE)

}

那里的绘图愚蠢地多余，但我认为它显示了一个开始。您需要找到哪些包含测试积累了最小的部分，然后将它们合并。对不起，我没有努力完成，但我认为这会奏效。