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

Question

假设我有两组形状文件，它们经常覆盖同一区域，但并不总是共享边界，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，即两者都不能被分割，但我仍然想要尽可能多的单位。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。有谁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

我认为你可以通过一组智能的收容测试来做到这一点。这得到了你的两个部分，简单的配对情况，其中puma1contains county1andcounty2和puma2contains county8and 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)

}

那里的情节是多余的，但我认为它表明了一个开始。您需要找到哪些包含测试累积了最小的部分，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。

Answer 2

这是一个相对简洁的解决方案：

• 用于rgeos::gRelate()识别重叠但不完全包含/覆盖每个县的美洲狮。要了解它的作用，请运行example(gRelate)并查看此 Wikipedia 页面。（对蒂姆·里夫（Tim Riffe））

• 用于RBGL::connectedComp()识别应该合并的美洲狮组。（有关安装RBGL包的提示，请参阅我对这个 SO 问题的回答。）

• 用于rgeos::gUnionCascaded()合并指定的美洲狮。

  library(rgeos)
  library(RBGL)
  
  ## Identify groups of Pumas that should be merged
  x <- gRelate(counties, Pumas, byid=TRUE)
  x <- matrix(grepl("2.2......", x), ncol=ncol(x), dimnames=dimnames(x))
  k <- x %*% t(x)
  l <- connectedComp(as(k, "graphNEL"))
  
  ## Extend gUnionCascaded so that each SpatialPolygon gets its own ID.
  gMerge <- function(ii) {
      x <- gUnionCascaded(Pumas[ii,])
      spChFIDs(x, paste(ii, collapse="_"))
  }
  
  ## Merge Pumas as needed
  res <- do.call(rbind, sapply(l, gMerge))
  
  plot(res)
  

Answer 3

经过多次反复试验，我提出了以下不雅的解决方案，而不是与@mdsummer 的提示保持一致，但添加了更多检查，删除了多余的合并多边形并进行了检查。哎呀。如果有人可以接受我所做的事情并使其更清洁，那么我会接受这个答案，而不是这个，如果可能的话，我想避免：

library(rgeos)
pbyc <- gCovers(Pumas, counties, byid = TRUE) | 
        gContains(Pumas, counties, byid = TRUE) | 
        gOverlaps(Pumas, counties, byid = TRUE) |

        t(gCovers(counties, Pumas, byid = TRUE) | 
            gContains(counties, Pumas, byid = TRUE) |  
            gOverlaps(counties, Pumas, byid = TRUE))


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

Potentials <- apply(pbyc.pairs, 1, function(x,counties,Pumas){
     gUnion(counties[x[1], ], Pumas[x[2], ])
    }, counties = counties, Pumas= Pumas)
for (i in 1:length(Potentials)){
  Potentials[[i]]@polygons[[1]]@ID <- paste0("p",i)
}
Potentials <- do.call("rbind",Potentials)

# remove redundant polygons:
Redundants <- gEquals(Potentials, byid = TRUE)
Redundants <- row(Redundants)[Redundants & lower.tri(Redundants)]
Potentials <- Potentials[-c(Redundants),]

# for each Potential summary polygon, see which counties and Pumas are contained:
keep.i <- vector(length=length(Potentials))

for (i in 1:length(Potentials)){
  ctyblocki <- gUnionCascaded(counties[c(gCovers(Potentials[i, ], counties, byid = TRUE)), ])
  Pumablocki <- gUnionCascaded(Pumas[c(gCovers(Potentials[i, ], Pumas, byid = TRUE)), ]) 
  keep.i[i] <- gEquals(ctyblocki, Potentials[i, ]) & gEquals(Pumablocki, Potentials[i, ])    
}
# what do we have left?
NewUnits <- Potentials[keep.i, ]

plot(NewUnits)