计算多个多边形之间共享边界的长度

Question

我有一个 shapefile，我想知道每个多边形有哪些其他多边形接触它。为此，我有这个代码：

require("rgdal")  
require("rgeos")

download.file("https://www.dropbox.com/s/vbxx9dic34qwz63/Polygons.zip?dl=1", "Polygons.zip")

Shapefile <- readOGR(".","Polygons")

Touching_List <- gTouches(Shapefile, byid = TRUE, returnDense=FALSE)

Touching_DF <- setNames(stack(lapply(Touching_List, as.character)), c("TOUCHING", "ORIGIN"))

我现在想进一步了解每个多边形与其他多边形接触的程度。对于Touching_DF 中的每一行，我所追求的是每个ORIGIN 多边形的总长度/周长以及每个TOUCHING 多边形接触原多边形的总长度。这将允许计算共享边界的百分比。我可以想象它的输出将是Touching_DF 中的 3 个新列（例如，对于第一行，它可能类似于原始参数 1000m，接触长度 500m，共享边界 50%）。谢谢。

编辑 1

我已将@StatnMap 的答案应用于我的真实数据集。如果多边形共享边和点，gTouches 似乎正在返回结果。这些点引起了问题，因为它们没有长度。我已经修改了 StatnMap 的部分代码来处理它，但是在最后创建数据框时，gTouches 返回的共享边/顶点数与有长度的边数之间存在不匹配。

以下是一些代码，使用我的实际数据集示例演示该问题：

library(rgdal)  
library(rgeos)
library(sp)
library(raster)

download.file("https://www.dropbox.com/s/hsnrdfthut6klqn/Sample.zip?dl=1", "Sample.zip")

unzip("Sample.zip")
Shapefile <- readOGR(".","Sample")

Touching_List <- gTouches(Shapefile, byid = TRUE, returnDense=FALSE)

# ---- Calculate perimeters of all polygons ----
perimeters <- sp::SpatialLinesLengths(as(Shapefile, "SpatialLines"))

# ---- All in a lapply loop ----
all.length.list <- lapply(1:length(Touching_List), function(from) {
  lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
  if(class(lines) != "SpatialLines"){lines <- lines@lineobj}
  l_lines <- sp::SpatialLinesLengths(lines, longlat=FALSE)
  results <- data.frame(origin = from,
                    perimeter = perimeters[from],
                    touching = Touching_List[[from]],
                    t.length = l_lines,
                    t.pc = 100*l_lines/perimeters[from])
  results
})

这特别显示了其中一个多边形的问题：

from <- 4
lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
if(class(lines) != "SpatialLines"){lines <- lines@lineobj}
l_lines <- sp::SpatialLinesLengths(lines, longlat=FALSE)

plot(Shapefile[c(from, Touching_List[[from]]),])
plot(lines, add = TRUE, col = 1 + 1:length(Touching_List[[from]]), lwd = 2)

我看到的两种可能的解决方案是 1. 让 gTouches 只返回长度大于零的共享边或 2. 当遇到点而不是边时返回长度为零（而不是错误）。到目前为止，我找不到任何可以做这些事情的东西。

编辑 2

@StatnMap 修改后的解决方案效果很好。但是，如果一个多边形不与其相邻的多边形共享一个捕捉边界（即它去一个点然后创建一个岛滑行多边形），那么它会在lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)

之后出现这个错误

   Error in RGEOSBinTopoFunc(spgeom1, spgeom2, byid, id, drop_lower_td, unaryUnion_if_byid_false,  : 
      Geometry collections may not contain other geometry collections

我一直在寻找一种解决方案，该解决方案能够识别边界绘制不良的多边形，并且不执行任何计算并在res 中返回“NA”（因此以后仍然可以识别它们）。但是，我一直无法找到将这些有问题的多边形与“正常”多边形区分开来的命令。

使用这 8 个多边形运行 @StatnMap 的修改后的解决方案证明了这个问题：

download.file("https://www.dropbox.com/s/ttg2mi2nq1gbbrq/Bad_Polygon.zip?dl=1", "Bad_Polygon.zip")
unzip("Bad_Polygon.zip")
Shapefile <- readOGR(".","Bad_Polygon")

Answer 1

两个只接触自己的多边形的交点是一条线。使用 R 中的空间库功能可以轻松计算线长。
当您使用库 sp 开始您的示例时，您会发现这个库的一个命题。不过，我也给你一个新库sf的提议。

使用库sp 计算多边形共享边界长度

require("rgdal")  
require("rgeos")
library(sp)
library(raster)

download.file("https://www.dropbox.com/s/vbxx9dic34qwz63/Polygons.zip?dl=1", "Polygons.zip")

unzip("Polygons.zip")
Shapefile <- readOGR(".","Polygons")

Touching_List <- gTouches(Shapefile, byid = TRUE, returnDense=FALSE)

# Touching_DF <- setNames(utils::stack(lapply(Touching_List, as.character)), c("TOUCHING", "ORIGIN"))

# ---- Calculate perimeters of all polygons ----
perimeters <- sp::SpatialLinesLengths(as(Shapefile, "SpatialLines"))

# ---- Example with the first object of the list and first neighbor ----
from <- 1
to <- 1
line <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]][to],])
l_line <- sp::SpatialLinesLengths(line)

plot(Shapefile[c(from, Touching_List[[from]][to]),])
plot(line, add = TRUE, col = "red", lwd = 2)

# ---- Example with the first object of the list and all neighbors ----
from <- 1
lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
l_lines <- sp::SpatialLinesLengths(lines)

plot(Shapefile[c(from, Touching_List[[from]]),])
plot(lines, add = TRUE, col = 1 + 1:length(Touching_List[[from]]), lwd = 2)

# ---- All in a lapply loop ----
all.length.list <- lapply(1:length(Touching_List), function(from) {
  lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
  l_lines <- sp::SpatialLinesLengths(lines)
  res <- data.frame(origin = from,
                    perimeter = perimeters[from],
                    touching = Touching_List[[from]],
                    t.length = l_lines,
                    t.pc = 100*l_lines/perimeters[from])
  res
})

# ---- Retrieve as a dataframe ----
all.length.df <- do.call("rbind", all.length.list)

在上表中，t.length 是接触长度，t.pc 是相对于原点多边形周长的接触百分比。

编辑：一些共享边界是点（sp）

如前所述，某些边界可能是一个独特的点而不是线。为了解决这种情况，我建议将点的坐标加倍以创建长度为 0 的线。这需要在出现这种情况时，一一计算与其他多边形的交点。
对于单个多边形，我们可以测试一下：

# Example with the first object of the list and all neighbours
from <- 4
lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
# If lines and points, need to do it one by one to find the point
if (class(lines) == "SpatialCollections") {
  list.Lines <- lapply(1:length(Touching_List[[from]]), function(to) {
    line.single <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]][to],])
    if (class(line.single) == "SpatialPoints") {
      # Double the point to create a line
      L1 <- rbind(line.single@coords, line.single@coords)
      rownames(L1) <- letters[1:2]
      Sl1 <- Line(L1)
      Lines.single <- Lines(list(Sl1), ID = as.character(to))
    } else if (class(line.single) == "SpatialLines") {
      Lines.single <- line.single@lines[[1]]
      Lines.single@ID <- as.character(to)
    }
    Lines.single
  })
  lines <- SpatialLines(list.Lines)
}

l_lines <- sp::SpatialLinesLengths(lines)

plot(Shapefile[c(from, Touching_List[[from]]),])
plot(lines, add = TRUE, col = 1 + 1:length(Touching_List[[from]]), lwd = 2)

对于 lapply 循环中的所有内容：

# Corrected for point outputs: All in a lapply loop
all.length.list <- lapply(1:length(Touching_List), function(from) {
  lines <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]],], byid = TRUE)
  if (class(lines) == "SpatialCollections") {
    list.Lines <- lapply(1:length(Touching_List[[from]]), function(to) {
      line.single <- rgeos::gIntersection(Shapefile[from,], Shapefile[Touching_List[[from]][to],])
      if (class(line.single) == "SpatialPoints") {
        # Double the point to create a line
        L1 <- rbind(line.single@coords, line.single@coords)
        rownames(L1) <- letters[1:2]
        Sl1 <- Line(L1)
        Lines.single <- Lines(list(Sl1), ID = as.character(to))
      } else if (class(line.single) == "SpatialLines") {
        Lines.single <- line.single@lines[[1]]
        Lines.single@ID <- as.character(to)
      }
      Lines.single
    })
    lines <- SpatialLines(list.Lines)
  }
  l_lines <- sp::SpatialLinesLengths(lines)
  res <- data.frame(origin = from,
                    perimeter = perimeters[from],
                    touching = Touching_List[[from]],
                    t.length = l_lines,
                    t.pc = 100*l_lines/perimeters[from])
  res
})

all.length.df <- do.call("rbind", all.length.list)

这也可能适用于库sf，但显然您选择使用sp，我不会更新这部分的代码。也许以后...

---- 编辑结束----

使用库sf 计算多边形共享边界长度

数字和输出是一样的。

library(sf)
Shapefile.sf <- st_read(".","Polygons")

# ---- Touching list ----
Touching_List <- st_touches(Shapefile.sf)
# ---- Polygons perimeters ----
perimeters <- st_length(Shapefile.sf)

# ---- Example with the first object of the list and first neighbour ----
from <- 1
to <- 1
line <- st_intersection(Shapefile.sf[from,], Shapefile.sf[Touching_List[[from]][to],])
l_line <- st_length(line)

plot(Shapefile.sf[c(from, Touching_List[[from]][to]),])
plot(line, add = TRUE, col = "red", lwd = 2)

# ---- Example with the first object of the list and all neighbours ----
from <- 1
lines <- st_intersection(Shapefile.sf[from,], Shapefile.sf[Touching_List[[from]],])
lines <- st_cast(lines) # In case of multiple geometries (ex. from=71)
l_lines <- st_length(lines)

plot(Shapefile.sf[c(from, Touching_List[[from]]),])
plot(lines, add = TRUE, col = 1:length(Touching_List[[from]]), lwd = 2)

# ---- All in a lapply loop ----
all.length.list <- lapply(1:length(Touching_List), function(from) {
  lines <- st_intersection(Shapefile.sf[from,], Shapefile.sf[Touching_List[[from]],])
  lines <- st_cast(lines) # In case of multiple geometries
  l_lines <- st_length(lines)
  res <- data.frame(origin = from,
                    perimeter = as.vector(perimeters[from]),
                    touching = Touching_List[[from]],
                    t.length = as.vector(l_lines),
                    t.pc = as.vector(100*l_lines/perimeters[from]))
  res
})

# ---- Retrieve as dataframe ----
all.length.df <- do.call("rbind", all.length.list)

Answer 2

只是为了添加到 Sébastien Rochette 的答案中，我认为来自 sfpackage 的函数 st_length 不适用于多边形（请参阅此 post）。相反，我建议在 lwgeom 包中使用函数 st_perimeter。

（我想评论答案但我没有足够的声誉）