r - rgeos::gCentroid() 和 sf::st_centroid() 返回的值是否不同？

Question

问题

执行 rgeos::gCentroid() 返回的值和 sf::st_centroid()不同？如果是这样，怎么办？

上下文

阅读 relevant commands exported by rgeos 后r-spatial/sf wiki 内的部分，我很高兴看到我只需要 sf包 - 不再需要导入 rgeos包 - 计算给定几何图形的质心。

但是，使用 sf::st_centroid() 给了我这个警告，which is addressed here :

Warning message:
   In st_centroid.sfc(x = comarea606$geometry) :
   st_centroid does not give correct centroids for longitude/latitude data

该警告促使我测试两种质心检索方法之间的相等性，只是为了确保无论使用哪种方法，坐标都是相同的。

虽然我使用identical()和 %in%导致不相同的匹配，all.equal()绘制每种方法质心的 map 似乎表明这两种方法几乎相同。

是否有任何原因导致一个方法返回一组与另一个方法不同的值？

可重现的示例

# load neccessary packages
library( sf )
library( rgeos )

# load data
comarea606 <-
    read_sf( 
      dsn = "https://data.cityofchicago.org/api/geospatial/cauq-8yn6?method=export&format=GeoJSON" 
      , layer = "OGRGeoJSON" 
    )

# find the centroid of each polygon
comarea606$centroids <-
  st_centroid( x = comarea606$geometry ) %>%
  st_geometry()

# Warning message:
#   In st_centroid.sfc(x = comarea606$geometry) :
#   st_centroid does not give correct centroids for longitude/latitude data

# Ensure the st_centroid() method
# contains identical values to gCentroid()
sf.centroids <-
  st_coordinates( x = comarea606$centroids )

rgeos.centroids <-
  gCentroid(
    spgeom = methods::as( 
      object = comarea606
      , Class = "Spatial"
    )
    , byid = TRUE 
  )@coords


# ensure the colnames are the same
colnames( rgeos.centroids ) <-
  colnames( sf.centroids )

# Test for equality
identical(
  x = sf.centroids
  , y = rgeos.centroids
) # [1] FALSE

all.equal(
  target = sf.centroids
  , current = rgeos.centroids
) # [1] TRUE

# View the first six results
head( sf.centroids )
#           X        Y
# 1 -87.61868 41.83512
# 2 -87.60322 41.82375
# 3 -87.63242 41.80909
# 4 -87.61786 41.81295
# 5 -87.59618 41.80892
# 6 -87.68752 41.97517
head( rgeos.centroids )
#           X        Y
# 1 -87.61868 41.83512
# 2 -87.60322 41.82375
# 3 -87.63242 41.80909
# 4 -87.61786 41.81295
# 5 -87.59618 41.80892
# 6 -87.68752 41.97517

# Identify the numbers which aren't identical
sf.centroids[ , "X" ] %in% rgeos.centroids[ , "X" ]
# [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [11] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [21] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [31] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [41] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [51] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [71] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
sf.centroids[ , "Y" ] %in% rgeos.centroids[ , "Y" ]
# [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [11] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [21] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [31] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [41] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [51] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
# [71] FALSE FALSE FALSE FALSE FALSE FALSE FALSE

# view results
par( 
  mar = c( 2, 0, 3, 0 )
  , bg = "black"
)
plot( 
  x = comarea606$geometry
  , main = "`sf` v. `rgeos`:\nComparing Centroid Coordinates"
  , col.main = "white"
  , col = "black"
  , border = "white"
)
plot( 
  x = comarea606$centroids
  , add = TRUE
  , pch = 24
  , col = "#B4DDF2"
  , bg  = "#B4DDF2"
  , cex = 1.2
)
points( 
  x = rgeos.centroids[ , "X" ]
  , y = rgeos.centroids[ , "Y" ]
  , pch = 24
  , col = "#FB0D1B"
  , bg  = "#FB0D1B"
  , cex = 0.6
)
legend(
  x = "left"
  , legend = c( 
    "Centroids from `sf::st_coordinate()`"
    , "Centroids from `rgeos::gCentroid()`"
  )
  , col      = c( "#B4DDF2", "#FB0D1B" )
  , pt.bg    = c( "#B4DDF2", "#FB0D1B" )
  , pch      = 24
  , bty      = "n"
  , cex      = 0.9
  , text.col = "white"
)
mtext(
  adj    = 0.99
  , line = 1
  , side = 1
  , cex  = 0.9
  , text = "Source: Chicago Data Portal"
  , col  = "white"
)

# end of script #

Session Info

R version 3.4.4 (2018-03-15)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.2

Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
[1] rgeos_0.3-26 sf_0.6-0    

loaded via a namespace (and not attached):
 [1] modeltools_0.2-21 kernlab_0.9-25    reshape2_1.4.3   
 [4] lattice_0.20-35   colorspace_1.3-2  htmltools_0.3.6  
 [7] stats4_3.4.4      viridisLite_0.3.0 yaml_2.1.18      
[10] utf8_1.1.3        rlang_0.2.0       R.oo_1.21.0      
[13] e1071_1.6-8       pillar_1.2.1      withr_2.1.2      
[16] DBI_0.8           prabclus_2.2-6    R.utils_2.6.0    
[19] sp_1.2-7          fpc_2.1-11        plyr_1.8.4       
[22] robustbase_0.92-8 stringr_1.3.0     munsell_0.4.3    
[25] gtable_0.2.0      raster_2.6-7      R.methodsS3_1.7.1
[28] devtools_1.13.5   mvtnorm_1.0-7     memoise_1.1.0    
[31] evaluate_0.10.1   knitr_1.20        flexmix_2.3-14   
[34] class_7.3-14      DEoptimR_1.0-8    trimcluster_0.1-2
[37] Rcpp_0.12.16      udunits2_0.13     scales_0.5.0     
[40] backports_1.1.2   diptest_0.75-7    classInt_0.1-24  
[43] squash_1.0.8      gridExtra_2.3     ggplot2_2.2.1    
[46] digest_0.6.15     stringi_1.1.6     grid_3.4.4       
[49] rprojroot_1.3-2   rgdal_1.2-18      cli_1.0.0        
[52] tools_3.4.4       magrittr_1.5      lazyeval_0.2.1   
[55] tibble_1.4.2      cluster_2.0.6     crayon_1.3.4     
[58] whisker_0.3-2     dendextend_1.7.0  MASS_7.3-49      
[61] assertthat_0.2.0  rmarkdown_1.9     rstudioapi_0.7   
[64] viridis_0.5.0     mclust_5.4        units_0.5-1      
[67] nnet_7.3-12       compiler_3.4.4   

Answer 1

这个问题简化为:all.equal() 与 identical() 有何不同，我们查看这些函数的文档:

all.equal(x, y) is a utility to compare R objects x and y testing ‘near equality’.

对于identical()

The safe and reliable way to test two objects for being exactly equal. It returns TRUE in this case, FALSE in every other case.

让我们仔细看看 all.equal.numeric()，这是在这两个对象上调用的方法，因为两者都返回 "double" 以及 >typeof() 。我们看到 all.equal.numeric() 中有一个 tolerance 参数，它被设置为 sqrt(.Machine$double.eps) ， 默认情况下。 .Machine$double.eps 是您的机器可以添加到 1 并能够将其与 1 区分开来的最小数字。虽然不准确，但也差不多是这个数量级。 all.equal.numeric() 本质上是检查一个向量中的所有值是否都 near() 另一个向量中的所有值。您可以查看源代码(主要是错误检查)以了解它是如何执行此操作的。

为了让自己相信它们实际上不是 identical()，请尝试查看 sf.centroids - rgeos.centroids 的输出。

head(sf.centroids - rgeos.centroids)
#               X             Y
# 1 -5.056506e-10  2.623175e-09
# 2 -2.961613e-09 -4.269602e-09
# 3  4.235119e-10  4.358100e-09
# 4 -7.688925e-10 -1.051717e-09
# 5  1.226582e-09  1.668568e-10
# 6 -2.957009e-09  4.875247e-10

这两个矩阵毫无疑问非常接近相同(但没有一个值完全相同)。