Distance between points along path in R

I want to compute distance between nodes along a path (network).

I have two shapefiles.

One is a point layer representing train stations:

train_station  <- structure(list(geometry = structure(list(structure(c(1789781.1763, 
1036140.3792), class = c("XY", "POINT", "sfg")), structure(c(1391746.6168, 
-336142.520399998), class = c("XY", "POINT", "sfg")), structure(c(1322725.335, 
-446160.425799999), class = c("XY", "POINT", "sfg")), structure(c(1079349.8399, 
-389421.086099999), class = c("XY", "POINT", "sfg")), structure(c(993051.089600001, 
604054.897600002), class = c("XY", "POINT", "sfg")), structure(c(1734176.6467, 
803503.679300002), class = c("XY", "POINT", "sfg")), structure(c(1639866.0629, 
386133.173800001), class = c("XY", "POINT", "sfg")), structure(c(1658998.0956, 
593818.4364), class = c("XY", "POINT", "sfg")), structure(c(1436011.5057, 
750318.722999998), class = c("XY", "POINT", "sfg")), structure(c(1616310.3521, 
-137545.4903), class = c("XY", "POINT", "sfg")), structure(c(1907821.16828945, 
846114.131303993), class = c("XY", "POINT", "sfg")), structure(c(960998.947599998, 
136060.9786), class = c("XY", "POINT", "sfg")), structure(c(1433751.8485, 
-368676.099499998), class = c("XY", "POINT", "sfg")), structure(c(1016693.4823, 
-307540.433600002), class = c("XY", "POINT", "sfg")), structure(c(1178486.7964, 
535962.089599999), class = c("XY", "POINT", "sfg")), structure(c(1805904.0874, 
608223.609200002), class = c("XY", "POINT", "sfg")), structure(c(1027750.5026, 
-503417.115600001), class = c("XY", "POINT", "sfg")), structure(c(756089.969799999, 
-277720.935699999), class = c("XY", "POINT", "sfg")), structure(c(1783381.519, 
580457.243600001), class = c("XY", "POINT", "sfg")), structure(c(1638164.0169, 
-179512.823000001), class = c("XY", "POINT", "sfg")), structure(c(1834362.883, 
693158.698699999), class = c("XY", "POINT", "sfg")), structure(c(923737.611100001, 
-522394.597200001), class = c("XY", "POINT", "sfg")), structure(c(564090.517499997, 
-564609.5142), class = c("XY", "POINT", "sfg")), structure(c(1700622.4846, 
461411.774400001), class = c("XY", "POINT", "sfg")), structure(c(1884814.7315, 
844470.2333), class = c("XY", "POINT", "sfg")), structure(c(1035880.12193273, 
421102.600903689), class = c("XY", "POINT", "sfg")), structure(c(981168.882900001, 
553358.567199998), class = c("XY", "POINT", "sfg")), structure(c(1630589.1227, 
96992.7936000023), class = c("XY", "POINT", "sfg")), structure(c(1469206.5633, 
-382122.280600001), class = c("XY", "POINT", "sfg")), structure(c(1074513.95508099, 
495379.397144308), class = c("XY", "POINT", "sfg")), structure(c(1699926.7821, 
84351.6904), class = c("XY", "POINT", "sfg")), structure(c(882981.990499998, 
157627.906599999), class = c("XY", "POINT", "sfg")), structure(c(1595222.2689, 
789366.362099998), class = c("XY", "POINT", "sfg")), structure(c(1908684.48408199, 
961557.436709222), class = c("XY", "POINT", "sfg")), structure(c(855655.5085, 
583468.712600001), class = c("XY", "POINT", "sfg")), structure(c(1610618.85711065, 
834001.601766967), class = c("XY", "POINT", "sfg")), structure(c(1566028.408, 
769176.095699999), class = c("XY", "POINT", "sfg")), structure(c(651005.479500001, 
516407.979799999), class = c("XY", "POINT", "sfg")), structure(c(1960849.6649, 
695124.517400001), class = c("XY", "POINT", "sfg")), structure(c(1629478.9974, 
133719.900100002), class = c("XY", "POINT", "sfg")), structure(c(866660.977081273, 
327406.378158199), class = c("XY", "POINT", "sfg")), structure(c(1888541.8058, 
965703.314599999), class = c("XY", "POINT", "sfg")), structure(c(818778.823500002, 
-284285.364000002), class = c("XY", "POINT", "sfg")), structure(c(1819753.2004, 
576574.899499998), class = c("XY", "POINT", "sfg")), structure(c(1034127.7749, 
-500619.4664), class = c("XY", "POINT", "sfg")), structure(c(1025609.63045605, 
561660.937523897), class = c("XY", "POINT", "sfg")), structure(c(1636066.2798, 
46453.162800001), class = c("XY", "POINT", "sfg")), structure(c(998866.904199997, 
314104.5522), class = c("XY", "POINT", "sfg")), structure(c(869039.779816974, 
274039.376250103), class = c("XY", "POINT", "sfg")), structure(c(1997476.0478, 
758688.154200002), class = c("XY", "POINT", "sfg")), structure(c(895392.7311, 
286313.070300001), class = c("XY", "POINT", "sfg")), structure(c(1626409.4785, 
115297.873900001), class = c("XY", "POINT", "sfg")), structure(c(861712.417868644, 
236019.781593506), class = c("XY", "POINT", "sfg")), structure(c(1790018.5253, 
1038861.7706), class = c("XY", "POINT", "sfg")), structure(c(2041967.16, 
1032950.1021), class = c("XY", "POINT", "sfg")), structure(c(984555.844500002, 
241438.559699999), class = c("XY", "POINT", "sfg")), structure(c(973641.5209, 
130616.517499998), class = c("XY", "POINT", "sfg")), structure(c(1599820.5337, 
503161.733600002), class = c("XY", "POINT", "sfg")), structure(c(934106.738068492, 
151012.678032866), class = c("XY", "POINT", "sfg")), structure(c(1066256.3405, 
478270.1672), class = c("XY", "POINT", "sfg")), structure(c(998786.0674, 
248416.298899999), class = c("XY", "POINT", "sfg")), structure(c(898954.390099998, 
585362.516200001), class = c("XY", "POINT", "sfg")), structure(c(1089219.3091, 
384944.430199998), class = c("XY", "POINT", "sfg")), structure(c(879570.594300003, 
140318.559200001), class = c("XY", "POINT", "sfg")), structure(c(1967917.7789, 
734179.189899999), class = c("XY", "POINT", "sfg")), structure(c(1163775.6374, 
-437352.831), class = c("XY", "POINT", "sfg")), structure(c(804352.802499998, 
325736.7382), class = c("XY", "POINT", "sfg")), structure(c(1803875.4943, 
569225.790599999), class = c("XY", "POINT", "sfg")), structure(c(1128963.9914, 
-744183.866400001), class = c("XY", "POINT", "sfg")), structure(c(1770957.5691, 
805746.836800001), class = c("XY", "POINT", "sfg")), structure(c(988506.472554391, 
-306585.319089635), class = c("XY", "POINT", "sfg")), structure(c(1623615.0261, 
65123.377399998), class = c("XY", "POINT", "sfg")), structure(c(1813966.00682923, 
747354.132971282), class = c("XY", "POINT", "sfg")), structure(c(1810188.2763, 
599796.673199999), class = c("XY", "POINT", "sfg")), structure(c(1730950.3197, 
481928.7466), class = c("XY", "POINT", "sfg")), structure(c(1677962.4344, 
401142.464600001), class = c("XY", "POINT", "sfg")), structure(c(1499813.8947, 
377704.453299999), class = c("XY", "POINT", "sfg")), structure(c(1018653.1621, 
532501.8235), class = c("XY", "POINT", "sfg")), structure(c(1073041.347, 
-351619.053599999), class = c("XY", "POINT", "sfg")), structure(c(845590.0237, 
268438.064900001), class = c("XY", "POINT", "sfg")), structure(c(1659137.2895, 
636686.545600002), class = c("XY", "POINT", "sfg")), structure(c(1112088.3617, 
-363777.257399998), class = c("XY", "POINT", "sfg")), structure(c(1648355.6038, 
817969.682499998), class = c("XY", "POINT", "sfg")), structure(c(1577769.1144, 
29475.7759999994), class = c("XY", "POINT", "sfg")), structure(c(1833188.4238, 
624230.7403), class = c("XY", "POINT", "sfg")), structure(c(1248577.0722, 
-421305.326399999), class = c("XY", "POINT", "sfg")), structure(c(1401770.9769, 
-250586.986099999), class = c("XY", "POINT", "sfg")), structure(c(1138454.93786688, 
-468998.793998615), class = c("XY", "POINT", "sfg")), structure(c(1278419.3896, 
-360659.6984), class = c("XY", "POINT", "sfg")), structure(c(1805730.9206, 
948829.385000001), class = c("XY", "POINT", "sfg")), structure(c(470851.421300002, 
-606116.116699999), class = c("XY", "POINT", "sfg")), structure(c(1645230.84874413, 
530230.950080516), class = c("XY", "POINT", "sfg")), structure(c(1999545.8601, 
700401.906199998), class = c("XY", "POINT", "sfg")), structure(c(1994419.6808, 
881676.706700002), class = c("XY", "POINT", "sfg")), structure(c(2034741.5997, 
996244.286199999), class = c("XY", "POINT", "sfg")), structure(c(942471.565243789, 
141421.790646283), class = c("XY", "POINT", "sfg")), structure(c(1543009.8395, 
213848.643900001), class = c("XY", "POINT", "sfg")), structure(c(1798326.7849, 
868541.1359), class = c("XY", "POINT", "sfg")), structure(c(1782057.5672, 
511232.749300001), class = c("XY", "POINT", "sfg")), structure(c(1885808.6044, 
892449.070900001), class = c("XY", "POINT", "sfg")), structure(c(1073760.3311, 
-383907.573599999), class = c("XY", "POINT", "sfg")), structure(c(993137.776299999, 
-471923.767000002), class = c("XY", "POINT", "sfg")), structure(c(1989063.7363, 
814352.786499998), class = c("XY", "POINT", "sfg")), structure(c(1828529.27269656, 
580189.513793761), class = c("XY", "POINT", "sfg")), structure(c(1100803.69046699, 
507733.762471826), class = c("XY", "POINT", "sfg")), structure(c(1812955.381, 
615110.873300001), class = c("XY", "POINT", "sfg")), structure(c(1024713.23007655, 
388992.310031539), class = c("XY", "POINT", "sfg")), structure(c(1604067.1606, 
369553.743400002), class = c("XY", "POINT", "sfg")), structure(c(911925.112100003, 
149712.111800001), class = c("XY", "POINT", "sfg")), structure(c(1116396.6834, 
-428339.4431), class = c("XY", "POINT", "sfg")), structure(c(1841484.2858, 
985101.774399999), class = c("XY", "POINT", "sfg")), structure(c(1872455.65309627, 
650970.743640346), class = c("XY", "POINT", "sfg")), structure(c(1431706.181, 
734441.091800002), class = c("XY", "POINT", "sfg")), structure(c(1839101.1539, 
656239.636300001), class = c("XY", "POINT", "sfg")), structure(c(612590.528283355, 
-837105.972100253), class = c("XY", "POINT", "sfg")), structure(c(1618102.33490128, 
314462.004229404), class = c("XY", "POINT", "sfg")), structure(c(1726754.4763, 
100139.048), class = c("XY", "POINT", "sfg")), structure(c(1780180.6206, 
478468.505999999), class = c("XY", "POINT", "sfg")), structure(c(1228225.1302, 
-367002.7696), class = c("XY", "POINT", "sfg")), structure(c(2217986.8999, 
1142426.3355), class = c("XY", "POINT", "sfg")), structure(c(1151631.7614, 
504259.408000001), class = c("XY", "POINT", "sfg")), structure(c(1716894.2736, 
662331.7544), class = c("XY", "POINT", "sfg")), structure(c(1957983.3795, 
849471.493), class = c("XY", "POINT", "sfg")), structure(c(1746336.26448134, 
1033512.35489174), class = c("XY", "POINT", "sfg")), structure(c(1223274.6366, 
-424578.403699998), class = c("XY", "POINT", "sfg")), structure(c(1820464.5335, 
860400.633200001), class = c("XY", "POINT", "sfg")), structure(c(1555352.8218, 
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774097.181700001), class = c("XY", "POINT", "sfg")), structure(c(1347594.454, 
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420306.6254), class = c("XY", "POINT", "sfg")), structure(c(1611955.8166, 
306115.1928), class = c("XY", "POINT", "sfg")), structure(c(1544309.535, 
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-732425.392000001), class = c("XY", "POINT", "sfg")), structure(c(1917368.1319, 
611474.272399999), class = c("XY", "POINT", "sfg")), structure(c(1879591.0405, 
914739.573199999), class = c("XY", "POINT", "sfg"))), class = c("sfc_POINT", 
"sfc"), precision = 0, bbox = structure(c(xmin = 440431.433800001, 
ymin = -837105.972100253, xmax = 2217986.8999, ymax = 1142426.3355
), class = "bbox"), crs = structure(list(input = NA_character_, 
    wkt = "PROJCS[\"USA_Contiguous_Albers_Equal_Area_Conic\",\n    GEOGCS[\"GCS_North_American_1983\",\n        DATUM[\"North_American_Datum_1983\",\n            SPHEROID[\"GRS_1980\",6378137.0,298.257222101]],\n        PRIMEM[\"Greenwich\",0.0],\n        UNIT[\"Degree\",0.0174532925199433]],\n    PROJECTION[\"Albers_Conic_Equal_Area\"],\n    PARAMETER[\"False_Easting\",0.0],\n    PARAMETER[\"False_Northing\",0.0],\n    PARAMETER[\"longitude_of_center\",-96.0],\n    PARAMETER[\"Standard_Parallel_1\",29.5],\n    PARAMETER[\"Standard_Parallel_2\",45.5],\n    PARAMETER[\"latitude_of_center\",37.5],\n    UNIT[\"Meter\",1.0]]"), class = "crs"), n_empty = 0L), 
    station = 1:301), row.names = c(NA, -301L), class = c("sf", 
"data.frame"), sf_column = "geometry", agr = structure(c(station = NA_integer_), .Label = c("constant", 
"aggregate", "identity"), class = "factor"))

And the other one is a multiline layer representing railroads:

Simple feature collection with 3818 features and 8 fields
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 439362.5 ymin: -837106 xmax: 2223894 ymax: 1144527
CRS:           102003
First 10 features:
       track VxCount Gauge             RRname InOpBy ExactDate FIDAll Edited                       geometry
1  0.0921356       4  51.0  Delaware & Hudson   1830      1829      0      0 LINESTRING (1703095 643192....
2  0.6290380       5  51.0  Delaware & Hudson   1830      1829      1      0 LINESTRING (1703228 643134....
3  0.0368666       2  56.5 Baltimore and Ohio   1830      1830      2      0 LINESTRING (1644112 371237,...
4  0.1132930       2  56.5 Baltimore and Ohio   1830      1830      3      0 LINESTRING (1644112 371237,...
5  0.2250440       4  60.0 Charleston Hamburg   1830      1830     11      0 LINESTRING (1482645 -394401...
6  0.1246240       2  60.0 Charleston Hamburg   1830      1830     12      0 LINESTRING (1482960 -394567...
7  0.9672450       9  60.0 Charleston Hamburg   1830      1830     13      0 LINESTRING (1483158 -394600...
8  1.5411200      12  60.0 Charleston Hamburg   1830      1830     14      0 LINESTRING (1484580 -395087...
9  0.2888170       4  60.0 Charleston Hamburg   1830      1830     15      0 LINESTRING (1486418 -396682...
10 0.0888595       2  60.0 Charleston Hamburg   1830      1830     16      0 LINESTRING (1486523 -397130...

I would like to know how to merge these nodes (train stations) to these edges (railroads) in order to create a network, and then compute all the distance of nodes that are in the same network.

I tried unsuccessfully this (from this answer) but it created more nodes than I want

library(sfnetworks)

network <- railroad_1850 %>% as_sfnetwork()

nodes <- train_station %>% as_sfnetwork()

new_network <- network %>% 
  st_network_blend(., nodes, tolerance = 10) 

Note that my path is not composed of straight lines.

I'm not 100% sure of what your desired output is, but check the following code which might achieve your goal.

First, load packages

library(sf)
#> Linking to GEOS 3.10.2, GDAL 3.4.1, PROJ 7.2.1; sf_use_s2() is TRUE
library(tidygraph)
#> 
#> Attaching package: 'tidygraph'
#> The following object is masked from 'package:stats':
#> 
#>     filter
library(sfnetworks)

Load data

rail <- st_read("railroad_station/rail_data/counties1850_Atack_1850.shp", quiet = TRUE)
station <- st_read("railroad_station/train_station/station_1850.shp", quiet = TRUE)

Convert rail data to sfnetwork class. Are you sure that the segments are defined in the proper order? Is it safe to assume that we need to define a directed network?

rail_sfn <- as_sfnetwork(rail)

Plot

par(mar = rep(0, 4))
plot(rail_sfn, cex = 0.3)
plot(st_geometry(station), add = TRUE, col = sf.colors(301, categorical = TRUE), lwd = 2)

Looking at the plot, I would say that the “station” data represent a subset of the nodes that already belong to the sfn object. Anyway, we can merge the two objects:

joint_sfn <- st_network_blend(rail_sfn, st_geometry(station))
#> Warning: st_network_blend assumes attributes are constant over geometries

and compute distances between all nodes

all_distances <- st_network_cost(joint_sfn)
all_distances[1:5, 1:5]
#> Units: [m]
#>      [,1]     [,2]     [,3] [,4]     [,5]
#> [1,]    0 148.2781 1160.619  Inf      Inf
#> [2,]  Inf   0.0000 1012.341  Inf      Inf
#> [3,]  Inf      Inf    0.000  Inf      Inf
#> [4,]  Inf      Inf      Inf    0 59.33121
#> [5,]  Inf      Inf      Inf  Inf  0.00000

Inf means that it is not possible to reach node i from node j and the Matrix is not symmetric since we created a directed network.

^{Created on 2023-01-13 with reprex v2.0.2}

Edit

The following code can be used to get the matrix of distances across the stations:

station_distances <- st_network_cost(
  x = joint_sfn,
  from = station,
  to = station
)
dim(station_distances)
#> [1] 301 301