[10]{.chapter-number}  [Euclidean and routing distances]{.chapter-title}

10 Euclidean and routing distances

We will show how to estimate euclidean distances (as crown flights) using sf package, and the distances using a road network using r5r package (demonstrative).

10.1 Euclidean distances

Taking the survey respondents’ location, we will estimate the distance to the university (IST) using the sf package.

Import survey data frame convert to sf

We will use a survey dataset with 200 observations, with the following variables: ID, Affiliation, Age, Sex, Transport Mode to IST, and latitude and longitude coordinates.

Code

library(dplyr)

SURVEY = read.csv("data/SURVEY.txt", sep = "\t") # tab delimiter
names(SURVEY)

[1] "ID"   "AFF"  "AGE"  "SEX"  "MODE" "lat"  "lon"

As we have the coordinates, we can convert this data frame to a spatial feature, as explained in the Introduction to spatial data section.

Code

library(sf)

SURVEYgeo = st_as_sf(SURVEY, coords = c("lon", "lat"), crs = 4326) # convert to as sf data

Create new point at the university

Using coordinates from Instituto Superior Técnico, we can directly create a simple feature and assign its crs.

Code

UNIVERSITY = data.frame(place = "IST",
                        lon = -9.1397404,
                        lat = 38.7370168) |>  # first a dataframe
  st_as_sf(coords = c("lon", "lat"), # then a spacial feature
           crs = 4326)

Visualize in a map:

Code

library(mapview)
mapview(SURVEYgeo, zcol = "MODE") + mapview(UNIVERSITY, col.region = "red", cex = 12)

Straight lines

First we will create lines connecting the survey locations to the university, using the st_nearest_points() function.

This function finds returns the nearest points between two geometries, and creates a line between them. This can be useful to find the nearest train station to each point, for instance.

As we only have 1 point at UNIVERSITY layer, we will have the same number of lines as number of surveys = 200.

Code

SURVEYeuclidean = st_nearest_points(SURVEYgeo, UNIVERSITY, pairwise = TRUE) |>
  st_as_sf() # this creates lines

mapview(SURVEYeuclidean)

Warning in cbind(`Feature ID` = fid, mat): number of rows of result is not a
multiple of vector length (arg 1)

Note that if we have more than one point in the second layer, the pairwise = TRUE will create a line for each combination of points. Set to FALSE if, for instance, you have the same number of points in both layers and want to create a line between the corresponding points.

Distance

Now we can estimate the distance using the st_length() function.

Code

# compute the line length and add directly in the first survey layer
SURVEYgeo = SURVEYgeo |> 
  mutate(distance = st_length(SURVEYeuclidean))

# remove the units - can be useful
SURVEYgeo$distance = units::drop_units(SURVEYgeo$distance)

We could also estimate the distance using the st_distance() function directly, although we would not get and sf with lines.

Code

SURVEYgeo = SURVEYgeo |> 
  mutate(distance = st_distance(SURVEYgeo, UNIVERSITY)[,1] |>  # in meters
           units::drop_units()) |>  # remove units
  mutate(distance = round(distance)) # round to integer

summary(SURVEYgeo$distance)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    298    1106    2186    2658    3683    8600

SURVEYgeo is still a points’ sf.

10.2 Routing Engines

There are different types of routing engines, regarding the type of network they use, the type of transportation they consider, and the type of data they need. We can have:

Uni-modal vs. Multi-modal
- One mode per trip vs. One trip with multiple legs that can be made with different modes
- Multi-modal routing may require GTFS data (realistic Public Transit)
Output level of the results
- Routes (1 journey = 1 route)
- Legs
- Segments
Routing profiles
- Type of user
- fastest / shortest path
- avoid barriers / tolls, etc

Local vs. Remote (service request - usually web API)
- Speed vs. Quota limits / price
- Hard vs. Easy set up
- Hardware limitations in local routing
- Global coverage in remote routing, with frequent updates

Examples: OSRM, Dodgr, r5r, Googleway, CycleStreets, HERE.

Routing distances with `r5r`

We use the r5r package to estimate the distance using a road network (Pereira et al. 2021).

To properly the setup r5r model for the area you are working on, you need to download the road network data from OpenStreetMap and, if needed, add a GTFS and DEM file, as it will be explained in the next section.

We will use only respondents with a distance to the university less than 2 km.

Code

SURVEYsample = SURVEYgeo |> filter(distance <= 2000)
nrow(SURVEYsample)

[1] 95

We need an id (unique identifier) for each survey location, to be used in the routing functions of r5r.

Code

# create id columns for both datasets
SURVEYsample = SURVEYsample |> 
  mutate(id = c(1:nrow(SURVEYsample))) # from 1 to the number of rows

UNIVERSITY = UNIVERSITY |> 
  mutate(id = 1) # only one row

Distances by car

Estimate the routes with time and distance by car, from survey locations to University.

Code

SURVEYcar = detailed_itineraries(
  r5r_core = r5r_network,
  origins = SURVEYsample,
  destinations = UNIVERSITY,
  mode = "CAR",
  all_to_all = TRUE # if false, only 1-1 would be calculated
)

names(SURVEYcar)

 [1] "from_id"          "from_lat"         "from_lon"         "to_id"           
 [5] "to_lat"           "to_lon"           "option"           "departure_time"  
 [9] "total_duration"   "total_distance"   "segment"          "mode"            
[13] "segment_duration" "wait"             "distance"         "route"           
[17] "geometry"

The detailed_itineraries() function is super detailed!

If we want to know only time and distance, and not the route itself, we can use the travel_time_matrix().

Distances by foot

Repeat the same for WALK¹.

Code

SURVEYwalk = detailed_itineraries(
  r5r_core = r5r_network,
  origins = SURVEYsample,
  destinations = UNIVERSITY,
  mode = "WALK",
  all_to_all = TRUE # if false, only 1-1 would be calculated
)

Distances by PT

For Public Transit (TRANSIT) you may specify the egress mode, the departure time, and the maximum number of transfers.

Code

SURVEYtransit = detailed_itineraries(
  r5r_core = r5r_network,
  origins = SURVEYsample,
  destinations = UNIVERSITY,
  mode = "TRANSIT",
  mode_egress = "WALK",
  max_rides = 1, # The maximum PT rides allowed in the same trip
  departure_datetime =  as.POSIXct("20-09-2023 08:00:00",
                                 format = "%d-%m-%Y %H:%M:%S"),
  all_to_all = TRUE # if false, only 1-1 would be calculated
)

10.3 Compare distances

We can now compare the euclidean and routing distances that we estimated for the survey locations under 2 km.

Code

summary(SURVEYsample$distance) # Euclidean

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    298     790    1046    1112    1470    1963

Code

summary(SURVEYwalk$distance) # Walk

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    569    1090    1465    1505    1925    2710

Code

summary(SURVEYcar$distance) # Car

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    228    1401    1823    1893    2431    3177

What can you understand from this results?

Circuity

Compare 1 single route.

Code

mapview(SURVEYeuclidean[165,], color = "black") + # 1556 meters
  mapview(SURVEYwalk[78,], color = "red") + # 1989 meters
  mapview(SURVEYcar[78,], color = "blue") # 2565 meters

With this we can see the circuity of the routes, a measure of route / transportation efficiency, which is the ratio between the routing distance and the euclidean distance.

The cicuity for car (1.65) is usually higher than for walking (1.28) or biking, for shorter distances.

10.4 Visualize routes

Visualize with transparency of 30%, to get a clue when they overlay.

Code

mapview(SURVEYwalk, alpha = 0.3)

Code

mapview(SURVEYcar, alpha = 0.3, color = "red")

We can also use the overline() function from stplanr package to break up the routes when they overline, and add them up.

Code

# we create a value that we can later sum
# it can be the number of trips represented by this route
SURVEYwalk$trips = 1 # in this case is only one respondent per route

SURVEYwalk_overline = stplanr::overline(
  SURVEYwalk,
  attrib = "trips",
  fun = sum
)

mapview(SURVEYwalk_overline, zcol = "trips", lwd = 3)

With this we can visually inform on how many people travel along a route, from the survey dataset².

For bike you would use BICYCLE.↩︎
Assuming all travel by the shortest path.↩︎

--- number-depth: 2 format: pdf: prefer-html: true --- # Euclidean and routing distances We will show how to estimate euclidean distances (*as crown flights*) using `sf` package, and the distances using a road network using `r5r` package (demonstrative). ## Euclidean distances Taking the survey respondents' location, we will estimate the distance to the university (IST) using the `sf` package. ### Import survey data frame convert to sf We will use a survey dataset with 200 observations, with the following variables: ID, Affiliation, Age, Sex, Transport Mode to IST, and latitude and longitude coordinates. ```{r} #| message: false library(dplyr) SURVEY = read.csv("data/SURVEY.txt", sep = "\t") # tab delimiter names(SURVEY) ``` As we have the coordinates, we can convert this data frame to a spatial feature, as explained in the [Introduction to spatial data](spatial-data.qmd#create-spatial-data-from-coordinates) section. ```{r} #| message: false library(sf) SURVEYgeo = st_as_sf(SURVEY, coords = c("lon", "lat"), crs = 4326) # convert to as sf data ``` ### Create new point at the university Using coordinates from Instituto Superior Técnico, we can directly create a simple feature and assign its crs. ```{r} UNIVERSITY = data.frame(place = "IST", lon = -9.1397404, lat = 38.7370168) |> # first a dataframe st_as_sf(coords = c("lon", "lat"), # then a spacial feature crs = 4326) ``` Visualize in a map: ```{r} #| fig-format: png #| message: false library(mapview) mapview(SURVEYgeo, zcol = "MODE") + mapview(UNIVERSITY, col.region = "red", cex = 12) ``` ### Straight lines First we will create lines connecting the survey locations to the university, using the `st_nearest_points()` function. This function finds returns the nearest points between two geometries, and creates a line between them. This can be useful to find the nearest train station to each point, for instance. As we only have 1 point at UNIVERSITY layer, we will have the same number of lines as number of surveys = `r nrow(SURVEY)`. ```{r} #| fig-format: png SURVEYeuclidean = st_nearest_points(SURVEYgeo, UNIVERSITY, pairwise = TRUE) |> st_as_sf() # this creates lines mapview(SURVEYeuclidean) ``` Note that if we have more than one point in the second layer, the `pairwise = TRUE` will create a line for each combination of points. Set to `FALSE` if, for instance, you have the same number of points in both layers and want to create a line between the corresponding points. ### Distance Now we can estimate the distance using the `st_length()` function. ```{r} #| eval: false # compute the line length and add directly in the first survey layer SURVEYgeo = SURVEYgeo |> mutate(distance = st_length(SURVEYeuclidean)) # remove the units - can be useful SURVEYgeo$distance = units::drop_units(SURVEYgeo$distance) ``` We could also estimate the distance using the `st_distance()` function **directly**, although we would not get and sf with lines. ```{r} SURVEYgeo = SURVEYgeo |> mutate(distance = st_distance(SURVEYgeo, UNIVERSITY)[,1] |> # in meters units::drop_units()) |> # remove units mutate(distance = round(distance)) # round to integer summary(SURVEYgeo$distance) ``` `SURVEYgeo` is still a points' sf. ## Routing Engines There are different types of routing engines, regarding the type of network they use, the type of transportation they consider, and the type of data they need. We can have: - Uni-modal vs. Multi-modal - One mode per trip vs. One trip with multiple legs that can be made with different modes - Multi-modal routing may require GTFS data (realistic Public Transit) - Output level of the results - Routes (1 journey = 1 route) - Legs - Segments - Routing profiles - Type of user - fastest / shortest path - avoid barriers / tolls, etc ![Routing options in [OpenRouteService](https://maps.openrouteservice.org/)](images/clipboard-1370155720.png){fig-align="center"} - Local vs. Remote (service request - usually web API) - Speed vs. Quota limits / price - Hard vs. Easy set up - Hardware limitations in local routing - Global coverage in remote routing, with frequent updates Examples: [OSRM](https://project-osrm.org/), [Dodgr](https://urbananalyst.github.io/dodgr/), [r5r](https://ipeagit.github.io/r5r/), [Googleway](https://symbolixau.github.io/googleway/reference/access_result.html), [CycleStreets](https://m.cyclestreets.net/journey), [HERE](https://munterfi.github.io/hereR/). ### Routing distances with `r5r` We use the `r5r` package to estimate the distance using a road network [@Pereira2021r5r]. ::: {.callout-note appearance="simple"} To properly the setup r5r model for the area you are working on, you need to download the **road network** data from OpenStreetMap and, if needed, add a **GTFS** and **DEM** file, as it will be explained in the [next section](r5r.qmd). ::: ```{r} #| message: false #| warning: false #| include: false options(java.parameters = "-Xmx4G") # allocate memory url = "https://github.com/U-Shift/EITcourse/releases/download/2024.09/network.dat" download.file(url, destfile = "data/network.dat", mode = "wb") library(r5r) r5r_network = setup_r5("data/", overwrite = FALSE) # load existing network ``` We will use only respondents with a distance to the university less than 2 km. ```{r} #| warning: false SURVEYsample = SURVEYgeo |> filter(distance <= 2000) nrow(SURVEYsample) ``` We need an id (unique identifier) for each survey location, to be used in the routing functions of `r5r`. ```{r} # create id columns for both datasets SURVEYsample = SURVEYsample |> mutate(id = c(1:nrow(SURVEYsample))) # from 1 to the number of rows UNIVERSITY = UNIVERSITY |> mutate(id = 1) # only one row ``` #### Distances by car Estimate the routes with time and distance by car, from survey locations to University. ```{r} #| warning: false SURVEYcar = detailed_itineraries( r5r_core = r5r_network, origins = SURVEYsample, destinations = UNIVERSITY, mode = "CAR", all_to_all = TRUE # if false, only 1-1 would be calculated ) names(SURVEYcar) ``` The [`detailed_itineraries()`](https://ipeagit.github.io/r5r/reference/detailed_itineraries.html) function is super detailed! ::: {.callout-note appearance="simple"} If we want to know only time and distance, and **not the route** itself, we can use the [`travel_time_matrix()`](https://ipeagit.github.io/r5r/reference/travel_time_matrix.html). ::: #### Distances by foot Repeat the same for `WALK`[^distances-1]. [^distances-1]: For bike you would use `BICYCLE`. ```{r} #| warning: false #| code-fold: true SURVEYwalk = detailed_itineraries( r5r_core = r5r_network, origins = SURVEYsample, destinations = UNIVERSITY, mode = "WALK", all_to_all = TRUE # if false, only 1-1 would be calculated ) ``` #### Distances by PT For Public Transit (`TRANSIT`) you may specify the egress mode, the departure time, and the maximum number of transfers. ```{r} #| warning: false #| code-fold: true #| eval: false SURVEYtransit = detailed_itineraries( r5r_core = r5r_network, origins = SURVEYsample, destinations = UNIVERSITY, mode = "TRANSIT", mode_egress = "WALK", max_rides = 1, # The maximum PT rides allowed in the same trip departure_datetime = as.POSIXct("20-09-2023 08:00:00", format = "%d-%m-%Y %H:%M:%S"), all_to_all = TRUE # if false, only 1-1 would be calculated ) ``` ## Compare distances We can now compare the euclidean and routing distances that we estimated for the survey locations under 2 km. ```{r} summary(SURVEYsample$distance) # Euclidean summary(SURVEYwalk$distance) # Walk summary(SURVEYcar$distance) # Car ``` > What can you understand from this results? ```{r} #| echo: false distances = data.frame(euclidean = SURVEYsample$distance, walk = SURVEYwalk$distance, car = SURVEYcar$distance) distances = distances |> arrange(euclidean) # Define the number of observations n <- nrow(distances) # Create an empty plot with the appropriate y-axis limits plot(1:n, distances$euclidean, type = "n", ylim = range(distances), xlab = "Observation (sorted by Euclidean distance)", ylab = "Distance [m]", main = "Distances by Euclidean, Walk, and Car") # Add lines for each type of distance lines(1:n, distances$euclidean, lwd = 2) lines(1:n, distances$walk, col = "red", lwd = 2) lines(1:n, distances$car, col = "blue", lwd = 2) # Optional: Add points for better visibility points(1:n, distances$euclidean, pch = 16) points(1:n, distances$walk, col = "red", pch = 16) points(1:n, distances$car, col = "blue", pch = 16) # Add a legend to distinguish the lines legend("topleft", legend = c("Euclidean", "Walk", "Car"), col = c("black", "red", "blue"), lwd = 2, lty = c(1, 2, 3), pch = 16) ``` ### Circuity Compare 1 single route. ```{r} #| fig-format: png #| code-fold: true mapview(SURVEYeuclidean[165,], color = "black") + # 1556 meters mapview(SURVEYwalk[78,], color = "red") + # 1989 meters mapview(SURVEYcar[78,], color = "blue") # 2565 meters ``` With this we can see the **circuity** of the routes, a measure of route / transportation efficiency, which is the ratio between the routing distance and the euclidean distance. The cicuity for car (`r round(2565/1556,2)`) is usually higher than for walking (`r round(1989/1556,2)`) or biking, for shorter distances. ## Visualize routes Visualize with transparency of 30%, to get a clue when they overlay. ```{r} #| fig-format: png mapview(SURVEYwalk, alpha = 0.3) mapview(SURVEYcar, alpha = 0.3, color = "red") ``` We can also use the [`overline()`](https://docs.ropensci.org/stplanr/reference/overline.html) function from `stplanr` package to break up the routes when they *overline*, and add them up. ```{r} #| message: false #| fig-format: png # we create a value that we can later sum # it can be the number of trips represented by this route SURVEYwalk$trips = 1 # in this case is only one respondent per route SURVEYwalk_overline = stplanr::overline( SURVEYwalk, attrib = "trips", fun = sum ) mapview(SURVEYwalk_overline, zcol = "trips", lwd = 3) ``` With this we can visually inform on how many people travel along a route, from the survey dataset[^distances-2]. [^distances-2]: Assuming all travel by the shortest path.

10.1 Euclidean distances

Import survey data frame convert to sf

Create new point at the university

Straight lines

Distance

10.2 Routing Engines

Routing distances with r5r

Distances by car

Distances by foot

Distances by PT

10.3 Compare distances

Circuity

10.4 Visualize routes

Routing distances with `r5r`