Stop, Slow, Go, how stops affect bike travel efficieny
Sophia Wentkowski & Jan Burri
Juli 02, 2023
Juli 02, 2023
1 Introduction
Getting from A to B is a matter we humans have been dealing with since the day of age. From only being able to get around by foot, technological advances have made it possible to move with more sophisticated methods such as cars, trains or planes. However, to this day, non motorized means of transportation remain a part of our life, such as the bicycle. The propulsion of bicycles is generated by the cyclist and hence requires some form of strength and energy from the operator. Jan Burri, one of the authors, cycles to rugby training twice a week and wants to know the most efficient way on how to get to training.
2 Background and Research Questions
According to the TomTom Traffic Index, Zurich City has the most traffic in Switzerland (TomTom Traffic Index, 2022). A survey made by the same navigation system also uncovered that over a quarter of the roads in Switzerland’s primary business conglomeration are experiencing congestion (TomTom Traffic Index, 2023). This is mostly due to junctions with traffic lights according to research by the ETH Zürich (Kelly, 2022). According to the article by SWI in 2011 and the ETH, traffic lights in Zurich have mostly been programmed to prioritize trams for the last 20-30 years and thus slowing down the traffic altogether (Kelly, 2022; swissinfo.ch, 2011). Since then, some traffic signals have become traffic-dependent and adjust their phase timings according to the traffic volume.
In Switzerland, traffic participants like cyclists must follow four traffic signal phases: green, yellow, red, and red-yellow (Ampelphasen: Diese Ampelfarben gibt es, 2023). The phases of the red lights must be at least 2 seconds long (Fueter, 2019). The duration of the yellow phase depends on the maximum permitted speed and is regulated in the administrative regulations for road traffic rules. This can vary from 3-5 seconds (Ampelphasen: Diese Ampelfarben gibt es, 2023). These delays can cost road participants up to 10 seconds per traffic light (Levinson, 2018).
This paper will in the first step give an overview of the used methodology, whereas the code of the different steps will be visible in the different chapters of the paper. The results will show where the cyclist stops and why these halts occur. As a next step, the tracked trajectories will be split into different segments, which can then be cross-checked. This way, one trajectory can be built from the different segments. This will allow us to determine the most efficient trajectory. To finalize the evaluation, the most efficient determined trajectory by the authors will be compared with the trajectory suggested by stplanr to see, whether these are identical.
The following research questions were posed in this project:
How do traffic lights affect the travel efficiency of a cyclist on the route from Seefeld to the Allmend Brunau in Zurich Switzerland?
Is there a combination of sub-trajectories which would have fewer stops and is ultimately the most efficient route?
And the according hypotheses are the following:
Traffic lights decrease the travel efficiency of a cyclist, even if it is the most direct path.
The shortest path in the analysis is similar to the calculated shortest path using stplanr
3 Material and Methods
This paper analyzes primary data collected by Jan Burri in the time period from 01.04.2023 to 31.05.2023 by using the application POSMO project (app version 22.01.16). Only data was considered from the paths between the Allmend Brunau, Zürich, Switzerland (rugby field) and the author’s home (Seefeldstrasse, Zürich Switzerland).
The following libraries were used: igraph, tidyverse, mapview, sf, tmap, raster, terra, leaflet, leaflet.extras, osrm, captioner and stplanr
In instances where the authors were stuck with coding, professors and or ChatGPT were consulted for aid. The code was, however, only interpreted and not copied, and is hence still considered our own work.
3.1 Pre-Processing
Datapoints which were not of the category bike were eliminated. Given there are numerous fields on the Allmend Brunau, a point (LV 95: 2681900, 1245462) which all trajectories have in common was set as an end point. Also, an identical starting point was set for all trajectories (LV 95: 2684685, 1245190).
The allocation of trajectory IDs was conducted by inserting empty rows between trajectories (identified by date and time) if not already done so by Posmo. This was necessary in one instance (2023-04-27 20:42:23).
posmo<-read_csv("posmo.csv") |>
st_as_sf(coords=c("lon_x", "lat_y"), crs=4326, remove=T) |>
st_transform(2056)## Rows: 2445 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): user_id, weekday, place_name, transport_mode
## dbl (2): lon_x, lat_y
## dttm (1): datetime
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.posmo$datetime <- as.POSIXct(posmo$datetime, tz= "UTC")
posmo_coordinates <- st_coordinates(posmo)
posmo <- cbind(posmo, posmo_coordinates)
#cleaning the data
posmo <- posmo[posmo$transport_mode=="Bike",]
#Adding new convenience variables to identify trajectories
posmo <- posmo |>
mutate( traj = ((ifelse(is.na(user_id)== T, "BREAK", "COMBINE")))
)
#currently twice in file, needed to index trajectories
rle_id <- function(vec) {
x <- rle(vec)$lengths
as.factor(rep(seq_along(x), times = x))
}
posmo <- posmo |>
mutate(traj_id = rle_id(traj))#visualizing it
posmo |>
ggplot(aes(X,Y))+
geom_point(aes(color=traj_id))+
facet_wrap(~traj_id)The allocation of trajectory IDs was conducted by inserting empty rows between trajectories (identified by date and time) if not already done so by Posmo. This was necessary in one instance (2023-04-27 20:42:23).Two times two trajectories had to be pasted together which were split up due to a prolonged stop at Coop.
#trajectory 19 seems to have combined two trajectries into one. An NA row is added between the two trajecotries that the rle_id can seperate them.
row_index <- which(posmo$datetime == as.POSIXct("2023-04-27 20:42:23", tz="UTC"))
posmo <- posmo |>
add_row(.after= row_index)
posmo[row_index+1, "traj"] <- "BREAK"
posmo <- posmo |>
mutate(traj_id = rle_id(traj))
#because of a stop at coop, trajectories 13 and 15 were split up. These will be recombined in the trajectory 15
posmo$traj_id <- ifelse(posmo$traj_id == 13, 15,posmo$traj_id)
# the same happend for traj_id 33 and 31. Will be comined in traj_id 31
posmo$traj_id <- ifelse(posmo$traj_id == 33, 31,posmo$traj_id)
#The break "trajectories" are not of interest and will be deleted and the real trajectories renumbered
posmo <- subset(posmo, !grepl("BREAK",traj,ignore.case = T))
posmo <- posmo |>
mutate(traj_id2 = rle_id(traj_id))The different parts of the trajectories were split up by visual analysis of the plot, determining bottlenecks and setting a beginning and end point. In total, there are three sub-trajectories per trajectory.
posmo |>
ggplot(aes(X,Y))+
geom_point(aes(color=traj_id2))+
facet_wrap(~traj_id2)The traffic lights data was provided to us by the ZHAW containing 734 osm ID’s and coordinates and 18 other attributes of traffic lights in Zurich. Only the attributes osm_id and geometry were kept for this analysis. Additionally, the gpkg object of the traffic lights has a CRS of WGS 84 (EPSG:4326), which is a geographic coordinate system using latitude and longitude. The posmo object has a CRS of CH1903+ / LV95 (EPSG:2056), which is a projected coordinate system specific to Switzerland.
To perform spatial operations between these two objects, they need to be in the same CRS. In this case, we can transform the lights object to CH1903+ / LV95 (EPSG:2056) using the st_transform function before using st_within.
#traffic lights sf object
lights <- read_sf("osm_traffic_lights.gpkg")
# traffic lights and the posmo data have to have the same crs
lights <- st_transform(lights, "+proj=longlat +datum=WGS84")
#checking if the CRS has changed
str(lights)## sf [734 × 20] (S3: sf/tbl_df/tbl/data.frame)
## $ full_id : chr [1:734] "n455542" "n455579" "n2114258" "n2114261" ...
## $ osm_id : chr [1:734] "455542" "455579" "2114258" "2114261" ...
## $ osm_type : chr [1:734] "node" "node" "node" "node" ...
## $ highway : chr [1:734] "traffic_signals" "traffic_signals" "traffic_signals" "traffic_signals" ...
## $ direction : chr [1:734] NA NA NA NA ...
## $ demolished:crossing : chr [1:734] NA NA NA NA ...
## $ traffic_signals : chr [1:734] NA NA NA NA ...
## $ check_date:tactile_paving: chr [1:734] NA NA NA NA ...
## $ crossing:island : chr [1:734] NA NA NA NA ...
## $ red_turn:right:bicycle : chr [1:734] NA NA NA NA ...
## $ crossing:markings : chr [1:734] NA NA "zebra" "zebra" ...
## $ traffic_signals:vibration: chr [1:734] NA "yes" "yes" "yes" ...
## $ traffic_signals:sound : chr [1:734] NA "no" "yes" "no" ...
## $ button_operated : chr [1:734] NA "no" NA "no" ...
## $ bicycle : chr [1:734] NA "yes" NA NA ...
## $ traffic_signals:direction: chr [1:734] "forward" "forward" "forward" "forward" ...
## $ tactile_paving : chr [1:734] "no" "yes" "no" "yes" ...
## $ crossing_ref : chr [1:734] "zebra" "zebra" "zebra" "zebra" ...
## $ crossing : chr [1:734] "traffic_signals" "traffic_signals" "traffic_signals" "traffic_signals" ...
## $ geom :sfc_POINT of length 734; first list element: 'XY' num [1:2] 8.52 47.38
## - attr(*, "sf_column")= chr "geom"
## - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
## ..- attr(*, "names")= chr [1:19] "full_id" "osm_id" "osm_type" "highway" ...#then keep only the columns of osm_id and geom, to facilitate the analysis
lights_clean <- lights[c("osm_id", "geom")]3.2 Definition efficiency and segmentation
The definition of efficiency for this paper is defined by two components:
Least amount of stops
Shortest distance travelled
The segmentation between static and non-static was done by calculating the step length using the methods of Laube & Purves (2011). The segmentation between static and non-static was done by calculating the step length using the methods of Laube & Purves (2011).
The splitting up of groups was conducted by conducting a visual analysis of the trajectories and knowledge of the route. The trajectories were split up according to the following coordinates (Swiss CH1903+ / LV95):
Part A: X <= 2682400; Y > 1245454.8177882368
Part B: X > 2682400); X <= 2683450
Part C: X > 2683450
4 Results
4.1 Segmentation of trajectories and static point analysis
Using the segmentation method, we find that there are 1168 moving points, 937 static points and 68 unclassifiable ones. Resulting in a total of 152 moving segments, 161 static segments, and 68 unclassifiable ones.
posmo_filter <- dplyr::select(posmo,datetime, X, Y, traj_id2)
posmo_filter <- posmo_filter |>
rename(traj_id = traj_id2 )
#ggplot(posmo_filter, aes(X,Y, color=datetime))+
# geom_point()
#segmentation
posmo_filter <- posmo_filter |>
mutate(steplength = sqrt((lead(X)-X)^2 +(lead(Y)-Y)^2))
posmo_filter <-posmo_filter |>
group_by(traj_id) |>
mutate(
n_plus1 = sqrt((lead(X,1)-X)^2 +(lead(Y,1)-Y)^2),
n_plus2 = sqrt((lead(X,2)-X)^2 +(lead(Y,2)-Y)^2),
n_minus1 = sqrt((lag(X,1)-X)^2 +(lag(Y,1)-Y)^2),
n_minus2 = sqrt((lag(X,2)-X)^2 +(lag(Y,2)-Y)^2)
)
#Static and moving
posmo_filter <- posmo_filter |>
rowwise() |>
mutate(
stepMean =mean(c(n_minus1, n_minus2, n_plus1, n_plus2))
) |>
ungroup()
posmo_filter <- posmo_filter |>
group_by(traj_id) |>
mutate(
traj_mean = mean(stepMean, na.rm = TRUE),
static = stepMean < traj_mean
)
#posmo_static <- posmo_filter |>
#ungroup() |>
#mutate(static = stepMean < mean(stepMean, na.rm = TRUE))
posmo_static <- posmo_filter |>
filter(static)
#indexing the trajectories
posmo_filter <- posmo_filter |>
mutate(segment_id = rle_id(static))
posmo_filter |>
group_by(static, traj_id) |>
summarize(count = length(unique(segment_id))) |>
group_by(static) |>
summarize(total = sum(count))## `summarise()` has grouped output by 'static'. You can override using the
## `.groups` argument.## Simple feature collection with 3 features and 2 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: 2681758 ymin: 1245168 xmax: 2684704 ymax: 1247108
## Projected CRS: CH1903+ / LV95
## # A tibble: 3 × 3
## static total geometry
## <lgl> <int> <MULTIPOINT [m]>
## 1 FALSE 152 ((2681803 1245662), (2681818 1245863), (2681829 1245771), (26818…
## 2 TRUE 161 ((2681758 1245742), (2681764 1245725), (2681768 1245765), (26817…
## 3 NA 68 ((2681817 1245527), (2681823 1245529), (2681825 1245581), (26818…The resulting static and moving points were visualized in the plot below.
#visualizing segment trajectories
posmo_filter |>
mutate(static =stepMean < mean(stepMean, na.rm =TRUE)) |>
ggplot(aes(X,Y))+
geom_path()+
geom_point(aes(color=static))+
coord_fixed()
Figure 0: Visualization of the static and moving points using the segmentation method by Laube & Purves 2011
4.2 Differentiation into sub-trajectories
Looking at the plot below, we can see two obvious bottlenecks. These were used as a segmentation to determine the most efficient sub trajectories. All three Parts (A, B, and C) consist of 17 trajectories. Many of these trajectories are, however, similar to one another. Grouping the trajectories with overlays of over 85%, resulted in 3, 6, and 4 groups for Parts A, B, and C respectively. Looking at the Table below, we can see the number of trajectories per group. The most commonly used path is the group 2 in Part A, group 3 in Part B, and group 1 in group C. Out of the three groups, B is the most evenly distributed.
| Group_ID | Part A | Part B | Part C |
|---|---|---|---|
| 1 | 1 | 4 | 12 |
| 2 | 13 | 1 | 1 |
| 3 | 3 | 5 | 3 |
| 4 | NA | 4 | 1 |
| 5 | NA | 2 | NA |
| 6 | NA | 1 | NA |
Table 1: Number of similar sub-trajectories per group ID
mapview(posmo_filter, zcol = "traj_id", col.regions = rainbow(length(unique(posmo_filter$traj_id))))Figure 1: All data points of the trajectories recorded
#Adding a starting and finish point to each Traj Id
posmo_filter <- posmo_filter |>
dplyr::select(datetime,X,Y,traj_id,geometry,segment_id,static)
n_traj <- length(unique(posmo_filter$traj_id))
start_end <- data.frame(traj_id = 1:n_traj,
X = rep(2681900, n_traj),
Y = rep(1245462, n_traj),
static = F,
datetime = NA,
segment_id= NA)
start_end <-bind_rows(start_end, data.frame(traj_id = 1:n_traj,
X = rep(2684685, n_traj),
Y = rep(1245190, n_traj),
static = F,
datetime = NA,
segment_id= NA))
start_end$traj_id <- as.factor(start_end$traj_id)
start_end <- st_as_sf(start_end, coords = c("X", "Y"), crs = 2056, remove = F)
head(posmo_filter)## Simple feature collection with 6 features and 6 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 2684550 ymin: 1245180 xmax: 2684681 ymax: 1245252
## Projected CRS: CH1903+ / LV95
## # A tibble: 6 × 7
## # Groups: traj_id [1]
## datetime X Y traj_id geometry segment_id
## <dttm> <dbl> <dbl> <fct> <POINT [m]> <fct>
## 1 2023-04-11 16:07:15 2.68e6 1.25e6 1 (2684681 1245185) 1
## 2 2023-04-11 16:07:27 2.68e6 1.25e6 1 (2684656 1245180) 2
## 3 2023-04-11 16:07:37 2.68e6 1.25e6 1 (2684645 1245180) 3
## 4 2023-04-11 16:07:58 2.68e6 1.25e6 1 (2684645 1245209) 3
## 5 2023-04-11 16:08:08 2.68e6 1.25e6 1 (2684590 1245208) 3
## 6 2023-04-11 16:08:21 2.68e6 1.25e6 1 (2684550 1245252) 4
## # ℹ 1 more variable: static <lgl>head(start_end)## Simple feature collection with 6 features and 6 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 2681900 ymin: 1245462 xmax: 2681900 ymax: 1245462
## Projected CRS: CH1903+ / LV95
## traj_id X Y static datetime segment_id geometry
## 1 1 2681900 1245462 FALSE NA NA POINT (2681900 1245462)
## 2 2 2681900 1245462 FALSE NA NA POINT (2681900 1245462)
## 3 3 2681900 1245462 FALSE NA NA POINT (2681900 1245462)
## 4 4 2681900 1245462 FALSE NA NA POINT (2681900 1245462)
## 5 5 2681900 1245462 FALSE NA NA POINT (2681900 1245462)
## 6 6 2681900 1245462 FALSE NA NA POINT (2681900 1245462)posmo_filter <-rbind(posmo_filter, start_end)
#Splitting the trajectory into different parts according to bottlenecks
A_part <- posmo_filter |>
filter(X <= 2682400) |>
filter(Y > 1245454.8177882368)
B_part <- posmo_filter |>
filter(X > 2682400) |>
filter(X <= 2683450)
C_part <- posmo_filter |>
filter(X > 2683450)#Visualizing the different sub-trajectories and checking individual trajectories for anomalies
A_part |>
filter(static ==F) |>
ggplot(aes(X,Y))+
geom_point(aes(color=traj_id))+
facet_wrap(~traj_id)
A_part |>
filter(traj_id==1) |>
mapview()4.2.1 Similarity and grouping of trajectories
We checked for overlaps between the trajectories of part A, part B, and part C. For part A, we grouped the trajectories by traj_id and created a new column do_union with the value FALSE. We then cast the data to LINESTRING geometry. Then, we created a buffer around the part A trajectories using a distance of 50 meters.
We calculated the number of rows in the part A buffer and created an
empty matrix A_mymat with the same number of rows and columns. THrough
each pair of trajectories in part A, we checked for self-intersection
and calculating the intersection area ratio. If the trajectories were
the same, we assigned NA to the matrix; otherwise, we calculated the
intersection area ratio using the
st_area() and
st_intersection() functions.
Using the intersection area ratio matrix, we constructed a graph object traj_group representing the connections between trajectories. We set a threshold of 0.85 for the adjacency matrix to define connections.
We repeated the same steps for part B and part C, calculating overlaps, creating buffers, calculating intersection area ratios, and assigning group IDs..
Finally, we visualized the trajectories of part C by grouping them by
group_id, casting to LINESTRING, and plotting them using the
plot() function.
#Checking for overlaps between the trajectories
A_part_lines <- A_part |>
group_by(traj_id) |>
summarise(do_union = FALSE) |>
st_cast("LINESTRING")
A_part_lines_buff <- A_part_lines |>
st_buffer(50)
A_n_traj <- nrow(A_part_lines_buff)
A_mymat <- matrix(nrow = A_n_traj, ncol = A_n_traj)
for (i in 1:A_n_traj) {
for (j in 1:A_n_traj) {
if (i == j) {
A_mymat[i, j] <- NA
} else {
inter <- st_intersection(A_part_lines_buff[i, ], A_part_lines_buff[j, ])
A_mymat[i, j] <- as.numeric(st_area(inter)) / as.numeric(st_area(A_part_lines_buff[i, ]))
}
}
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## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometriestraj_group <- graph_from_adjacency_matrix(A_mymat> 0.85, mode = "undirected", weighted = TRUE, diag = FALSE)
#plot(traj_group)
group_ids <- clusters(traj_group)$membership
A_part_lines$group_id<-group_ids
A_part <- left_join(A_part,st_drop_geometry(A_part_lines), by="traj_id")
#B_Part
B_part_lines <- B_part |>
group_by(traj_id) |>
summarise(do_union = FALSE) |>
st_cast("LINESTRING")
B_part_lines_buff <- B_part_lines |>
st_buffer(50)
B_n_traj <- nrow(B_part_lines_buff)
B_mymat <- matrix(nrow = B_n_traj, ncol = B_n_traj)
for (i in 1:B_n_traj) {
for (j in 1:B_n_traj) {
if (i == j) {
B_mymat[i, j] <- NA
} else {
inter <- st_intersection(B_part_lines_buff[i, ], B_part_lines_buff[j, ])
B_mymat[i, j] <- as.numeric(st_area(inter)) / as.numeric(st_area(B_part_lines_buff[i, ]))
}
}
}## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometriestraj_group <- graph_from_adjacency_matrix(B_mymat> 0.85, mode = "undirected", weighted = TRUE, diag = FALSE)
#plot(traj_group)
group_ids <- clusters(traj_group)$membership
B_part_lines$group_id<-group_ids
B_part <- left_join(B_part,st_drop_geometry(B_part_lines), by="traj_id")
#C_Part
C_part_lines <- C_part |>
group_by(traj_id) |>
summarise(do_union = FALSE) |>
st_cast("LINESTRING")
C_part_lines_buff <- C_part_lines |>
st_buffer(50)
C_n_traj <- nrow(C_part_lines_buff)
C_mymat <- matrix(nrow = C_n_traj, ncol = C_n_traj)
for (i in 1:C_n_traj) {
for (j in 1:C_n_traj) {
if (i == j) {
C_mymat[i, j] <- NA
} else {
inter <- st_intersection(C_part_lines_buff[i, ], C_part_lines_buff[j, ])
C_mymat[i, j] <- as.numeric(st_area(inter)) / as.numeric(st_area(C_part_lines_buff[i, ]))
}
}
}## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometries
## Warning: attribute variables are assumed to be spatially constant throughout
## all geometriestraj_group <- graph_from_adjacency_matrix(C_mymat> 0.85, mode = "undirected", weighted = TRUE, diag = FALSE)
#plot(traj_group)
group_ids <- clusters(traj_group)$membership
C_part_lines$group_id<-group_ids
C_part <- left_join(C_part,st_drop_geometry(C_part_lines), by="traj_id")
#counting the number of trajectories per group_id
A_part |>
group_by(group_id) |>
summarize(n = n_distinct(traj_id))## Simple feature collection with 3 features and 2 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: 2681758 ymin: 1245462 xmax: 2682397 ymax: 1246518
## Projected CRS: CH1903+ / LV95
## # A tibble: 3 × 3
## group_id n geometry
## <dbl> <int> <MULTIPOINT [m]>
## 1 1 1 ((2681758 1245742), (2681764 1245725), (2681768 1245765), (268…
## 2 2 13 ((2681802 1245688), (2681803 1245662), (2681822 1245749), (268…
## 3 3 3 ((2681858 1245876), (2681860 1245846), (2681862 1245942), (268…B_part |>
group_by(group_id) |>
summarize(n = n_distinct(traj_id))## Simple feature collection with 6 features and 2 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: 2682402 ymin: 1246403 xmax: 2683449 ymax: 1247108
## Projected CRS: CH1903+ / LV95
## # A tibble: 6 × 3
## group_id n geometry
## <dbl> <int> <MULTIPOINT [m]>
## 1 1 4 ((2682402 1246536), (2682404 1246521), (2682424 1246518), (268…
## 2 2 1 ((2682413 1246510), (2682466 1246549), (2682467 1246537), (268…
## 3 3 5 ((2682405 1246521), (2682417 1246520), (2682421 1246531), (268…
## 4 4 4 ((2682414 1246508), (2682429 1246511), (2682441 1246521), (268…
## 5 5 2 ((2682417 1246522), (2682418 1246515), (2682443 1246536), (268…
## 6 6 1 ((2682413 1246512), (2682477 1246549), (2682529 1246592), (268…C_part |>
group_by(group_id) |>
summarize(n = n_distinct(traj_id))## Simple feature collection with 4 features and 2 fields
## Geometry type: MULTIPOINT
## Dimension: XY
## Bounding box: xmin: 2683456 ymin: 1245168 xmax: 2684704 ymax: 1246839
## Projected CRS: CH1903+ / LV95
## # A tibble: 4 × 3
## group_id n geometry
## <dbl> <int> <MULTIPOINT [m]>
## 1 1 12 ((2683456 1246823), (2683461 1246827), (2683467 1246812), (268…
## 2 2 1 ((2683551 1246769), (2683611 1246670), (2683645 1246596), (268…
## 3 3 3 ((2683461 1246812), (2683489 1246816), (2683493 1246810), (268…
## 4 4 1 ((2683473 1246817), (2683501 1246820), (2683522 1246808), (268…B_part |>
filter(traj_id==1) ## Simple feature collection with 23 features and 7 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: 2682402 ymin: 1246405 xmax: 2683444 ymax: 1246817
## Projected CRS: CH1903+ / LV95
## # A tibble: 23 × 8
## # Groups: traj_id [1]
## datetime X Y traj_id geometry
## * <dttm> <dbl> <dbl> <fct> <POINT [m]>
## 1 2023-04-11 16:14:17 2683444. 1246817. 1 (2683444 1246817)
## 2 2023-04-11 16:14:31 2683342. 1246775. 1 (2683342 1246775)
## 3 2023-04-11 16:14:42 2683278. 1246762. 1 (2683278 1246762)
## 4 2023-04-11 16:15:07 2683147. 1246676. 1 (2683147 1246676)
## 5 2023-04-11 16:15:17 2683088. 1246622. 1 (2683088 1246622)
## 6 2023-04-11 16:15:27 2683046. 1246595. 1 (2683046 1246595)
## 7 2023-04-11 16:15:37 2683022. 1246579. 1 (2683022 1246579)
## 8 2023-04-11 16:15:48 2682996. 1246572. 1 (2682996 1246572)
## 9 2023-04-11 16:15:58 2682932. 1246498. 1 (2682932 1246498)
## 10 2023-04-11 16:16:12 2682849. 1246441. 1 (2682849 1246441)
## # ℹ 13 more rows
## # ℹ 3 more variables: segment_id <fct>, static <lgl>, group_id <dbl>#Visualizing it
C_part |>
group_by(group_id) |>
summarise(do_union = FALSE) |>
st_cast("LINESTRING") |>
plot()
C_part |>
group_by(group_id) |>
ggplot(aes(X,Y, color=group_id))+
geom_path()4.2.2 Number of stops per sub-trajectory
In the analysis of sub-trajectories and stops, we started by
examining the number of stops per sub-trajectory. We focused on three
different parts: A, B, and C. For part A, we filtered the data to
include only the rows where the static variable was set to TRUE. Then,
we identified the unique combinations of traj_id and segment_id”and
grouped the data by traj_id. By calculating the count of stops using the
n() function, we obtained the number of
stops per sub-trajectory for part A.
Similarly, we followed the same approach for parts B and C, filtering the data and computing the count of stops for each part. Afterward, we moved on to examining the number of stops per group.
To calculate the mean number of stops per group for part A, we
introduced the “group_id” column to the “A_stop” data frame. Using the
mutate() function and matching the traj_id
values, we assigned the corresponding group ID to each sub-trajectory.
Next, we grouped the data by “group_id” and computed the mean number of
stops per group using the mean() function.
We repeated this process for parts B and C, obtaining the mean number of
stops per group for each part.
To consolidate the information, we created new columns labeled “Part”
in each of the mean stop data frames: “A_stop_mean,” “B_stop_mean,” and
“C_stop_mean.” These columns indicated the respective parts A, B, or C.
Finally, we merged the three mean stop data frames using the
bind_rows() function, resulting in the
stop_mean data frame. The geometry column was dropped using the
st_drop_geometry() function, leaving us
with a comprehensive dataset that captured the mean number of stops per
group across all three parts.
# Want to count the number of stops per part per trajectory
A_stop <- A_part |>
filter(static == T) |>
distinct(traj_id, segment_id) |>
group_by(traj_id) |>
summarize(Stops = n())
B_stop <- B_part |>
filter(static == T) |>
distinct(traj_id, segment_id) |>
group_by(traj_id) |>
summarize(Stops = n())
C_stop <- C_part |>
filter(static == T) |>
distinct(traj_id, segment_id) |>
group_by(traj_id) |>
summarize(Stops = n())
#Now per group
A_stop_mean <- A_stop |>
mutate(group_id = A_part$group_id[match(traj_id, A_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_stops = mean(Stops))
B_stop_mean <- B_stop |>
mutate(group_id = B_part$group_id[match(traj_id, B_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_stops = mean(Stops))
C_stop_mean <- C_stop |>
mutate(group_id = C_part$group_id[match(traj_id, C_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_stops = mean(Stops))
#combination of the three
A_stop_mean<- A_stop_mean |>
mutate(Part= "A")
B_stop_mean<- B_stop_mean |>
mutate(Part= "B")
C_stop_mean<- C_stop_mean |>
mutate(Part= "C")
stop_mean <- bind_rows(A_stop_mean, B_stop_mean, C_stop_mean) |>
st_drop_geometry()4.2.3 Length of the sub-trajectories
In this analysis, our goal was to determine the length of each sub-trajectory, specifically focusing on the moving segments. We followed a series of steps for each part (A, B, and C) to compute the lengths accurately.
First, we filtered the data to include only the rows where the “static” variable was set to “FALSE,” indicating the moving segments. Then, we grouped the data by “traj_id” and calculated the Euclidean distance between consecutive points using their X and Y coordinates. This was done by applying the formula sqrt((lead(X,1)-X)^2 +(lead(Y,1)-Y)^2). By grouping the data again by “traj_id” and summarizing the distances, we obtained the lengths of the sub-trajectories.
Moving on to the mean length calculations per group, we added a
“group_id” column to each length data frame. To do this, we matched the
“traj_id” values with the corresponding group ID from the respective
part (A_part, B_part, or C_part). We then grouped the data by “group_id”
and computed the mean length of the sub-trajectories within each group
using the mean() function.
To combine the results from all three parts, we included a “Part”
column in each mean length data frame: “A_length_mean,” “B_length_mean,”
and “C_length_mean.” This column indicated the respective part (A, B, or
C) for each row. Finally, we merged the three mean length data frames
using the bind_rows() function and removed
the geometry column using the
st_drop_geometry() function. The resulting
data frame, named “Length_mean,” provided the mean length of
sub-trajectories per group across all three parts.
#Want to know the length of each trajectory, we have to recompute this to know only the length of the moving segments
A_length<- A_part |>
filter(static==F) |>
group_by(traj_id) |>
mutate(distance = sqrt((lead(X,1)-X)^2 +(lead(Y,1)-Y)^2))|>
group_by(traj_id) |>
summarize(length = sum(distance, na.rm=T))
B_length<- B_part |>
filter(static==F) |>
group_by(traj_id) |>
mutate(distance = sqrt((lead(X,1)-X)^2 +(lead(Y,1)-Y)^2))|>
group_by(traj_id) |>
summarize(length = sum(distance, na.rm=T))
C_length<- C_part |>
filter(static==F) |>
group_by(traj_id) |>
mutate(distance = sqrt((lead(X,1)-X)^2 +(lead(Y,1)-Y)^2))|>
group_by(traj_id) |>
summarize(length = sum(distance, na.rm=T))
#Now per group
A_length_mean <- A_length |>
mutate(group_id = A_part$group_id[match(traj_id, A_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_length = mean(length))
B_length_mean <- B_length |>
mutate(group_id = B_part$group_id[match(traj_id, B_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_length = mean(length))
C_length_mean <- C_length |>
mutate(group_id = C_part$group_id[match(traj_id, C_part$traj_id)]) |>
group_by(group_id) |>
summarize(mean_length = mean(length))
#combination of the three
A_length_mean<- A_length_mean |>
mutate(Part= "A")
B_length_mean<- B_length_mean |>
mutate(Part= "B")
C_length_mean<- C_length_mean |>
mutate(Part= "C")
Length_mean <- bind_rows(A_length_mean, B_length_mean, C_length_mean) |>
st_drop_geometry()4.3 Assessment of the most efficient route
Looking at the different groups which have been created, we wanted to determine what the average number of stops per group_id is. The segmentation of movement allowed us to compute the length of moving segments and with it the number of stops per sub-trajectory. The analysis resulted in the following different average numbers of stops per group (visualization). One can see, that group C shows the largest variation in the number of stops per group, ranging from three to six stops. Group B shows less of a deviation, however, does have one outlier with only two stops. Group A shows the smallest number of stops, also being the most constant.
stop_mean |>
ggplot(aes(Part,mean_stops))+
geom_boxplot(color = "steelblue", fill = "lightblue", width = 0.5) +
labs( x = "Group", y = "Number of Stops") +
theme_minimal()
Figure 2: Boxplot of number of stops per Part
The mean length per group_id was computed in a similar manner. In the first step, the distances between moving points on a trajectory level were computed and summed. These were afterwards averaged per group. The following graph shows the variation of lengths per the three parts of travel. One can see that Group C is the longest part of the trip averaging 2200 m, having however an outlier at over 3250 m. Part B is the shortest group with an average of 1250 m. Its outlier of 1500 m is shorter than the mean of Part A at 1700 m. Part A does however have a trajectory that is comparably long to the mean of Part B.
Length_mean |>
ggplot(aes(Part,mean_length))+
geom_boxplot(color = "steelblue", fill = "lightblue", width = 0.5) +
labs( x = "Group", y = "Mean Length per Group (in meters)") +
theme_minimal()
Figure 3: Boxplot of length of different trajectories
4.3.1 Linear Normalization and Scoring
Knowing the average length and number of stops per group, a linear normalization was applied to make the figures compatible with one another. Stops being perceived as more tedious by the cyclist, these were multiplied by a factor of 0.6, whereas the length with a factor of 0.4.
A <- left_join(A_length_mean, A_stop_mean, by= "group_id") |>
st_drop_geometry()
B <- left_join(B_length_mean, B_stop_mean, by= "group_id")|>
st_drop_geometry()
C <- left_join(C_length_mean, C_stop_mean, by= "group_id")|>
st_drop_geometry()
#Normalizing (linear) the stops and distances and valuing stops over distance
A <- A |>
mutate(
normalized_stops = (mean_stops - min(mean_stops)) / (max(mean_stops) - min(mean_stops)),
normalized_distance = ((mean_length - min(mean_length)) / (max(mean_length) - min(mean_length))),
score = 0.6 * normalized_stops + 0.4 * normalized_distance
)
B <- B |>
mutate(
normalized_stops = (mean_stops - min(mean_stops)) / (max(mean_stops) - min(mean_stops)),
normalized_distance =((mean_length - min(mean_length)) / (max(mean_length) - min(mean_length))),
score = 0.6 * normalized_stops + 0.4 * normalized_distance
)
C <- C |>
mutate(
normalized_stops = (mean_stops - min(mean_stops)) / (max(mean_stops) - min(mean_stops)),
normalized_distance = ((mean_length - min(mean_length)) / (max(mean_length) - min(mean_length))),
score = 0.6 * normalized_stops + 0.4 * normalized_distance
)
# Assigning the score to the sub-trajectories
A_part <- A |>
dplyr::select(group_id, score) |>
left_join(A_part, A, by= "group_id")
B_part <- B |>
dplyr::select(group_id, score) |>
left_join(B_part, B, by= "group_id")
C_part <- C |>
dplyr::select(group_id, score) |>
left_join(C_part, C, by= "group_id")
# the most efficient trajectory
best_path <- A_part |>
filter(score == min(score))
best_path <- bind_rows(best_path, B_part |>
filter(score == min(score)))
best_path <- bind_rows(best_path, C_part |>
filter(score == min(score)))
best_path <- st_as_sf(best_path, sf_column_name= "geometry")
best_path_trajectory <- best_path |>
group_by(group_id) |>
summarize(geometry = st_combine(geometry)) |>
st_cast("MULTILINESTRING")mapview(best_path_trajectory)Figure 4: The most efficient trajectory according to the weighted normalization.
The results show, that in Part A group 3 showed the most efficient score according to our definition. An average of 2.3 stops proved to be the least amount of stops for this Part of the trip. The trajectory is however 1636m the second longest.Part B proves that group 1 is the obvious choice out of the six groups, containing the smallest number of stops (2) and the shortest distance (1107m).Part C too shows to have a group trajectory in which both have the smallest number of stops (3) and is the shortest in distance (2032m), group_id 2.
The combined trajectory is 4775m long and contains 7.3 stops.
4.4 Intersection of traffic lights during the trip
4.4.1 Buffering and Spatial Join
A buffer was created around the lights_clean object using the
st_buffer function. The buffer distance
was set to 5 meters. The result of the operation was assigned to the
variable lights_buffer. A spatial join was conducted using the
st_join function with the posmo_map and
lights_buffer objects. The join operation was specified as
st_intersects, which returns the intersecting geometries between the two
objects. The result of the join was assigned to the joined_data object.
Next, any NA values in the joined_data object were removed using the
na.omit function. This step eliminated data points that
were not within the buffer. With this step we could see that in total 57
traffic lights intersected 12 trajectories including also non-static
points.
# Creating a buffer around the lights_clean object
lights_buffer <- st_buffer(lights_clean, dist = 5)
#spatial join using st_intersects
posmo_map <- st_transform(posmo_filter, "+proj=longlat +datum=WGS84")
joined_data <- st_join(posmo_map, lights_buffer, join = st_intersects)
#NA values removal of the data points that were not in the buffer
joined_data<- na.omit(joined_data)Because we already established which points are static, the joined dataset was filtered to retain static points. The dataset (See Table 2 below), presented a total of 34 static points in 12 trajectories, which were at a buffered traffic light.
# Filtering the joined data for points with static = TRUE
joined_data <- filter(joined_data, joined_data$static==T)
#keeps only the first (earliest) record within each group
joined_data <- joined_data |>
group_by(traj_id, osm_id) |>
slice_min(datetime, n = 1) |>
ungroup()knitr::kable(joined_data)| datetime | X | Y | traj_id | geometry | segment_id | static | osm_id |
|---|---|---|---|---|---|---|---|
| 2023-04-11 16:17:17 | 2682695 | 1246427 | 1 | POINT (8.533356 47.3635) | 9 | TRUE | 1388680654 |
| 2023-04-11 18:25:02 | 2681822 | 1245749 | 2 | POINT (8.521683 47.35751) | 4 | TRUE | 268119117 |
| 2023-04-13 18:23:44 | 2682722 | 1246413 | 3 | POINT (8.533716 47.36337) | 7 | TRUE | 1388636638 |
| 2023-04-13 18:23:54 | 2682699 | 1246425 | 3 | POINT (8.533414 47.36348) | 7 | TRUE | 1388680654 |
| 2023-04-13 18:27:24 | 2682187 | 1246264 | 3 | POINT (8.52661 47.36209) | 9 | TRUE | 1809767409 |
| 2023-04-13 18:23:05 | 2682833 | 1246414 | 3 | POINT (8.535182 47.36336) | 7 | TRUE | 2844153085 |
| 2023-04-13 18:28:28 | 2681924 | 1246052 | 3 | POINT (8.523086 47.36023) | 11 | TRUE | 7669479373 |
| 2023-04-25 18:41:49 | 2683041 | 1247038 | 7 | POINT (8.538056 47.36895) | 8 | TRUE | 1388659051 |
| 2023-04-25 18:47:14 | 2683837 | 1246352 | 7 | POINT (8.548465 47.36268) | 14 | TRUE | 3960665913 |
| 2023-04-25 18:37:29 | 2682155 | 1246227 | 7 | POINT (8.526179 47.36176) | 4 | TRUE | 5795905670 |
| 2023-04-27 18:20:45 | 2683564 | 1246753 | 8 | POINT (8.544923 47.36633) | 5 | TRUE | 2114258 |
| 2023-05-09 16:43:26 | 2682619 | 1246681 | 10 | POINT (8.532402 47.3658) | 13 | TRUE | 549319417 |
| 2023-05-11 18:21:26 | 2682841 | 1246774 | 12 | POINT (8.535363 47.3666) | 17 | TRUE | 1388636705 |
| 2023-05-11 18:21:56 | 2682769 | 1246882 | 12 | POINT (8.534424 47.36759) | 19 | TRUE | 1388636728 |
| 2023-05-11 20:20:05 | 2682953 | 1246530 | 13 | POINT (8.536796 47.36439) | 16 | TRUE | 1811282788 |
| 2023-05-11 20:22:50 | 2683624 | 1246618 | 13 | POINT (8.545698 47.3651) | 18 | TRUE | 94580802 |
| 2023-05-23 16:30:04 | 2682777 | 1246756 | 14 | POINT (8.534507 47.36645) | 12 | TRUE | 1388636700 |
| 2023-05-23 16:26:57 | 2683566 | 1246748 | 14 | POINT (8.544956 47.36628) | 8 | TRUE | 2114258 |
| 2023-05-23 16:25:12 | 2683834 | 1246359 | 14 | POINT (8.548431 47.36275) | 4 | TRUE | 3960665913 |
| 2023-05-23 18:38:48 | 2683038 | 1247039 | 15 | POINT (8.53802 47.36896) | 14 | TRUE | 1388659051 |
| 2023-05-23 18:42:12 | 2683572 | 1246756 | 15 | POINT (8.545028 47.36635) | 20 | TRUE | 300390846 |
| 2023-05-25 17:26:54 | 2683570 | 1246751 | 16 | POINT (8.545001 47.3663) | 11 | TRUE | 2114258 |
| 2023-05-25 17:26:44 | 2683570 | 1246757 | 16 | POINT (8.545009 47.36635) | 11 | TRUE | 300390846 |
| 2023-05-25 17:25:14 | 2683841 | 1246368 | 16 | POINT (8.548519 47.36282) | 9 | TRUE | 3960665911 |
| 2023-05-25 17:30:34 | 2682617 | 1246673 | 16 | POINT (8.532373 47.36572) | 17 | TRUE | 549319417 |
| 2023-05-25 20:17:39 | 2682601 | 1246670 | 17 | POINT (8.532161 47.3657) | 11 | TRUE | 3237857062 |
| 2023-05-25 20:20:10 | 2683137 | 1246909 | 17 | POINT (8.539297 47.36778) | 17 | TRUE | 3961895975 |
| 2023-05-25 20:20:04 | 2683122 | 1246918 | 17 | POINT (8.539105 47.36786) | 17 | TRUE | 3961895978 |
Table 2: Output of the traffic lights that affected the travel efficiency on different trajectories
To visualize the affected trajectories, and the points belonging to
the selected trajectories we grouped them by trajectory ID. These points
were then combined into a single LineString representation for each
trajectory using the summarize and
st_combine functions. The dataset,
Trajectories_with_stops, consisted of the combined LineString geometries
representing the affected trajectories. The interactive map using
mapview is shown below.
# Group points by trajectory ID and combine them into a single LineString for each trajectory that was affected by the stop.
posmo_map <- na.omit(posmo_map)
selected_trajectories <- c(1, 2, 3, 7,8,10,12, 13,14, 15,16,17)
Trajectories_with_stops <- posmo_map |>
filter(traj_id %in% selected_trajectories) |>
group_by(traj_id) |>
summarize(geometry = st_combine(geometry)) |>
st_cast("MULTILINESTRING")
#plot the interactive map with mapview
Traffic_Lights <- joined_data
lights_map <- mapview(Traffic_Lights)
# Create a mapview object for the GPS points
lines_map <- mapview(Trajectories_with_stops)
# Combine the two mapview objects into a single map
combined_map <- lights_map + lines_map# Viewing the combined map
combined_mapFigure 6: Mapview of the trajectories that were affected by traffic lights
4.4.1 Possible traffic lights on the most efficient route
For the three sub-trajectories we performed a spatial join using the
st_intersects function to join the
best_path and lights_buffer datasets. The best_path was transformed to
the WGS84 coordinate system. The resulting dataset, best_path_lights,
was obtained by joining the two datasets based on their spatial
intersection.
To ensure data consistency, we removed any NA values from the
best_path_lights dataset and selected only the osm_id and geom columns
for further analysis.To convert the polygons in the best_path_lights
dataset into points, we used the
st_centroid function. For the
visualization, we utilized the mapview
package to create interactive maps.
#spatial join using st_intersects
best_path<- st_transform(best_path, "+proj=longlat +datum=WGS84")
best_path_lights <- st_join(lights_buffer, best_path, join = st_intersects)
#NA values removal of the data points that were not in the buffer
best_path_lights<- na.omit(best_path_lights)
best_path_lights<- dplyr::select(best_path_lights, osm_id, geom)
#Converting polygons into points
best_path_lights <- st_centroid(best_path_lights)## Warning: st_centroid assumes attributes are constant over geometries#plotting the interactive map with mapview
Traffic_Lights <- mapview(best_path_lights)
Best_path_map <- mapview(best_path_trajectory)
# Combining the two mapview objects into a single map
combined_map_3 <- Traffic_Lights + Best_path_map# Viewing the combined map
combined_map_3Figure 7: Interactive map of the trajectory of the most efficient path and the traffic lights, which could possibly delay the travelling time
The most efficient path of three sub-trajectories intersects 8 traffic lights in total.
4.5 Computation of the shortest path with stplanr
The route() function of the stplanr
package was used to compute the route between paths between the Allmend
Brunau, Zürich, Switzerland (8.5230702, 47.3550564) and Seefeldstrasse(
8.5593665, 47.3526167) using the OSRM back-end as the route calculation
method and setting returnclass to “sf”. The computed route was stored in
the computed_route object. By performing a spatial join between the
lights_buffer and computed_route objects, we identified the traffic
lights along the computed route. We used the
mapview function to create an interactive
map of both objects, resulting in the interactive map below.
# The start and endpoint coordinates
start <- c(8.5593665, 47.3526167)
end <- c(8.5230702, 47.3550564)
#Computing the shortest path
computed_route <- route(from = start, to = end, route_fun = osrmRoute, returnclass = "sf")## Warning: "returnclass" is deprecated.## Most common output is sf# Including the traffic lights
computed_route<- st_transform(computed_route, "+proj=longlat +datum=WGS84")
computed_route_stops <- st_join( lights_buffer,computed_route,join = st_intersects)
computed_route_stops <- na.omit(computed_route_stops)
computed_route_lights <- dplyr::select(computed_route_stops, osm_id, geom)
#Converting polygons into points
computed_route_lights <- st_centroid(computed_route_lights)## Warning: st_centroid assumes attributes are constant over geometries#plotting the interactive map with mapview
computed_lights_map <- mapview(computed_route_lights)
computed_map<- mapview(computed_route)
# Combining the two mapview objects into a single map
combined_map_2 <- computed_map + computed_lights_mapcombined_map_2Figure 8: Interactive map of the computed shortest path and possible traffic lights along the path from the set start and end points
The computed shortest path has a length of 5052 meters and crosses 31 traffic lights.
5 Discussion
5.1 Problems with Map matching
Map matching is not only difficult to conduct, but it can also cause more harm than benefits by positioning points on false roads or other items. Due to this, we refrained from conducting this and kept the points at their position placed by Posmo. The not-classifiable segments can be routed back to the splitting of trajectories of Posmo, which leads to a row containing NAs.
5.2 Missing temporal analysis
In our pre-processing, we decided not to determine the duration of the trajectories as the most efficient path, because they were influenced by the cyclists changing cycling behaviour from going to the training and back. We, therefore, chose not to use this biased data and rather focused on the shortest route and the least amount of stops. In the future, we would consider collecting data, that involves the time duration without these circumstances.
5.3 Assessment of traffic lights
The number of stops (static segments) can partially be accounted for by the traffic lights, although out of 937 static points, only 34 could be determined as stops at traffic lights. As metioned before, the unprecise data points could have influenced the intersection analysis with the traffic lights. In addition, it could also be due to other factors influencing the cyclist like f.e. right-of-way markings. Another factor is that at most junctions’ traffic lights occur as tight clusters and are computed in the buffer. This phenomenon can be observed in trajectory 16 (2023-05-25T17:26) where during this one minute the traffic lights with the osm_id 2114258, 300390846 were considered as the cause of the stop. If we had more precise data, we would consider reducing the buffer size or applying a clustering algorithm to the traffic lights.
In the joined_data table, we can observe, that the trajectory with the most stops is trajectory 3. There were in total 5 stops at a traffic light at different times and coordinates. Unfortunately, trajectory 3 does present a lot of problems with the incorrect GPS coordinates and so the stops should be interpreted with care. In addition, the traffic lights data does contain all the traffic lights within a junction, so some traffic lights could be buffered within the trajectory, even though it was not causing a stop.
In general, we can say, that there were not many static hotspots, where the cyclists stopped the most at traffic lights throughout all trajectories. One of the most stops was at Utoquai, which contains a complex junction. Trajectories 14, 15, 16, and 8 all had a static point at one traffic light (osm_id: 2114258). We can therefore say, that this stop was most likely due to a traffic light.
Altogether we can only guess, that taking the side roads, would lead to fewer stops for the cyclist. For a more precise interpretation, we would have to map and match the trajectories exactly to the streets and then repeat our analysis.
5.4 Comparison with computed path
combined_map_2Figure 9: Interactive map of the computed trajectory of the most efficient path and the traffic lights, which could possibly delay the travelling time
combined_map_3Figure 10: Interactive map of the calculated trajectory of the most efficient path from our data sets and the traffic lights, which could possibly delay the travelling time
In the comparison of the computed shortest path and the three sub-trajectories we determined as the shortest path, the sub-trajectories groups 1 and 3 align almost with the computed path. The sub-trajectory 1 contains many jitters in one part, but as we can make out, the route that the program chose is better through the Alfred-Escher Strasse. The sub-trajectory group 2 aligns in the first part with the computed trajectory and then diverges at the Höschgasse. Although this route presumably doesn’t contain any traffic lights like in the computed route, we can also observe, that they do not match perfectly to the road network. So in this case, the cyclist could still be delayed by traffic lights. By looking at the distance our calculated path is shorter than the computed path. In this case, we would recommend using our calculated route.
5.5 Perception of the cyclist
The computed most efficient trajectory is also perceived as the most efficient one in real life. This is shown by the number of times the trajectory was taken by the cyclist in Part A and Part B. The trajectory in Part A goes along the main road (as all trajectories), followed by a parallel stream where only pedestrians and cyclists are permitted. Hence, no traffic lights are present. Part B shows a lot of movement, especially around the train station Enge. This is due to the many possible and taken trajectories. The data collection interval, however, was not fast enough in locating the cyclist and hence has led to confusions. It was considered by correcting this by using map matching, was however not conducted due to likelihood of the quality of data deteriorating further. Part C is however slightly astonishing, given this route was only taken once. It leads along the main road and does cross several intersections, some of them which also contain traffic lights. Due to the buffer issue with the traffic lights however, these were not caught by the code. The cyclist deems the trajectory along Dufourstrasse more efficient, given it is the same length, however with less lights given the trams and main traffic runs along the Seefeldstrasse.
6 Conclusion
Altogether opting to avoid main roads and choosing alternative routes depending on the daytime, amounts of traffic lights and traffic conditions can potentially turn out to be the most efficient and shortest path. Additionally, using navigation apps or computing systems can provide real-time information on the current traffic conditions, helping to make informed decisions about the most efficient route to take.
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