sfnetworks: Tidy Geospatial Networks in R

class: center, middle, inverse, title-slide

# <code>sfnetworks</code>: Tidy Geospatial Networks in R
## useR! 2021
### Lucas van der Meer, Lorena Abad, Andrea Gilardi, Robin Lovelace
### 2021-07-06

---

class: center, middle, hide-logo

<STYLE type='text/css' scoped>
PRE.fansi SPAN {padding-top: .25em; padding-bottom: .25em};
</STYLE>

The slides can be found here: https://sfnetworks.github.io/useR2021/slides

The code to create them can be found here: https://github.com/sfnetworks/useR2021

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R

.left[
.pull-left-70[
![](figs/river_network.png)
]
]

.pull-right-30[

Nodes and edges embedded in geographical space

Nodes usually associated with **POINT** geometries

Edges usually associated with **LINESTRING** geometries

The network topology does not contain *all* information of a geospatial network

Both topological *and* spatial information are essential when analyzing them

]

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R

.left[
.pull-left-70[

```r
library(tidyverse)
library(sfnetworks)
roxel %>%
  as_tibble() %>%
  select(name, type)
```

<PRE class="fansi fansi-output"><CODE># A tibble: 851 x 2
 name type 
 &lt;chr&gt; &lt;fct&gt; 
 1 Havixbecker Strasse residential
 2 Pienersallee secondary 
 3 Schulte-Bernd-Strasse residential
 4 NA path 
 5 Welsingheide residential
 6 NA footway 
 7 NA footway 
 8 NA path 
 9 NA track 
10 NA track 
# ... with 841 more rows
</CODE></PRE>
]
]

.pull-right-30[

![:scale 15%](https://raw.githubusercontent.com/tidyverse/tidyverse/master/man/figures/logo.png)

**The tidyverse**

Collection of R packages for data science

Shared design philosophy

Tidy data structures

]

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R

.left[
.pull-left-70[

```r
library(sf)
roxel
```

<PRE class="fansi fansi-output"><CODE>Simple feature collection with 851 features and 2 fields
Geometry type: LINESTRING
Dimension: XY
Bounding box: xmin: 7.522594 ymin: 51.94151 xmax: 7.546705 ymax: 51.9612
Geodetic CRS: WGS 84
# A tibble: 851 x 3
 name type geometry
 * &lt;chr&gt; &lt;fct&gt; &lt;LINESTRING [°]&gt;
 1 Havixbecker ~ residen~ (7.533722 51.95556, 7.533461 51.95576)
 2 Pienersallee seconda~ (7.532442 51.95422, 7.53236 51.95377, 7.532~
 3 Schulte-Bern~ residen~ (7.532709 51.95209, 7.532823 51.95239, 7.53~
 4 NA path (7.540063 51.94468, 7.539696 51.94479, 7.53~
 5 Welsingheide residen~ (7.537673 51.9475, 7.537614 51.94562)
 6 NA footway (7.543791 51.94733, 7.54369 51.94686, 7.543~
 7 NA footway (7.54012 51.94478, 7.539931 51.94514)
 8 NA path (7.53822 51.94546, 7.538131 51.94549, 7.538~
 9 NA track (7.540063 51.94468, 7.540338 51.94468, 7.54~
10 NA track (7.5424 51.94599, 7.54205 51.94629, 7.54196~
# ... with 841 more rows
</CODE></PRE>
]
]

.pull-right-30[

![:scale 15%](https://user-images.githubusercontent.com/520851/34887433-ce1d130e-f7c6-11e7-83fc-d60ad4fae6bd.gif)

**The sf package**

R package for spatial data science

Standardized storage of geographic features (points, lines, polygons)

Geometric operations (intersections, unions, ..)

Compatible with the tidyverse

New specific *verbs* for spatial data

]

---
class: top, center, hide-logo

## Tidy Geospatial Networks in R

.pull-left-30[
.left[

```r
lines = roxel %>%
  st_transform(3035)
  
plot(st_geometry(lines))
```
]
]

.pull-left-70[
<img src="slides_files/figure-html/unnamed-chunk-3-1.png" width="864" />
]

---
class: top, hide-logo

## Tidy Geospatial Networks in R

.pull-left-40[

```r
points = c(st_point(c(4151358, 3208045)),
           st_point(c(4151340, 3207520)), 
           st_point(c(4151756, 3207506)),
           st_point(c(4151774, 3208031)))

polygon = st_multipoint(points) %>%
  st_cast("POLYGON") %>%
  st_sfc(crs = 3035)

plot(polygon)
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-5-1.png" width="864" />
]

---
class: top, hide-logo

## Tidy Geospatial Networks in R

.pull-left-40[

```r
plot(st_geometry(lines))
plot(
 polygon,
 border = "red", 
 lty = 4, lwd = 4, 
 add = TRUE
)
```
]
.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-7-1.png" width="864" />
]

---
class: top, hide-logo

## Tidy Geospatial Networks in R

.pull-left-30[
.left[

```r
lines %>%
  st_filter(
    polygon,
    .pred = st_intersects
  ) %>%
  st_geometry() %>%
  plot()
```
]
]

.pull-left-70[
<img src="slides_files/figure-html/unnamed-chunk-9-1.png" width="864" />
]

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R

.pull-left-70[
.left[

```r
library(tidygraph)
nodes = tibble(name = letters[1:4])
edges = tibble(from = c(1,2,3,4), to = c(2,3,4,1))
tbl_graph(nodes, edges)
```

<PRE class="fansi fansi-output"><CODE># A tbl_graph: 4 nodes and 4 edges
#
# A directed simple graph with 1 component
#
# Node Data: 4 x 1 (active)
 name 
 &lt;chr&gt;
1 a 
2 b 
3 c 
4 d 
#
# Edge Data: 4 x 2
 from to
 &lt;int&gt; &lt;int&gt;
1 1 2
2 2 3
3 3 4
# ... with 1 more row
</CODE></PRE>
]
]

.pull-right-30[

![:scale 15%](https://raw.githubusercontent.com/thomasp85/tidygraph/master/man/figures/logo.png)

**The tidygraph package**

Tidy interface to the **igraph** library for graph analysis

Models a graph as a collection of two tibbles

Graph algorithms (centralities, clustering, shortest paths, ..)

Compatible with the tidyverse

New specific *verbs* for graph structures

]

---
class: top, center, hide-logo

## Tidy Geospatial Networks in R

.pull-left[
.left[

```r
graph = tbl_graph(nodes, edges) %>%
  activate(nodes) %>%
  mutate(degree = centrality_degree()) %>%
  activate(edges) %>%
  mutate(centrality = centrality_edge_betweenness()) %>%
  arrange(centrality)

graph
```
]
]

.pull-right[
.left[
<PRE class="fansi fansi-output"><CODE># A tbl_graph: 4 nodes and 4 edges
#
# A directed simple graph with 1 component
#
# Edge Data: 4 x 3 (active)
 from to centrality
 &lt;int&gt; &lt;int&gt; &lt;dbl&gt;
1 1 2 6
2 2 3 6
3 3 4 6
4 4 1 6
#
# Node Data: 4 x 2
 name degree
 &lt;chr&gt; &lt;dbl&gt;
1 a 1
2 b 1
3 c 1
# ... with 1 more row
</CODE></PRE>
]
]

---
class: top, center, hide-logo

## Tidy Geospatial Networks in R

.pull-left[
.left[

```r
geoms = roxel[1:4, ] %>%
  st_geometry() %>%
  st_transform(3035) %>%
  st_centroid()

nodes = st_sf(name = letters[1:4], geometry = geoms)
edges = tibble(from = c(1,2,3,4), to = c(2,3,4,1))

graph = tbl_graph(nodes, edges)
graph
```
]
]

.pull-right[
.left[
<PRE class="fansi fansi-output"><CODE># A tbl_graph: 4 nodes and 4 edges
#
# A directed simple graph with 1 component
#
# Node Data: 4 x 2 (active)
 name geometry
 &lt;chr&gt; &lt;POINT [m]&gt;
1 a (4151482 3207934)
2 b (4151387 3207724)
3 c (4151415 3207565)
4 d (4151824 3206744)
#
# Edge Data: 4 x 2
 from to
 &lt;int&gt; &lt;int&gt;
1 1 2
2 2 3
3 3 4
# ... with 1 more row
</CODE></PRE>
]
]

---
class: top, center, hide-logo

## Tidy Geospatial Networks in R

.left[

```r
plot(geoms, pch = 20, cex = 4, col = "#ffa500", axes = TRUE)
```

<img src="slides_files/figure-html/unnamed-chunk-16-1.png" width="864" />
]

---
class: top, center, hide-logo

## Tidy Geospatial Networks in R

.left[

```r
plot(graph)
```

<img src="slides_files/figure-html/unnamed-chunk-18-1.png" width="864" />
]

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R?

<center><blockquote class="twitter-tweet">One of the biggest reasons we still have ArcGIS licenses is for Network Analysis (drive times, service areas etc). Does anyone have <a href="https://twitter.com/hashtag/foss4g?src=hash&amp;ref_src=twsrc%5Etfw">#foss4g</a> tools for this they like? Last time we tried pgRouting (yrs ago) it didn&#39;t feel fully formed yet, <a href="https://twitter.com/hashtag/gischat?src=hash&amp;ref_src=twsrc%5Etfw">#gischat</a>&mdash; Zev Ross (@zevross) <a href="https://twitter.com/zevross/status/1089908839816794118?ref_src=twsrc%5Etfw">January 28, 2019</a></blockquote></center> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R!

.pull-left[
![](https://user-images.githubusercontent.com/520851/34887433-ce1d130e-f7c6-11e7-83fc-d60ad4fae6bd.gif)
]

.pull-right[
![:scale 38%](https://raw.githubusercontent.com/thomasp85/tidygraph/master/man/figures/logo.png)
]

.center[
![:scale 20%](https://raw.githubusercontent.com/luukvdmeer/sfnetworks/master/man/figures/logo.png)
]

---
class: center, top, hide-logo

## Tidy Geospatial Networks in R!

**tidygraph:**

>  Relational data cannot in any meaningful way be encoded as a single tidy data frame. On the other hand, both node and edge data by itself fits very well within the tidy concept as each node and edge is, in a sense, a single observation. Thus, a close approximation of tidyness for relational data is two tidy data frames, one describing the node data and one describing the edge data.

**sfnetworks:**

> A close approximation of tidyness for relational geospatial data is two sf objects, one describing the node data and one describing the edge data
  
---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  st_geometry() %>%
  plot()
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-20-1.png" width="864" />
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  as_sfnetwork() %>%
  plot()
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-22-1.png" width="864" />
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel
```
]

.pull-right-60[
<PRE class="fansi fansi-output"><CODE>Simple feature collection with 851 features and 2 fields
Geometry type: LINESTRING
Dimension: XY
Bounding box: xmin: 7.522594 ymin: 51.94151 xmax: 7.546705 ymax: 51.9612
Geodetic CRS: WGS 84
# A tibble: 851 x 3
 name type geometry
 * &lt;chr&gt; &lt;fct&gt; &lt;LINESTRING [°]&gt;
 1 Havixbecker ~ residen~ (7.533722 51.95556, 7.533461 51.95576)
 2 Pienersallee seconda~ (7.532442 51.95422, 7.53236 51.95377, 7.532~
 3 Schulte-Bern~ residen~ (7.532709 51.95209, 7.532823 51.95239, 7.53~
 4 NA path (7.540063 51.94468, 7.539696 51.94479, 7.53~
 5 Welsingheide residen~ (7.537673 51.9475, 7.537614 51.94562)
 6 NA footway (7.543791 51.94733, 7.54369 51.94686, 7.543~
 7 NA footway (7.54012 51.94478, 7.539931 51.94514)
 8 NA path (7.53822 51.94546, 7.538131 51.94549, 7.538~
 9 NA track (7.540063 51.94468, 7.540338 51.94468, 7.54~
10 NA track (7.5424 51.94599, 7.54205 51.94629, 7.54196~
# ... with 841 more rows
</CODE></PRE>
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  as_sfnetwork()
```
]

.pull-right-60[
<PRE class="fansi fansi-output"><CODE># A sfnetwork with 701 nodes and 851 edges
#
# CRS: EPSG:4326 
#
# A directed multigraph with 14 components with spatially explicit edges
#
# Node Data: 701 x 1 (active)
# Geometry type: POINT
# Dimension: XY
# Bounding box: xmin: 7.522622 ymin: 51.94151 xmax: 7.546705 ymax:
# 51.9612
 geometry
 &lt;POINT [°]&gt;
1 (7.533722 51.95556)
2 (7.533461 51.95576)
3 (7.532442 51.95422)
4 (7.53209 51.95328)
5 (7.532709 51.95209)
6 (7.532869 51.95257)
# ... with 695 more rows
#
# Edge Data: 851 x 5
# Geometry type: LINESTRING
# Dimension: XY
# Bounding box: xmin: 7.522594 ymin: 51.94151 xmax: 7.546705 ymax:
# 51.9612
 from to name type geometry
 &lt;int&gt; &lt;int&gt; &lt;chr&gt; &lt;fct&gt; &lt;LINESTRING [°]&gt;
1 1 2 Havixbecke~ reside~ (7.533722 51.95556, 7.533461 51.955~
2 3 4 Pienersall~ second~ (7.532442 51.95422, 7.53236 51.9537~
3 5 6 Schulte-Be~ reside~ (7.532709 51.95209, 7.532823 51.952~
# ... with 848 more rows
</CODE></PRE>
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  as_sfnetwork() %>%
  activate(nodes) %>%
  st_as_sf()
```
]

.pull-right-60[
<PRE class="fansi fansi-output"><CODE>Simple feature collection with 701 features and 0 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 7.522622 ymin: 51.94151 xmax: 7.546705 ymax: 51.9612
Geodetic CRS: WGS 84
# A tibble: 701 x 1
 geometry
 &lt;POINT [°]&gt;
 1 (7.533722 51.95556)
 2 (7.533461 51.95576)
 3 (7.532442 51.95422)
 4 (7.53209 51.95328)
 5 (7.532709 51.95209)
 6 (7.532869 51.95257)
 7 (7.540063 51.94468)
 8 (7.53822 51.94546)
 9 (7.537673 51.9475)
10 (7.537614 51.94562)
# ... with 691 more rows
</CODE></PRE>
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  as_sfnetwork() %>%
  activate(edges) %>%
  st_geometry()
```
]

.pull-right-60[

```
Geometry set for 851 features 
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 7.522594 ymin: 51.94151 xmax: 7.546705 ymax: 51.9612
Geodetic CRS:  WGS 84
First 5 geometries:
```

```
LINESTRING (7.533722 51.95556, 7.533461 51.95576)
```

```
LINESTRING (7.532442 51.95422, 7.53236 51.95377...
```

```
LINESTRING (7.532709 51.95209, 7.532823 51.9523...
```

```
LINESTRING (7.540063 51.94468, 7.539696 51.9447...
```

```
LINESTRING (7.537673 51.9475, 7.537614 51.94562)
```
]

---
class: top, hide-logo

## The sfnetwork class

.pull-left-40[

```r
roxel %>% 
  as_sfnetwork() %>%
  st_transform(3035)
```
]

.pull-right-60[
<PRE class="fansi fansi-output"><CODE># A sfnetwork with 701 nodes and 851 edges
#
# CRS: EPSG:3035 
#
# A directed multigraph with 14 components with spatially explicit edges
#
# Node Data: 701 x 1 (active)
# Geometry type: POINT
# Dimension: XY
# Bounding box: xmin: 4150707 ymin: 3206375 xmax: 4152367 ymax:
# 3208565
 geometry
 &lt;POINT [m]&gt;
1 (4151491 3207923)
2 (4151474 3207946)
3 (4151398 3207777)
4 (4151370 3207673)
5 (4151408 3207539)
6 (4151421 3207592)
# ... with 695 more rows
#
# Edge Data: 851 x 5
# Geometry type: LINESTRING
# Dimension: XY
# Bounding box: xmin: 4150707 ymin: 3206375 xmax: 4152367 ymax:
# 3208565
 from to name type geometry
 &lt;int&gt; &lt;int&gt; &lt;chr&gt; &lt;fct&gt; &lt;LINESTRING [m]&gt;
1 1 2 Havixbecker~ reside~ (4151491 3207923, 4151474 3207946)
2 3 4 Pienersallee second~ (4151398 3207777, 4151390 3207727,~
3 5 6 Schulte-Ber~ reside~ (4151408 3207539, 4151417 3207573,~
# ... with 848 more rows
</CODE></PRE>
]

---
class: top, hide-logo

## Apply sf functions

.pull-left-40[

```r
net = roxel %>% 
  as_sfnetwork() %>%
  st_transform(3035)

plot(net)
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-34-1.png" width="864" />
]

---
class: top, hide-logo

## Apply sf functions

.pull-left-40[

```r
plot(net)

plot(
  polygon, 
  border = "red", 
  lty = 4, 
  lwd = 4, 
  add = TRUE
)
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-36-1.png" width="864" />
]
---
class: top, hide-logo

## Apply sf functions

.pull-left-40[

```r
net %>%
  st_filter(polygon, .pred = st_intersects) %>%
  plot()
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-38-1.png" width="864" />
]

---
class: top, hide-logo

## Apply tidygraph functions

.pull-left-40[

```r
net = as_sfnetwork(roxel) %>%
  activate(nodes) %>%
  mutate(betweenness = centrality_betweenness()) %>%
  activate(edges) %>%
  mutate(length = edge_length())

net
```
]

.pull-right-60[
<PRE class="fansi fansi-output"><CODE># A sfnetwork with 701 nodes and 851 edges
#
# CRS: EPSG:4326 
#
# A directed multigraph with 14 components with spatially explicit edges
#
# Edge Data: 851 x 6 (active)
# Geometry type: LINESTRING
# Dimension: XY
# Bounding box: xmin: 7.522594 ymin: 51.94151 xmax: 7.546705 ymax:
# 51.9612
 from to name type geometry length
 &lt;int&gt; &lt;int&gt; &lt;chr&gt; &lt;fct&gt; &lt;LINESTRING [°]&gt; [m]
1 1 2 Havixbe~ resid~ (7.533722 51.95556, 7.533461 5~ 28.859~
2 3 4 Pieners~ secon~ (7.532442 51.95422, 7.53236 51~ 107.704~
3 5 6 Schulte~ resid~ (7.532709 51.95209, 7.532823 5~ 54.362~
4 7 8 NA path (7.540063 51.94468, 7.539696 5~ 155.230~
5 9 10 Welsing~ resid~ (7.537673 51.9475, 7.537614 51~ 208.663~
6 11 12 NA footw~ (7.543791 51.94733, 7.54369 51~ 63.023~
# ... with 845 more rows
#
# Node Data: 701 x 2
# Geometry type: POINT
# Dimension: XY
# Bounding box: xmin: 7.522622 ymin: 51.94151 xmax: 7.546705 ymax:
# 51.9612
 geometry betweenness
 &lt;POINT [°]&gt; &lt;dbl&gt;
1 (7.533722 51.95556) 12936.
2 (7.533461 51.95576) 11824 
3 (7.532442 51.95422) 11926.
# ... with 698 more rows
</CODE></PRE>
]

---
class: top, hide-logo

## Apply tidygraph functions

.pull-left-40[

```r
ggplot() +
  geom_sf(
    data = st_as_sf(net, "edges"),
    col = "grey50"
  ) +
  geom_sf(
    data = st_as_sf(net, "nodes"),
    aes(size = betweenness)
  ) +
  ggtitle("Betweenness centrality")
```
]

.pull-right-60[
<img src="slides_files/figure-html/unnamed-chunk-42-1.png" width="864" />
]

---
class: center, middle

### What can we do?

#### Network pre-processing and cleaning

---
class: middle

### Network pre-processing and cleaning

#### Initial network

---
class: middle
### Network pre-processing and cleaning

#### Simplifying edges

---
class: middle
### Network pre-processing and cleaning

#### Subdividing edges

---
class: middle
### Network pre-processing and cleaning

#### Removing pseudo-nodes

---
class: middle
### Network pre-processing and cleaning

#### Simplifying intersections

---
class: center, middle

### What can we do?

#### Snapping

---
class: middle

count: false
### Snapping 
 #### Snapping points to their nearest node
<img src="slides_files/figure-html/snap_user_01_output-1.png" width="864" />

---
count: false
### Snapping 
 #### Snapping points to their nearest node
<img src="slides_files/figure-html/snap_user_02_output-1.png" width="864" />

---
count: false
### Snapping 
 #### Snapping points to their nearest node
<img src="slides_files/figure-html/snap_user_03_output-1.png" width="864" />

---
count: false
### Snapping 
 #### Snapping points to their nearest node
<img src="slides_files/figure-html/snap_user_04_output-1.png" width="864" />

---
class: middle

count: false
### Snapping 
 #### Blending points into a network
<img src="slides_files/figure-html/blend_user_01_output-1.png" width="864" />

---
count: false
### Snapping 
 #### Blending points into a network
<img src="slides_files/figure-html/blend_user_02_output-1.png" width="864" />

---
count: false
### Snapping 
 #### Blending points into a network
<img src="slides_files/figure-html/blend_user_03_output-1.png" width="864" />

---
class: center, middle

### What can we do?

#### Routing

---
class: top

count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_01_output-1.png" width="864" />

---
count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_02_output-1.png" width="864" />

---
count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_03_output-1.png" width="864" />

---
count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_04_output-1.png" width="864" />

---
count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_05_output-1.png" width="864" />

---
count: false
### Routing 
 #### Calculating shortest paths
<img src="slides_files/figure-html/plotpath_user_06_output-1.png" width="864" />

---
class: top

### Routing

#### Retrieving an OD cost matrix

```r
st_network_cost(
  net, 
  from = c(p1, p2, p3),
  to = c(p1, p2, p3)
)
```

```
         [,1]     [,2]     [,3]
[1,]    0.000 1614.252 2094.555
[2,] 1614.252    0.000 1315.965
[3,] 2094.555 1315.965    0.000
```

---
class: center, middle

### What more?

#### Much more...!

---
class: center, middle
## Installation

Install from CRAN:

```r
install.packages("sfnetworks")
```

Install the development version from GitHub:

```r
remotes::install_github("luukvdmeer/sfnetworks")
```

---
class: center, middle

### Want more?

See the docs and find more examples [in the package website](https://luukvdmeer.github.io/sfnetworks/index.html)

### Have your own examples or ideas for the package?

Join the [Discussion on GitHub](https://github.com/luukvdmeer/sfnetworks/discussions)

### Found a bug?

Let us know with an [issue here](https://github.com/luukvdmeer/sfnetworks/issues)!

---
class: center, middle

### Thank you!

#### Q&A

.note[
.pull-left-70[
.pull-left[
Project financed by: ![:scale 50%](https://raw.githubusercontent.com/RConsortium/artwork/main/r_consortium/R_Consortium-logo-horizontal-color.png)
]

.pull-right[
Slides powered by [xaringan](https://github.com/yihui/xaringan), [xaringanthemer](https://github.com/gadenbuie/xaringanthemer) and [flipbookr](https://github.com/EvaMaeRey/flipbookr) 
]
]
.pull-right-30[
![:scale 50%](https://www.r-project.org/conferences/useR.png)
]
]