# 5. Spatial morphers

#### 2024-12-06

In some of the previous vignettes they were already mentioned here and there: spatial morpher functions. This vignette describes in more detail what they are and how to use them.

    library(sfnetworks)
    library(sf)
    library(tidygraph)
    library(igraph)

## Morphing and unmorphing

Morphing networks is a functionality that has its roots in `tidygraph`. It allows you to temporarily change the topology of the original network with the `tidygraph::morph()` verb, perform some actions on this “morphed state” of the network using `dplyr` verbs, and finally merge the changes back into the original network with the `tidygraph::unmorph()` verb. How the topology is changed during morphing depends on the used morpher function, which you provide to `tidygraph::morph()`.

You can choose between a wide range of available morpher functions in `tidygraph`. The names of these functions all start with `to_`. The `sfnetworks` package adds a set of dedicated spatial morphers, having names starting with `to_spatial_`. They will be presented later in this vignette. Lets first show a practical example to get a better idea of how morphing can be useful.

In network analysis, community detection algorithms allow you to discover cohesive groups in networks, based on specific network properties. There is a large offer of (wrappers around) such algorithms in `tidygraph`, see here. Most of them are intended for and can only be applied to the nodes. For example, the often used Louvain algorithm, that seeks to optimize modularity of the partition.

But what if we want to detect communities within edges? Then, the `tidygraph::to_linegraph()` morpher comes in handy. It converts a network into its linegraph, where nodes become edges and edges become nodes. That is, we can morph the network into its linegraph, run the community detection algorithm on the nodes of the morphed state, attach to each node information about the group it is assigned to, and automatically merge those changes back into the edges of the original network.

    net = as_sfnetwork(roxel, directed = FALSE) %>%
      st_transform(3035)

    grouped_net = net %>%
      morph(to_linegraph) %>%
      mutate(group = group_louvain()) %>%
      unmorph()

    grouped_net

    #> # A sfnetwork with 701 nodes and 851 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected multigraph with 14 components with spatially explicit edges
    #> #
    #> # Node data: 701 × 1 (active)
    #>            geometry
    #>         <POINT [m]>
    #> 1 (4151491 3207923)
    #> 2 (4151474 3207946)
    #> 3 (4151398 3207777)
    #> 4 (4151370 3207673)
    #> 5 (4151408 3207539)
    #> 6 (4151421 3207592)
    #> # ℹ 695 more rows
    #> #
    #> # Edge data: 851 × 6
    #>    from    to name                  type                          geometry group
    #>   <int> <int> <chr>                 <fct>                 <LINESTRING [m]> <int>
    #> 1     1     2 Havixbecker Strasse   residential (4151491 3207923, 4151474…    17
    #> 2     3     4 Pienersallee          secondary   (4151398 3207777, 4151390…     3
    #> 3     5     6 Schulte-Bernd-Strasse residential (4151408 3207539, 4151417…     3
    #> # ℹ 848 more rows

    # The algorithm detected 34 communities.
    grouped_net %>%
      activate("edges") %>%
      pull(group) %>%
      unique() %>%
      length()
    #> [1] 34

In all grouping functions in `tidygraph`, the group index `1` belongs the largest group, the index `2` to the second largest group, et cetera. Lets plot only the first third of the 34 groups, to keep the plot clear.

    plot(st_geometry(net, "edges"), col = "grey", lwd = 0.5)

    grouped_net %>%
      activate("edges") %>%
      st_as_sf() %>%
      transmute(group = as.factor(group)) %>%
      filter(group %in% c(1:11)) %>%
      plot(lwd = 4, add = TRUE)

Another application of the `tidygraph::to_linegraph()` morpher is to find “cut edges” in the network. These are edges that break the connectivity of a connected component when they are removed. Hence, they have a crucial function in preserving the connectivity of a network.

    new_net = net %>%
      mutate(is_cut = node_is_cut()) %>%
      morph(to_linegraph) %>%
      mutate(is_cut = node_is_cut()) %>%
      unmorph()

    cut_nodes = new_net %>%
      activate("nodes") %>%
      filter(is_cut) %>%
      st_geometry()

    cut_edges = new_net %>%
      activate("edges") %>%
      filter(is_cut) %>%
      st_geometry()

    plot(net, col = "grey", main = "Cut nodes")
    plot(cut_nodes, col = "red", pch = 20, cex = 2, add = TRUE)
    plot(net, col = "grey", main = "Cut edges")
    plot(cut_edges, col = "red", lwd = 4, add = TRUE)

Internally, a morphed state of a network is a list, in which each element is a network on its own. Some morphers create a list with only a single element, like the linegraph example above, while others create a list with multiple elements. For example, the `tidygraph::to_components()` morpher splits the original network into its unconnected components, storing each component as a separate network in the list.

    morphed_net = morph(net, to_components)

    morphed_net

    #> # A sfnetwork temporarily morphed to a components representation
    #> #
    #> # Original graph is an undirected multigraph with 14 components
    #> # consisting of 701 nodes and 851 edges
    #> # with CRS EPSG:3035
    #>

    class(morphed_net)
    #> [1] "morphed_sfnetwork" "morphed_tbl_graph" "list"

    length(morphed_net)
    #> [1] 14

All dplyr verbs for which a tbl_graph method exists can also be applied to a morphed state. Technically, that means that the same operation is applied to each element in the list. In `sfnetworks`, it is also possible to use `sf::st_join()` and `sf::st_filter()` on morphed states of networks.

The mapping back to the original network is stored in .tidygraph_node_index and .tidygraph_edge_index columns, for nodes and edges respectively. These columns contain the indices (i.e. rownumber) of the original nodes and edges. During unmorphing these indices are used to join the changes made in the morphed state back into the original network. A `dplyr::left_join()` semantic is applied here. That means that the network has the same number of nodes and edges after unmorphing as it had before morphing, no matter if either the morpher function or the subsequent operations on the morphed state added or removed any nodes or edges. Whenever an original node or edge index occurs more than once in a morphed state, only the information added to its first instance is merged back into the original network.

## Converting

Morphing is meant to make temporary changes to your network. However, what if you want to make lasting changes? Good news! The same morpher functions that are used for temporary conversions during morphing can be used for lasting conversions when you provide them to the `tidygraph::convert()` verb instead. In that case, the morphed state of the original network will be returned as a new network itself. This is mainly meant for those morpher functions that produce a morphed state with a single element. For example converting the network into its complement, where nodes are connected only if they were not connected in the original graph.

    convert(net, to_complement)

    #> # A sfnetwork with 701 nodes and 244503 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected simple graph with 1 component with spatially implicit edges
    #> #
    #> # Node data: 701 × 2 (active)
    #>            geometry .tidygraph_node_index
    #>         <POINT [m]>                 <int>
    #> 1 (4151491 3207923)                     1
    #> 2 (4151474 3207946)                     2
    #> 3 (4151398 3207777)                     3
    #> 4 (4151370 3207673)                     4
    #> 5 (4151408 3207539)                     5
    #> 6 (4151421 3207592)                     6
    #> # ℹ 695 more rows
    #> #
    #> # Edge data: 244,503 × 2
    #>    from    to
    #>   <int> <int>
    #> 1     1   701
    #> 2     1   700
    #> 3     1   699
    #> # ℹ 244,500 more rows

The internally created .tidygraph_node_index and/or .tidygraph_edge_index columns are present in the network returned by `tidygraph::convert()`. If you rather don’t have that, set `.clean = TRUE`.

Whenever the morphed state consists of multiple elements, only one of them is returned as the new network. By default that is the first one, but you can pick an element yourself by setting the `.select` argument, e.g. `.select = 2`.

## Spatial morphers

A lot of morpher functions are offered by `tidygraph`. See the overview of them here. Most of them should work without problems on sfnetworks, and can be useful for spatial network analysis. On top of that offer, `sfnetworks` adds some additional spatial morphers that fit use-cases for which `tidygraph` does not have an implemented morpher function. See the overview of them here. Below they will all be shortly introduced.

### to_spatial_contracted

The `to_spatial_contracted()` morpher groups nodes based on given grouping variables, and merges each group of nodes into a single, new node. The geometry of this new node will be the centroid of the geometries of all group members. Edges that were incidents to any of the group members are updated such that they are now incident to the new node. Their boundaries are updated accordingly to preserve the valid spatial network structure. The morphed state contains a single sfnetwork.

To create the groups of nodes, the morpher accepts grouping variables as `...` argument. These will be evaluated in the same way as arguments to `dplyr::group_by()`. That means you can group the nodes based on any (combination of) attribute(s). For an example of grouping based on a spatial clustering algorithm, see the Network pre-processing and cleaning vignette.

A point of attention is that contraction introduces new multiple edges and/or loop edges. Multiple edges are introduced by contraction when there are several connections between the same groups of nodes. Loop edges are introduced by contraction when there are connections within a group. Setting `simplify = TRUE` will remove the multiple and loop edges after contraction. However, note that this also removes multiple and loop edges that already existed before contraction.

The `to_spatial_contracted()` morpher gives the options to summarise attributes of nodes in a group. By setting the `summarise_attributes` argument you can specify on a per-attribute basis how the attributes of the new node should be inferred from the attributes of the group members. There are two ways to specify the combination technique for an attribute:

- As a character, referring to the name of a pre-defined combination technique in `igraph`. Examples include `mean`, `sum`, `first` and `last`. See here for an overview of all implemented techniques.
- As a function, taking a vector of attribute values as input and returning a single value. This is helpful when you want to combine attributes in a way that is not pre-defined in `igraph`.

Providing a single character or a single function (e.g. `summarise_attributes = "sum"`) will apply the same technique to each attribute. Instead, you can provide a named list with a different technique for each attribute. This list can also include one unnamed element containing the technique that should be applied to all attributes that were not referenced in any of the other elements.

    new_net = net %>%
      activate("nodes") %>%
      filter(group_components() == 1) %>%
      mutate(foo = sample(c(1:10), graph_order(), replace = TRUE)) %>%
      mutate(bar = sample(c(TRUE, FALSE), graph_order(), replace = TRUE)) %>%
      mutate(louvain = as.factor(group_louvain()))

    contracted_net = convert(
      new_net,
      to_spatial_contracted,
      louvain,
      simplify = TRUE,
      summarise_attributes = list(
        foo = "sum",
        bar = function(x) any(x),
        louvain = "first"
      )
    )

    plot(st_geometry(new_net, "edges"), main = "Grouped nodes")
    plot(st_as_sf(new_net)["louvain"], key.pos = NULL, pch = 20, add = TRUE)
    plot(st_geometry(contracted_net, "edges"), main = "Contracted network")
    plot(
      st_as_sf(contracted_net)["louvain"],
      cex = 2, key.pos = NULL,
      pch = 20, add = TRUE
    )

### to_spatial_directed

The `to_spatial_directed()` morpher turns an undirected network into a directed one based on the direction given by the linestring geometries of the edges. Hence, from the node corresponding to the first point of the linestring, to the node corresponding to the last point of the linestring. This in contradiction to `tidygraph::to_directed()`, which bases the direction on the node indices given in the to and from columns of the edges. In undirected networks the lowest node index is always used as from index, no matter the order of endpoints in the edges’ linestring geometry. Therefore, the from and to node indices of an edge may not always correspond to the first and last endpoint of the linestring geometry, and `to_spatial_directed()` gives different results as `tidygraph::to_directed()`.

    net %>%
      activate("nodes") %>%
      mutate(bc_undir = centrality_betweenness()) %>%
      morph(to_spatial_directed) %>%
      mutate(bc_dir = centrality_betweenness()) %>%
      unmorph() %>%
      mutate(bc_diff = bc_dir - bc_undir) %>%
      arrange(desc(bc_diff))

    #> # A sfnetwork with 701 nodes and 851 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected multigraph with 14 components with spatially explicit edges
    #> #
    #> # Node data: 701 × 4 (active)
    #>            geometry bc_undir bc_dir bc_diff
    #>         <POINT [m]>    <dbl>  <dbl>   <dbl>
    #> 1 (4152048 3207854)    1159. 38279.  37120.
    #> 2 (4152205 3207787)    1259. 38104.  36845.
    #> 3 (4152057 3207685)   15129. 51935.  36806.
    #> 4 (4152035 3207851)    1794. 37512.  35719.
    #> 5 (4152207 3207791)    2453. 37754.  35301.
    #> 6 (4152085 3207577)   17974. 52110.  34136.
    #> # ℹ 695 more rows
    #> #
    #> # Edge data: 851 × 5
    #>    from    to name                  type                                geometry
    #>   <int> <int> <chr>                 <fct>                       <LINESTRING [m]>
    #> 1   166   500 Havixbecker Strasse   residential (4151491 3207923, 4151474 32079…
    #> 2   606   688 Pienersallee          secondary   (4151398 3207777, 4151390 32077…
    #> 3   607   664 Schulte-Bernd-Strasse residential (4151408 3207539, 4151417 32075…
    #> # ℹ 848 more rows

### to_spatial_explicit

If your original network is spatially implicit (i.e. edges do not have a geometry list column), the `to_spatial_explicit()` morpher explicitizes the edges by creating a geometry list column for them. If the edges table can be directly converted to an sf object using `sf::st_as_sf()`, extra arguments can be provided as `...`, which will be forwarded to `sf::st_as_sf()` internally. Otherwise, straight lines will be drawn between the end nodes of each edge. The morphed state contains a single sfnetwork.

    implicit_net = st_set_geometry(activate(net, "edges"), NULL)
    explicit_net = convert(implicit_net, to_spatial_explicit)

    plot(implicit_net, draw_lines = FALSE, main = "Implicit edges")
    plot(explicit_net, main = "Explicit edges")

### to_spatial_neighborhood

The `to_spatial_neighborhood()` morpher limits the original network to those nodes that are part of the neighborhood of a specified origin node. This origin node can be specified by a node index, but also by any geospatial point (as sf or sfc object). Internally, such a point will be snapped to its nearest node before calculating the neighborhood. A neighborhood contains all nodes that can be reached within a certain cost threshold from the origin node. The morphed state contains a single sfnetwork. See the Routing vignette for more details and examples.

    # Define the origin location.
    p = net %>%
      st_geometry() %>%
      st_combine() %>%
      st_centroid()

    # Subset neighborhood.
    neigh_net = net %>%
      activate("edges") %>%
      convert(to_spatial_neighborhood, p, threshold = 500, weights = edge_length())

    plot(net, col = "grey")
    plot(neigh_net, col = "red", add = TRUE)

### to_spatial_shortest_paths

The `to_spatial_shortest_paths()` morpher limits the original network to those nodes and edges that are part of the shortest path between two nodes. Just as with the other shortest path calculation functionalities presented in the Routing vignette, besides node indices or names, any geospatial point (as sf or sfc object) can be provided as from and to node. Internally, such points will be snapped to their nearest node before calculating the shortest path.

The morpher only accepts a single from node. If also a single to node is provided, the morphed state of the network contains a single sfnetwork. However, it is also possible to provide multiple to nodes. Then, the morphed state of the network contains multiple sfnetworks, one for each from-to combination.

    net %>%
      activate("edges") %>%
      convert(
        to_spatial_shortest_paths,
        from = 1, to = 100,
        weights = edge_length()
      )

    #> # A sfnetwork with 26 nodes and 25 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An unrooted tree with spatially explicit edges
    #> #
    #> # Edge data: 25 × 6 (active)
    #>    from    to name         type                   geometry .tidygraph_edge_index
    #>   <int> <int> <chr>        <fct>          <LINESTRING [m]>                 <int>
    #> 1     2     3 Pienersallee seco… (4151398 3207777, 415139…                     2
    #> 2     6     7 Wilhelm-Raa… resi… (4151350 3207279, 415131…                    20
    #> 3     9    11 NA           path  (4151322 3207076, 415132…                    96
    #> 4    11    12 NA           path  (4151324 3207081, 415132…                    97
    #> 5    13    14 Am Meckelba… resi… (4151323 3207085, 415134…                   107
    #> 6     8    10 Pienersallee seco… (4151340 3207612, 415133…                   115
    #> # ℹ 19 more rows
    #> #
    #> # Node data: 26 × 2
    #>            geometry .tidygraph_node_index
    #>         <POINT [m]>                 <int>
    #> 1 (4151491 3207923)                     1
    #> 2 (4151398 3207777)                     3
    #> 3 (4151370 3207673)                     4
    #> # ℹ 23 more rows

    new_net = net %>%
      activate("edges") %>%
      morph(
        to_spatial_shortest_paths,
        from = 1, to = seq(10, 100, 10),
        weights = edge_length()
      ) %>%
      mutate(in_paths = TRUE) %>%
      unmorph()

    new_net %>%
      st_geometry() %>%
      plot(col = "grey", lwd = 2)

    new_net %>%
      filter(in_paths) %>%
      st_geometry() %>%
      plot(col = "red", lwd = 4, add = TRUE)

### to_spatial_simple

The `to_spatial_simple()` morpher removes loop edges from the network and merges multiple edges into one. Loop edges are edges that start and end at the same node. Multiple edges are sets of edges that connect the same pair of nodes. The morphed state contains a single sfnetwork. See the Network pre-processing and cleaning vignette for more details and examples.

In the same way as `to_spatial_contracted()`, the `to_spatial_simple()` morpher gives the option to specify how attributes from merged edges should be inferred from the attributes of the set members. The geometry of a merged edge however is always equal to the geometry of the first set member.

    # Add a flow attribute to the edges.
    # When merging multiple edges, we want the flow of the new edge to be:
    # --> The sum of the flows of the merged edges.
    new_net = net %>%
      activate("edges") %>%
      mutate(flow = sample(c(1:100), ecount(net), replace = TRUE))

    # Select a set of multiple edges to inspect before simplifying.
    a_multiple = new_net %>%
      filter(edge_is_multiple()) %>%
      slice(1)

    new_net %>%
      filter(edge_is_between(pull(a_multiple, from), pull(a_multiple, to))) %>%
      st_as_sf()

    #> Simple feature collection with 2 features and 5 fields
    #> Geometry type: LINESTRING
    #> Dimension:     XY
    #> Bounding box:  xmin: 4150715 ymin: 3207067 xmax: 4150752 ymax: 3207108
    #> Projected CRS: ETRS89-extended / LAEA Europe
    #> # A tibble: 2 × 6
    #>    from    to name         type                                   geometry  flow
    #>   <int> <int> <chr>        <fct>                          <LINESTRING [m]> <int>
    #> 1   118   119 NA           service (4150716 3207080, 4150715 3207108, 415…     9
    #> 2   118   119 Pienersallee service      (4150716 3207080, 4150752 3207067)    26

    # Simplify the network.
    # We summarise the flow attribute by taking the sum of the merged edge flows.
    # For all the other attributes we simply take the first value in the set.
    simple_net = new_net %>%
      convert(
        to_spatial_simple,
        summarise_attributes = list(flow = "sum", "first")
      )

    # The multiple edges are merged into one.
    # The flow is summarised by taking the sum of the merged edge flows.
    simple_net %>%
      filter(edge_is_between(pull(a_multiple, from), pull(a_multiple, to))) %>%
      st_as_sf()

    #> Simple feature collection with 1 feature and 6 fields
    #> Geometry type: LINESTRING
    #> Dimension:     XY
    #> Bounding box:  xmin: 4150715 ymin: 3207067 xmax: 4150752 ymax: 3207108
    #> Projected CRS: ETRS89-extended / LAEA Europe
    #> # A tibble: 1 × 7
    #>    from    to name  type                    geometry  flow .tidygraph_edge_index
    #>   <int> <int> <chr> <fct>           <LINESTRING [m]> <dbl> <list>
    #> 1   118   119 NA    servi… (4150716 3207080, 415071…    35 <int [2]>

### to_spatial_smooth

The `to_spatial_smooth()` morpher creates a smoothed version of the original network by iteratively removing pseudo nodes. In the case of directed networks, pseudo nodes are those nodes that have only one incoming and one outgoing edge. In undirected networks, pseudo nodes are those nodes that have two incident edges. Connectivity of the network is preserved by concatenating the incident edges of each removed pseudo node. The morphed state contains a single sfnetwork. See the Network pre-processing and cleaning vignette for more details and examples.

    smoothed_net = convert(net, to_spatial_smooth)

    plot(net, main = "Original network")
    plot(net, col = "red", cex = 0.8, lwd = 0.1, main = "Smoothed network")
    plot(smoothed_net, col = "grey", add = TRUE)

### to_spatial_subdivision

The `to_spatial_subdivision()` morpher creates a subdivision of the original network by subdividing edges at each interior point that is equal to any other interior or boundary point of other edges. Interior points in this sense are those points that are included in a linestring geometry feature but are not endpoints of it, while boundary points are the endpoints of the linestrings. The network is reconstructed after subdivision such that connections are created at the points of subdivision. The morphed state contains a single sfnetwork. See the Network pre-processing and cleaning vignette for more details and examples.

    subdivided_net = convert(net, to_spatial_subdivision)
    #> Warning: to_spatial_subdivision assumes attributes are constant over geometries

    # Original network.
    paste("Number of edges: ", ecount(net))
    #> [1] "Number of edges:  851"
    paste("Number of components: ", count_components(net))
    #> [1] "Number of components:  14"

    # Subdivided network.
    # The whole network is now a single connected component!
    paste("Number of edges: ", ecount(subdivided_net))
    #> [1] "Number of edges:  876"
    paste("Number of components: ", count_components(subdivided_net))
    #> [1] "Number of components:  1"

### to_spatial_subset

The `to_spatial_subset()` morpher takes a subset of the network by applying a spatial filter. A spatial filter is a filter on a geometry list column based on a spatial predicate. The morphed state contains a single sfnetwork. We can use this for example to spatially join information only to a spatial subset of the nodes in the network. A tiny example just to get an idea of how this would work:

    codes = net %>%
      st_make_grid(n = c(2, 2)) %>%
      st_as_sf() %>%
      mutate(post_code = seq(1000, 1000 + n() * 10 - 10, 10))

    points = st_geometry(net, "nodes")[c(2, 3)]

    net %>%
      morph(to_spatial_subset, points, .pred = st_equals) %>%
      st_join(codes, join = st_intersects) %>%
      unmorph()
    #> Subsetting by nodes

    #> # A sfnetwork with 701 nodes and 851 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected multigraph with 14 components with spatially explicit edges
    #> #
    #> # Node data: 701 × 2 (active)
    #>            geometry post_code
    #>         <POINT [m]>     <dbl>
    #> 1 (4151491 3207923)        NA
    #> 2 (4151474 3207946)      1020
    #> 3 (4151398 3207777)      1020
    #> 4 (4151370 3207673)        NA
    #> 5 (4151408 3207539)        NA
    #> 6 (4151421 3207592)        NA
    #> # ℹ 695 more rows
    #> #
    #> # Edge data: 851 × 5
    #>    from    to name                  type                                geometry
    #>   <int> <int> <chr>                 <fct>                       <LINESTRING [m]>
    #> 1     1     2 Havixbecker Strasse   residential (4151491 3207923, 4151474 32079…
    #> 2     3     4 Pienersallee          secondary   (4151398 3207777, 4151390 32077…
    #> 3     5     6 Schulte-Bernd-Strasse residential (4151408 3207539, 4151417 32075…
    #> # ℹ 848 more rows

If you want to apply the spatial filter to the edges instead of the nodes, either activate edges before morphing, or set `subset_by = "edges"`.

For filters on attribute columns, use `tidygraph::to_subgraph()` instead. Again, a tiny fictional example just to get an idea of how this would work:

    net = net %>%
      activate("nodes") %>%
      mutate(building = sample(c(TRUE, FALSE), n(), replace = TRUE))

    net %>%
      morph(to_subgraph, building) %>%
      st_join(codes, join = st_intersects) %>%
      unmorph()

    #> Subsetting by nodes

    #> # A sfnetwork with 701 nodes and 851 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected multigraph with 14 components with spatially explicit edges
    #> #
    #> # Node data: 701 × 3 (active)
    #>            geometry building post_code
    #>         <POINT [m]> <lgl>        <dbl>
    #> 1 (4151491 3207923) TRUE          1020
    #> 2 (4151474 3207946) TRUE          1020
    #> 3 (4151398 3207777) TRUE          1020
    #> 4 (4151370 3207673) FALSE           NA
    #> 5 (4151408 3207539) TRUE          1020
    #> 6 (4151421 3207592) FALSE           NA
    #> # ℹ 695 more rows
    #> #
    #> # Edge data: 851 × 5
    #>    from    to name                  type                                geometry
    #>   <int> <int> <chr>                 <fct>                       <LINESTRING [m]>
    #> 1     1     2 Havixbecker Strasse   residential (4151491 3207923, 4151474 32079…
    #> 2     3     4 Pienersallee          secondary   (4151398 3207777, 4151390 32077…
    #> 3     5     6 Schulte-Bernd-Strasse residential (4151408 3207539, 4151417 32075…
    #> # ℹ 848 more rows

### to_spatial_transformed

The `to_spatial_transformed()` morpher temporarily transforms the network into a different coordinate reference system. An example of a situation in which this can be helpful, is the usage of the spatial edge measure function `edge_azimuth()`. This function calculates the azimuth (or bearing) of edge linestrings, but requires a geographic CRS for that.

    # Azimuth calculation fails with our projected CRS.
    # The function complains the coordinates are not longitude/latitude.
    net %>%
      activate("edges") %>%
      mutate(azimuth = edge_azimuth())

    #> Error in `stopifnot()`:
    #> ℹ In argument: `azimuth = edge_azimuth()`.
    #> Caused by error in `st_geod_azimuth()`:
    #> ! st_is_longlat(x) is not TRUE

    # We make it work by temporarily transforming to a different CRS.
    net %>%
      activate("edges") %>%
      morph(to_spatial_transformed, 4326) %>%
      mutate(azimuth = edge_azimuth()) %>%
      unmorph()

    #> # A sfnetwork with 701 nodes and 851 edges
    #> #
    #> # CRS:  EPSG:3035
    #> #
    #> # An undirected multigraph with 14 components with spatially explicit edges
    #> #
    #> # Edge data: 851 × 6 (active)
    #>    from    to name                  type                        geometry azimuth
    #>   <int> <int> <chr>                 <fct>               <LINESTRING [m]>   [rad]
    #> 1     1     2 Havixbecker Strasse   residenti… (4151491 3207923, 415147…  -0.670
    #> 2     3     4 Pienersallee          secondary  (4151398 3207777, 415139…  -2.91
    #> 3     5     6 Schulte-Bernd-Strasse residenti… (4151408 3207539, 415141…   0.203
    #> 4     7     8 NA                    path       (4151885 3206698, 415186…  -0.968
    #> 5     9    10 Welsingheide          residenti… (4151732 3207017, 415172…  -3.12
    #> 6    11    12 NA                    footway    (4152152 3206984, 415214…  -3.10
    #> # ℹ 845 more rows
    #> #
    #> # Node data: 701 × 2
    #>            geometry building
    #>         <POINT [m]> <lgl>
    #> 1 (4151491 3207923) TRUE
    #> 2 (4151474 3207946) TRUE
    #> 3 (4151398 3207777) TRUE
    #> # ℹ 698 more rows