## Introduction

It’s been a busy 12 months but with the Geocomputation with R book nearing completion^{1}
I’ve finally found some time to update my blog and do a bit of thinking, about the tangled topic of line aggregation.

## Why aggregate lines?

The transport ‘flow’ on any particular segment of the transport networks is the aggregate (sum) of trips that pass through it^{1}.
Finding the flow across a transport network based on input data composed of individual routes, is therefore an aggregation problem.
It requires a more complex solution than that provided by the `aggregate()`

function in the base R^{2} package **stats**, however, because the geometry of the output `LINESTRING`

s will be fundamentally different than the input `LINESTRINGS`

of the routes: a route network is composed of many small way segments, but a route is a single long `LINESTRING`

.

## Aggregating lines with overline() MKI

Creating such a route network, with aggregated values per segment, is the problem that the `overline()`

function in the R package **stplanr** was designed to solve (see a 3.5 yr-old question on gis.stackexchange.com for more context).

The function works well and is the basis of the Route Network layer (MSOA) in the Propensity to Cycle Tool (PCT). In fact it was developed precisely for this purpose, as illustrated in the image below, which shows a common visualization/analysis problem encountered by transport researchers when working with multiple routes: overlapping routes are not easy to identify from non-overlapping routes: notice the red lines in the centre of Leeds in the image look the same as the red lines on the outskirts, despite representing much more movement.

To overcome the problem `overline()`

was born (credit to Barry Rowlingson who wrote the foundations of the function), and it works (on a tiny dataset of 2 lines) as follows:

```
library(stplanr)
sl_sp = routes_fast[2:3, ]
sl_sp@data = data.frame(value = c(2, 5))
plot(sl_sp, lwd = 9, col = "yellow")
rnet_sp = overline(sl_sp, attr = "value")
plot(rnet_sp, add = TRUE, lwd = rnet_sp$value)
```

The utility of such a function is illustrated in the figure below, which shows the original route network layer of the PCT in action over a similar area of Leeds:

This works great and the resulting network is used for strategic network planning: you can download route network data in the ‘Region data’ tab of the PCT^{3}. The route network data for Leeds can, for example, be downloaded as a `.geojson`

file from here.

But there are some issues: the function works on the older `SpatialLinesDataFrame`

class defined in the **sp** package^{4}.
This data class has been superseded by the simpler `sf`

class in the **sf** package, which is faster than **sp** for some (if not many) operations.
Another issue with `overline()`

is that in some cases when 2 lines meet, the resulting aggregated line can be longer than it should be.
So there are performance and functionality issues to address.
Rather than solve them all here, this post sets-out the issue using reproducible code and suggests next steps for a new `overline()`

function (or perhaps just an updated `overline.sf()`

function which currently just wraps `overline.sp()`

).

## Aggregating lines with sf

Rather that starting from scratch and writing a geographic algorithm from the ground-up, we will start by exploring solutions provided by existing packages, notably **sf**, which provides an interface to the `GEOS`

library.

Let’s start simple, with just 2 lines, which have an associated amount of flow (with illustrative values of 2 and 5 in this case):

```
library(stplanr)
sl = routes_fast_sf[2:3, ]
sl$value = c(2, 5)
```

These lines clearly have a decent amount of overlap, which can be extracted using the function `st_intersection()`

:

```
sl_intersection = sf::st_intersection(sl[1, ], sl[2, ])
plot(sl$geometry, lwd = 9, col = sf::sf.colors(2, alpha = 0.5))
plot(sl_intersection, add = TRUE)
```

Furthermore, we can find the aggregated value associated with this new segment as follows:

`sl_intersection$value = sum(sl_intersection$value, sl_intersection$value.1)`

We still do not have a full route network composed of 3 non-overlapping lines, however:
the original lines need to be ‘clipped’ so that they do not overlap with `sl_intersection`

.
This can be done as follows:

```
sl_seg1 = sf::st_difference(sl[1, ], sl_intersection)
sl_seg2 = sf::st_difference(sl[2, ], sl_intersection)
plot(sl$geometry, lwd = 9, col = sf::sf.colors(2, alpha = 0.5))
plot(sl_seg1, add = TRUE)
plot(sl_seg2, add = TRUE)
```

We now have all the geographic components needed for a route network.
The only remaining task is to combine them, using `rbind`

, right?
Not quite: the following command fails:

`rnet = rbind(sl_seg1, sl_seg2, sl_intersection)`

`## Error in rbind.data.frame(...): numbers of columns of arguments do not match`

Lesson: we need to be more careful in isolating the value to aggregate.
We will therefore run the previous stages again, but with `attrib`

set to the attribute we would like to aggregate over (`value`

in this case):

```
attrib = "value"
attrib1 = paste0(attrib, ".1")
sl_intersection = sf::st_intersection(sl[1, attrib], sl[2, attrib])
sl_intersection[[attrib]] = sl_intersection[[attrib]] + sl_intersection[[attrib1]]
sl_intersection[[attrib1]] = NULL
```

That leaves us with a ‘clean’ object that only has a value (7) for the attribute column name we want (`value`

).

On this basis we can proceed to create the other segments, keeping only the column we’re interested in. To save time and typing, we’ll create both segments in a single command:

```
sl_seg = sf::st_difference(sl[attrib], sf::st_geometry(sl_intersection))
rnet = rbind(sl_intersection, sl_seg)
```

It worked! Now we’re in a position to plot the resulting route network, with ‘width’ proportional to the flow along each segment:

`plot(rnet, lwd = rnet$value)`

## A benchmark

To test that the method is fast, or is at least not slower than the original `overline()`

function, at least for this task, we’ll package-up the method in a new function:

```
overline_sf2 = function(sl, attrib) {
attrib = "value"
attrib1 = paste0(attrib, ".1")
sl_intersection = sf::st_intersection(sl[1, attrib], sl[2, attrib])
sl_intersection[[attrib]] = sl_intersection[[attrib]] + sl_intersection[[attrib1]]
sl_intersection[[attrib1]] = NULL
sl_seg = sf::st_difference(sl[attrib], sf::st_geometry(sl_intersection))
rnet = rbind(sl_intersection, sl_seg)
return(rnet)
}
```

If you are new to scripts/algorithms/functions, it may be worth taking a look at the new Algorithms chapter in our near-complete book that teaches a range of geographic methods that use R^{5}.
Now the method has been put in a function, we can compare its performance with the per-existing `overline()`

function for comparison:

```
bench::mark(check = F,
overline.sp = overline(sl_sp, attrib = "value"),
overline.sf = overline(sl, attrib = "value"),
overline_sf2 = overline_sf2(sl, attrib = "value")
)
```

```
## # A tibble: 3 x 10
## expression min mean median max `itr/sec` mem_alloc n_gc n_itr
## <bch:expr> <bch:> <bch:> <bch:> <bch:> <dbl> <bch:byt> <dbl> <int>
## 1 overline.sp 14.7ms 15.9ms 15.1ms 27.7ms 62.8 71.3KB 3 26
## 2 overline.sf 18.3ms 19.3ms 18.6ms 32.8ms 51.9 369.9KB 3 23
## 3 overline_sf2 12.2ms 12.7ms 12.6ms 18.3ms 78.5 125KB 6 32
## # … with 1 more variable: total_time <bch:tm>
```

The results are not Earth-shattering: the new function seems to be around the same speed as the original, if a little faster. This is great news, but remember: the new function only works on 2 lines so is much simpler. More work needed!

## Next steps

The next step is to generalist this method so it works for many (potentially thousands) of lines in a way that scales, something that should help on the visualization side, a topic that attracts much interest (see for example this gis.stackexchange post on the subject and, more broadly, a recent article showing how to make animated maps by Jakub Nowosad).
There is also work to do on performance but, as Donald Knuth said^{6}:

premature optimization is the root of all evil (or at least most of it) in programming

So a more complete `overline.sf()`

function is needed.
That will (hopefully) be the topic of the next blog post.

## References

1. Hollander, Y. *Transport Modelling for a Complete Beginner*. (CTthink!, 2016).

2. R Core Team. *R: A Language and Environment for Statistical Computing*. (R Foundation for Statistical Computing, 2018).

3. Lovelace, R. *et al.* The Propensity to Cycle Tool: An open source online system for sustainable transport planning. *Journal of Transport and Land Use* **10,** (2017).

4. Pebesma, E. Simple Features for R: Standardized Support for Spatial Vector Data. *The R Journal* (2018).

5. Lovelace, R., Nowosad, J. & Muenchow, J. *Geocomputation with R*. (CRC Press, 2019).

6. Knuth, D. E. Computer Programming As an Art. *Commun. ACM* **17,** 667–673 (1974).

Any input on that still welcome - see the contributing section for more.↩