movecost 3.0: a task-based guide

Introduction

This vignette shows the use of the movecost package through a sequence of practical tasks, in the same question-and-answer spirit as the guide that accompanied the 2.x series. In-built datasets are used throughout, so that you can reproduce every example. For full details of each function, its parameters, returned values, and references, see the package help documentation (start at ?movecost).

If you are coming from the 2.x series, two changes shape everything below.

1. Compute the cost surface once, then reuse it. In 2.x each function (movecost(), movecorr(), and so on) rebuilt the movement-cost surface from scratch every time it was called. In 3.0 you build that surface once with mc_surface(), and every analysis function takes it as its first argument and reuses it. Parameters that define the cost of movement (the cost function funct, the connectivity move, the terrain factor N, the body/load/speed parameters W, L, V, the critical slope sl.crit, the cognitive-slope and topographic-distance switches, and any barrier) belong to mc_surface(). Parameters that only affect accumulation, units, or display (the origin, the time unit, the isoline interval) belong to the analysis and plot functions. If you change a cost-defining parameter you rebuild the surface; if you only change the unit or the breaks you do not.

2. Visualise on demand. Every analysis function returns an object that stores its result; nothing is drawn until you call plot() on it. The plot is a ggplot object, so you can restyle it, add layers, and redraw it without re-running the analysis (in 2.x, a new look meant a new computation).

library(movecost)

dtm    <- mc_volc()        # sample DTM (a volcano), a terra SpatRaster
origin <- mc_volc_loc()    # a start location, an sf point
destin <- mc_destin_loc()  # nine destination locations, sf points

Task 1. Given an origin, how do I calculate an accumulated cost surface?

Build the surface once with mc_surface(), then accumulate cost outward from the origin with mc_accum(). Here the cost is walking time (Tobler’s on-path hiking function, funct = "t"), the time unit is minutes, and the isochrone interval is 2 minutes.

surf <- mc_surface(dtm, funct = "t", move = 16)
acc  <- mc_accum(surf, origin = origin, time = "m", breaks = 2)
plot(acc)

The isolines are white by default so that they read against the dark low-cost core; plot(acc, type = "contour") draws the isolines alone.

Task 2. Can I use a terrain factor for a given terrain type?

Yes. The terrain factor N defines the cost of movement, so it is set on mc_surface(); everything else is unchanged. Here N = 1.19 corresponds to loose beach sand.

surf_N <- mc_surface(dtm, funct = "t", move = 16, N = 1.19)
acc_N  <- mc_accum(surf_N, origin = origin, time = "m", breaks = 2)
plot(acc_N)

Task 3. Can cost be expressed as metabolic energy rather than time?

Yes. Many energetic cost functions are implemented. This example uses the Pandolf et al. function with downhill correction (funct = "pcf"), a body weight W of 60 kg and a carried load L of 5 kg. The walking speed V defaults to 1.2 m/s and is treated as uniform across the area.

surf_e <- mc_surface(dtm, funct = "pcf", move = 16, W = 60, L = 5)
acc_e  <- mc_accum(surf_e, origin = origin)
plot(acc_e)

Task 4. Can the walking speed be worked out internally?

Yes. Setting V = 0 makes the function derive the walking speed cell by cell from the Tobler hiking function, so the speed varies with the terrain slope instead of being a single value.

surf_v <- mc_surface(dtm, funct = "pcf", move = 16, W = 60, L = 5, V = 0)
acc_v  <- mc_accum(surf_v, origin = origin)
plot(acc_v)

Task 5. Can the ‘cognitive slope’ be used?

Yes. Setting cogn.slp = TRUE on mc_surface() multiplies positive slopes by 1.99 and negative slopes by 2.31 before the cost function is applied, following Pingel (2013).

surf_c <- mc_surface(dtm, funct = "t", move = 16, cogn.slp = TRUE)
acc_c  <- mc_accum(surf_c, origin = origin, time = "m", breaks = 2)
plot(acc_c)

Task 6. Can least-cost paths to one or more destinations be calculated?

Yes, with mc_paths(), which reuses the same surface from Task 1. Each path carries its accumulated cost and length; for time-based functions the destinations are labelled in sexagesimal format (hh:mm:ss).

lcp <- mc_paths(surf, origin = origin, destin = destin, time = "m")
plot(lcp)

Note the 3.0 idiom: the accumulated surface (Task 1) and the least-cost paths are two separate result objects from the same surface, each plotted when you want it. There is no oneplot parameter because you simply call plot() on whichever object you wish.

Task 7. Can the paths back to the origin be calculated?

Yes. Because the cost is anisotropic, the return route can differ from the outward one. Set return.base = TRUE; the return paths are drawn dashed.

lcp_b <- mc_paths(surf, origin = origin, destin = destin, time = "m",
                  return.base = TRUE)
plot(lcp_b)

Task 8. Can a least-cost corridor be calculated?

Yes, with mc_corridor(). By default (method = "reach") the corridor is the classic one of the 2.x series and the GIS literature (Mitchell 2012): the sum of the accumulated cost spreading outward from each location, so the value of a cell is the total cost to reach it from both. The two least-cost paths (A to B and B to A) are overlaid. Here the wheeled-vehicle cost function is used; its critical slope is set on the surface via sl.crit (default 10 percent).

surf_wcs <- mc_surface(dtm, funct = "wcs", move = 16, sl.crit = 10)
corr <- mc_corridor(surf_wcs, a = origin, b = destin[2, ])
plot(corr)

A new method = "through" option computes instead a directional A-to-B band, cost(A->x) + cost(x->B), whose minimum equals the A-to-B least-cost-path cost; it is intended for one-way journey analysis. See ?mc_corridor for when to prefer each.

Task 9. Can I compare paths from different cost functions?

Yes, with mc_comp(). Because each cost function defines its own surface, mc_comp() takes the DTM (not a pre-built surface) and builds one surface per function internally. Here four time-based functions are compared. All nine destinations are used, so that the comparison chart below has a distribution to summarise.

cmp <- mc_comp(dtm, origin = origin, destin = destin,
               functs = c("t", "ma", "ug", "gkrs"), move = 16)
plot(cmp)

Setting type = "chart" reproduces the add.chart output of the 2.x movecomp(): two boxplots showing, for each cost function, the distribution across the destinations of the path length and of the cost. As in the 2.x guide, one can see, for instance, whether a given function (here gkrs) tends to produce longer paths than the others.

plot(cmp, type = "chart")

Task 10. What if I do not have an elevation raster?

Use mc_dtm() to download elevation data for a study-area polygon (this needs the optional elevatr package). The resolution is set by the zoom level z (default 9). The code below is not executed here because it requires an internet connection.

boundary <- mc_etna_boundary()                 # sample study-area polygon
dtm_etna <- mc_dtm(boundary, z = 9)            # download elevation data
cmp_etna <- mc_comp(dtm_etna,
                    origin = mc_etna_start(),
                    destin = mc_etna_end(),
                    functs = c("t", "wcs"), move = 16)
plot(cmp_etna)

Task 11. Can I calculate a walking-cost boundary, e.g. a 45-minute catchment?

Yes, with mc_boundary(). The limit is the cost value defining the boundary. In 3.0 the boundary is obtained by polygonising the reachable area directly, so the returned polygons are closed and carry their area and perimeter (no extra parameter is needed for this). The example uses the larger Malta DTM, which gives a more informative result than the small volcano, to draw 30-minute walking boundaries (Tobler off-path function) around three springs.

malta_b <- mc_malta_dtm()
springs_b <- mc_springs()
surf_b <- mc_surface(malta_b, funct = "tofp", move = 8)
bnd <- mc_boundary(surf_b, origin = springs_b[c(5, 15, 30), ],
                   limit = 30, time = "m")
plot(bnd)

bnd
#> movecost cost-limit boundaries
#>   cost function : tofp
#>   cost limit    : 30 (m)
#>   origins       : 3
#>   origin_id limit          area perimeter
#> 1         1    30 4753600 [m^2] 13280 [m]
#> 2         2    30 2931200 [m^2] 10960 [m]
#> 3         3    30 6017600 [m^2] 13040 [m]
#> Use plot() to visualise; mc_export() to write to disk.

Task 12. Can I carry out a cost-allocation analysis?

Yes, with mc_alloc(). Each cell is assigned to the origin it can be reached from at the smallest cost. Here three origins are used and the Ardigo et al. metabolic function.

surf_a <- mc_surface(dtm, funct = "a", move = 16)
al <- mc_alloc(surf_a, origin = destin[c(3, 7, 9), ])
plot(al)

Each origin and its zone share the same index (the labels are drawn by default).

Task 13. Can I show isolines inside each allocation zone?

Yes. The allocation result already stores the isolines of the minimum-cost surface; set isolines = TRUE in the plot call to overlay them.

plot(al, isolines = TRUE)

Task 14. Can I calculate a network of least-cost paths?

Yes, with mc_network(). Two network types are available: "allpairs" connects every location to every other; "neigh" connects each location to its cost-wise nearest neighbour. The nodes are numbered to match the returned cost matrix.

surf_t <- mc_surface(dtm, funct = "t", move = 16)
nw_all <- mc_network(surf_t, nodes = destin, type = "allpairs")
plot(nw_all)

nw_nei <- mc_network(surf_t, nodes = destin, type = "neigh")
plot(nw_nei)

The full origin-to-origin cost matrix is returned; note that it is not symmetric, because the cost is anisotropic (A to B need not equal B to A):

round(nw_nei$cost.matrix, 2)
#>      1    2    3    4    5    6    7    8    9
#> 1 0.00 0.07 0.15 0.19 0.15 0.11 0.07 0.09 0.05
#> 2 0.05 0.00 0.09 0.15 0.14 0.11 0.08 0.06 0.06
#> 3 0.14 0.09 0.00 0.10 0.12 0.14 0.14 0.10 0.12
#> 4 0.14 0.11 0.07 0.00 0.06 0.08 0.11 0.08 0.11
#> 5 0.11 0.13 0.12 0.09 0.00 0.02 0.06 0.08 0.09
#> 6 0.09 0.12 0.14 0.11 0.03 0.00 0.03 0.07 0.07
#> 7 0.06 0.10 0.14 0.15 0.07 0.04 0.00 0.06 0.04
#> 8 0.06 0.05 0.08 0.11 0.08 0.06 0.04 0.00 0.03
#> 9 0.04 0.06 0.12 0.15 0.10 0.07 0.03 0.04 0.00

Task 15. Can I calculate the density of a network of paths?

Yes, for the all-pairs network. Pass density = TRUE, then plot the density output. The density is computed exactly from the cells each path traverses and expressed as a percentage of the busiest cell.

nw_d <- mc_network(surf_t, nodes = destin, type = "allpairs", density = TRUE)
plot(nw_d, type = "density")

Task 16. My DTM has NoData (sea); how do I stop paths crossing it?

In 3.0 you do nothing: NoData cells are excluded from the cost graph by construction, so accumulated costs and paths can never cross them. The irregular.dtm parameter of 2.x is no longer needed. Here the Malta DTM has sea cells set to NoData, and the path follows the coastline automatically.

malta <- mc_malta_dtm()
springs <- mc_springs()
surf_malta <- mc_surface(malta, funct = "t", move = 8)
lcp_coast  <- mc_paths(surf_malta, origin = springs[5, ], destin = springs[15, ])
plot(lcp_coast)

Task 17. Can I include a barrier (an area where movement is inhibited)?

Yes. A barrier (lines or polygons) is supplied to mc_surface(), since it changes the cost graph. Edges touching the barrier are given conductance 0 by default (impassable); set field to a small value to penalise rather than forbid. Here a path computed first is reused as a barrier.

# a path to reuse as a barrier
surf8 <- mc_surface(dtm, funct = "t", move = 8)
bar   <- mc_paths(surf8, origin = destin[1, ], destin = destin[4, ])$paths

# without the barrier
free <- mc_paths(surf8, origin = destin[3, ], destin = destin[6, ])
plot(free)


# with the barrier (built into a new surface)
surf_bar <- mc_surface(dtm, funct = "t", move = 8, barrier = bar)
blocked  <- mc_paths(surf_bar, origin = destin[3, ], destin = destin[6, ])
plot(blocked, plot.barrier = TRUE)

The path in the second plot makes a detour to avoid the barrier (drawn in blue). With move = 16, knight-move steps could jump a thin barrier; use move = 8 if that must not happen.

Task 18. Can I calculate sub-optimal (ranked) least-cost paths?

Yes, with mc_rank(). It returns the optimal path (rank 1) and progressively sub-optimal alternatives, found by penalising the edges of earlier paths and re-running the search. Unlike 2.x (capped at six), any number k of ranks can be requested, and the avoidance strength is the penalty argument.

rk <- mc_rank(surf8, origin = destin[3, ], destin = destin[6, ], k = 3)
plot(rk)

rk$paths                                   # rank, cost, length
#> Simple feature collection with 3 features and 4 fields
#> Geometry type: LINESTRING
#> Dimension:     XY
#> Bounding box:  xmin: 2667479 ymin: 6478947 xmax: 2667941 ymax: 6479135
#> Projected CRS: NZGD49 / New Zealand Map Grid
#>   rank      cost                       geometry cost_hms       length
#> 1    1 0.1518334 LINESTRING (2667941 6478947... 00:09:07 595.4477 [m]
#> 2    2 0.1634279 LINESTRING (2667941 6478947... 00:09:48 606.9999 [m]
#> 3    3 0.1746630 LINESTRING (2667941 6478947... 00:10:29 620.9939 [m]

Task 19. Can the ranked paths be drawn over a least-cost corridor?

Yes, directly: plot(rk, type = "corridor") draws the ranked paths over the least-cost corridor between the two locations, which mc_rank() has already computed and stored. This is the equivalent of 2.x’s use.corr, with no manual steps.

rk2 <- mc_rank(surf8, origin = destin[1, ], destin = destin[4, ], k = 3)
plot(rk2, type = "corridor")

Task 20. Can barriers be used with ranked paths?

Yes: build the surface with the barrier, then run mc_rank() on it. The ranked paths all avoid the barrier.

bar2 <- mc_paths(surf8, origin = destin[9, ], destin = destin[2, ])$paths
surf_bar2 <- mc_surface(dtm, funct = "t", move = 8, barrier = bar2)
rk3 <- mc_rank(surf_bar2, origin = destin[1, ], destin = destin[4, ], k = 3)
plot(rk3)

Task 21. Can I visualise the length and cost of each ranked path?

Yes, directly: plot(rk, type = "chart") draws the bubble plot, length against rank with bubble size proportional to cost, the equivalent of 2.x’s add.chart. No data assembly is needed.

rk_h <- mc_rank(surf8, origin = destin[1, ], destin = destin[4, ],
                k = 5, time = "m")
plot(rk_h, type = "chart")