Streamlines

Source: R/geom_streamline.R

Streamlines are paths that are always tangential to a vector field. In the case of a steady field, it's identical to the path of a massless particle that moves with the "flow".

geom_streamline(
  mapping = NULL,
  data = NULL,
  stat = "streamline",
  position = "identity",
  ...,
  L = 5,
  min.L = 0,
  res = 1,
  S = NULL,
  dt = NULL,
  xwrap = NULL,
  ywrap = NULL,
  skip = 1,
  skip.x = skip,
  skip.y = skip,
  n = NULL,
  nx = n,
  ny = n,
  jitter = 1,
  jitter.x = jitter,
  jitter.y = jitter,
  arrow.angle = 6,
  arrow.length = 0.5,
  arrow.ends = "last",
  arrow.type = "closed",
  arrow = grid::arrow(arrow.angle, grid::unit(arrow.length, "lines"), ends = arrow.ends,
    type = arrow.type),
  lineend = "butt",
  na.rm = TRUE,
  show.legend = NA,
  inherit.aes = TRUE
)

stat_streamline(
  mapping = NULL,
  data = NULL,
  geom = "streamline",
  position = "identity",
  ...,
  L = 5,
  min.L = 0,
  res = 1,
  S = NULL,
  dt = NULL,
  xwrap = NULL,
  ywrap = NULL,
  skip = 1,
  skip.x = skip,
  skip.y = skip,
  n = NULL,
  nx = n,
  ny = n,
  jitter = 1,
  jitter.x = jitter,
  jitter.y = jitter,
  arrow.angle = 6,
  arrow.length = 0.5,
  arrow.ends = "last",
  arrow.type = "closed",
  arrow = grid::arrow(arrow.angle, grid::unit(arrow.length, "lines"), ends = arrow.ends,
    type = arrow.type),
  lineend = "butt",
  na.rm = TRUE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

stat

The statistical transformation to use on the data for this layer, either as a ggproto Geom subclass or as a string naming the stat stripped of the stat_ prefix (e.g. "count" rather than "stat_count")

position

Position adjustment, either as a string naming the adjustment (e.g. "jitter" to use position_jitter), or the result of a call to a position adjustment function. Use the latter if you need to change the settings of the adjustment.

...

Other arguments passed on to layer(). These are often aesthetics, used to set an aesthetic to a fixed value, like colour = "red" or size = 3. They may also be parameters to the paired geom/stat.

L,

typical length of a streamline in x and y units

min.L

minimum length of segments to show

res,

resolution parameter (higher numbers increases the resolution)

S

optional numeric number of timesteps for integration

dt

optional numeric size "timestep" for integration

xwrap, ywrap

vector of length two used to wrap the circular dimension.

skip, skip.x, skip.y

numeric specifying number of gridpoints not to draw in the x and y direction

n, nx, ny

optional numeric indicating the number of points to draw in the x and y direction (replaces skip if not NULL)

jitter, jitter.x, jitter.y

amount of jitter of the starting points

arrow.length, arrow.angle, arrow.ends, arrow.type

parameters passed to grid::arrow

arrow

specification for arrow heads, as created by grid::arrow().

lineend

Line end style (round, butt, square).

na.rm

If FALSE, the default, missing values are removed with a warning. If TRUE, missing values are silently removed.

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders().

geom

The geometric object to use to display the data, either as a ggproto Geom subclass or as a string naming the geom stripped of the geom_ prefix (e.g. "point" rather than "geom_point")

Details

Streamlines are computed by simple integration with a forward Euler method. By default, stat_streamline() computes dt and S from L, res, the resolution of the grid and the mean magnitude of the field. S is then defined as the number of steps necessary to make a streamline of length L under an uniform mean field and dt is chosen so that each step is no larger than the resolution of the data (divided by the res parameter). Be aware that this rule of thumb might fail in field with very skewed distribution of magnitudes.

Alternatively, L and/or res are ignored if S and/or dt are specified explicitly. This not only makes it possible to fine-tune the result but also divorces the integration parameters from the properties of the data and makes it possible to compare streamlines between different fields.

The starting grid is a semi regular grid defined, either by the resolution of the field and the skip.x and skip.y parameters o the nx and ny parameters, jittered by an amount proportional to the resolution of the data and the jitter.x and jitter.y parameters.

It might be important that the units of the vector field are compatible to the units of the x and y dimensions. For example, passing dx and dy in m/s on a longitude-latitude grid will might misleading results (see spherical).

Missing values are not permitted and the field must be defined on a regular grid, for now.

Aesthetics

stat_streamline understands the following aesthetics (required aesthetics are in bold)

  • x

  • y

  • dx

  • dy

  • alpha

  • colour

  • linetype

  • size

Computed variables

step

step in the simulation

dx

dx at each location of the streamline

dy

dy at each location of the streamline

Examples

library(data.table)
library(ggplot2)
data(geopotential)

geopotential <- copy(geopotential)[date == date[1]]
geopotential[, gh.z := Anomaly(gh), by = .(lat)]
#>         lon   lat lev       gh       date     gh.z
#>    1:   0.0 -22.5 700 3163.839 1990-01-01 13.67219
#>    2:   2.5 -22.5 700 3162.516 1990-01-01 12.34968
#>    3:   5.0 -22.5 700 3162.226 1990-01-01 12.05939
#>    4:   7.5 -22.5 700 3162.323 1990-01-01 12.15607
#>    5:  10.0 -22.5 700 3163.097 1990-01-01 12.93024
#>   ---                                             
#> 4028: 347.5 -90.0 700 2715.936 1990-01-01  0.00000
#> 4029: 350.0 -90.0 700 2715.936 1990-01-01  0.00000
#> 4030: 352.5 -90.0 700 2715.936 1990-01-01  0.00000
#> 4031: 355.0 -90.0 700 2715.936 1990-01-01  0.00000
#> 4032: 357.5 -90.0 700 2715.936 1990-01-01  0.00000
geopotential[, c("u", "v") := GeostrophicWind(gh.z, lon, lat)]
#>         lon   lat lev       gh       date     gh.z  u           v
#>    1:   0.0 -22.5 700 3163.839 1990-01-01 13.67219 NA  1.08181190
#>    2:   2.5 -22.5 700 3162.516 1990-01-01 12.34968 NA  0.55189199
#>    3:   5.0 -22.5 700 3162.226 1990-01-01 12.05939 NA  0.06625043
#>    4:   7.5 -22.5 700 3162.323 1990-01-01 12.15607 NA -0.29800162
#>    5:  10.0 -22.5 700 3163.097 1990-01-01 12.93024 NA -0.75064329
#>   ---                                                            
#> 4028: 347.5 -90.0 700 2715.936 1990-01-01  0.00000 NA  0.00000000
#> 4029: 350.0 -90.0 700 2715.936 1990-01-01  0.00000 NA  0.00000000
#> 4030: 352.5 -90.0 700 2715.936 1990-01-01  0.00000 NA  0.00000000
#> 4031: 355.0 -90.0 700 2715.936 1990-01-01  0.00000 NA  0.00000000
#> 4032: 357.5 -90.0 700 2715.936 1990-01-01  0.00000 NA  0.00000000

(g <- ggplot(geopotential, aes(lon, lat)) +
    geom_contour2(aes(z = gh.z), xwrap = c(0, 360)) +
    geom_streamline(aes(dx = dlon(u, lat), dy = dlat(v)), L = 60,
                    xwrap = c(0, 360)))
#> Warning: 'xwrap' and 'ywrap' will be deprecated. Use ggperiodic::periodic insead.


# The circular parameter is particularly important for polar coordinates
g + coord_polar()


# If u and v are not converted into degrees/second, the resulting
# streamlines have problems, specially near the pole.
ggplot(geopotential, aes(lon, lat)) +
    geom_contour(aes(z = gh.z)) +
    geom_streamline(aes(dx = u, dy = v), L = 50)


# The step variable can be mapped to size or alpha to
# get cute "drops". It's important to note that ..dx.. (the calculated variable)
# is NOT the same as dx (from the data).
ggplot(geopotential, aes(lon, lat)) +
    geom_streamline(aes(dx = dlon(u, lat), dy = dlat(v), alpha = ..step..,
                        color = sqrt(..dx..^2 + ..dy..^2), size = ..step..),
                        L = 40, xwrap = c(0, 360), res = 2, arrow = NULL,
                        lineend = "round") +
    scale_size(range = c(0, 0.6))


# Using topographic information to simulate "rivers" from slope
topo <- GetTopography(295, -55+360, -30, -42, res = 1/20)  # needs internet!
topo[, c("dx", "dy") := Derivate(h ~ lon + lat)]
#>            lon     lat     h    dx dy
#>     1: 295.025 -30.025   178    NA NA
#>     2: 295.075 -30.025   180   -10 NA
#>     3: 295.125 -30.025   177   -30 NA
#>     4: 295.175 -30.025   177   -10 NA
#>     5: 295.225 -30.025   176    10 NA
#>    ---                               
#> 47996: 304.775 -41.975 -4525  -530 NA
#> 47997: 304.825 -41.975 -4589 -2270 NA
#> 47998: 304.875 -41.975 -4752 -2100 NA
#> 47999: 304.925 -41.975 -4799  -760 NA
#> 48000: 304.975 -41.975 -4828    NA NA
topo[h <= 0, c("dx", "dy") := 0]
#>            lon     lat     h  dx dy
#>     1: 295.025 -30.025   178  NA NA
#>     2: 295.075 -30.025   180 -10 NA
#>     3: 295.125 -30.025   177 -30 NA
#>     4: 295.175 -30.025   177 -10 NA
#>     5: 295.225 -30.025   176  10 NA
#>    ---                             
#> 47996: 304.775 -41.975 -4525   0  0
#> 47997: 304.825 -41.975 -4589   0  0
#> 47998: 304.875 -41.975 -4752   0  0
#> 47999: 304.925 -41.975 -4799   0  0
#> 48000: 304.975 -41.975 -4828   0  0

# See how in this example the integration step is too coarse in the
# western montanous region where the slope is much higher than in the
# flatlands of La Pampa at in the east.
ggplot(topo, aes(lon, lat)) +
    geom_relief(aes(z = h), interpolate = TRUE, data = topo[h >= 0]) +
    geom_contour(aes(z = h), breaks = 0, color = "black") +
    geom_streamline(aes(dx = -dx, dy = -dy), L = 10, skip = 3, arrow = NULL,
                    color = "#4658BD") +
    coord_quickmap()
#> Warning: Computation failed in `stat_streamline()`
#> Caused by error:
#> ! 'x' and 'y' do not define a regular grid.