library(riverbed)
library(dplyr)
library(ggplot2)

Example datasets

data(s1)
data(s2)

We consider two longitudinal series \(s_1=(l_1,z_1)\), and \(s_2=(l_2,z_2)\):

Principle of the area calculation

To calculate the area between the curves we need to interpolate the data and calculate intersects between the two curves:

Use of area_between()

This, as well as the calculation of corresponding trapezia, is realised by the function area_between().

result_area <- area_between(s1,s2)
result_area
#> $data
#> # A tibble: 237 x 13
#>        l    z1 p          z2        a type  l_obs z_obs series  zmin  zmax  lmin
#>    <dbl> <dbl> <chr>   <dbl>    <dbl> <fct> <dbl> <dbl> <chr>  <dbl> <dbl> <dbl>
#>  1  10.1  228. observ…  228.  0       <NA>   10.1  228. s1        NA    NA    NA
#>  2  10.1  228. observ…  228.  8.68e-4 upper  10.1  228. s2        NA    NA    NA
#>  3  10.3  228. inters…  228. NA       upper  NA     NA  <NA>      NA    NA    NA
#>  4  10.3  228. inters…  228. -1.13e-1 lower  NA     NA  <NA>      NA    NA    NA
#>  5  12.3  227. observ…  227.  0       <NA>   12.3  227. s1        NA    NA    NA
#>  6  12.3  227. interp…  227. -2.40e-2 lower  NA     NA  s2        NA    NA    NA
#>  7  12.7  227. inters…  227. NA       lower  NA     NA  <NA>      NA    NA    NA
#>  8  12.7  227. inters…  227.  4.79e-3 upper  NA     NA  <NA>      NA    NA    NA
#>  9  12.9  227. interp…  227.  0       <NA>   NA     NA  s1        NA    NA    NA
#> 10  12.9  227. observ…  227.  1.14e+0 upper  12.9  227. s2        NA    NA    NA
#> # … with 227 more rows, and 1 more variable: lmax <dbl>
#> 
#> $area
#> [1] -98.07248
#> 
#> $area_by_type
#> # A tibble: 2 x 2
#>   type     area
#>   <fct>   <dbl>
#> 1 upper    7.76
#> 2 lower -106.  
#> 
#> $sigma_area
#> [1] 0

The output of the function corresponds to

total area between curves (i.e. positive area - negative area)
area between curves according to whether first curve is above the second curve (“upper”) or below (“lower”)
data with all coordinates of interpolated points and intersects, used to calculate the area of trapezia (and which will be used by function plot_area())

Note that it is also possible to calculate the area between one longitudinal series \(s_1=(l_1,z_1)\) and a constant horizontal value \(h\).

result_area_h <- area_between(s1,h=225)

Plot of area

plot_area(result_area)

If the distinction between upper and lower area is irrelevant then it is possible not to distinguish these two types on the plot:

plot_area(result_area,distinguish_type=FALSE)

The plotting function plot_area() can also be used with just one series and constant horizontal level \(h\), as calculated earlier:

plot_area(result_area_h)