HI Luciano,

Is it sufficient for you purpose to calculate difference between two function evaluations (difference between two plot lines)? If so, the following may be useful.

Let x include the function evaluation points, y1 is the outcome from function1 and y2 from function2. After setting the functions, the difference is obtained via integration over the x-axis. For example, if y1 is the normal probability density (mean = 0, sd = 1) and y2 the normal cumulative density function (mean = 1, sd = 1.1), the following commands compute the approximate difference (dif) between the functions:

x

Alternatively, you could try R package [pathmapping] available on CRAN (https://cran.r-project.org/web/packages/pathmapping/index.html). While the package is designed to handle paths, its underlying algorithm (ALCAMP) would be sensitive to calculating the area between two curves and could get you an answer in a couple of lines of code using points along your actual curves as input data.

install.packages('pathmapping')

library(pathmapping)

out

Note that if you don't have any crossings in the curves, the surveyor's function or the shoelace function are efficient ways of computing this, as they compute the area of an arbitrary polygon. You just need to form a polygon from the two paths by lining them up start-end-end-start to form a polygon. These functions are available as part of the pathmapping package. If you have crossovers, loops, or want to map points on one path to another, it is more complicated, and the R pathmapping has implemented the ALCAMP algorithm for these situations.

Have a look at this documentation. It might be of some use.

https://www.rdocumentation.org/packages/geiger/versions/0.2-5/topics/area.between.curves