I have two points in a 2D space (A and B) and a curve that starts in A and ends in B. I don't have the function of that curve, but an array of n points on that curve.
I wish to calculate the area that is locked between the imaginary line AB, and the curve.
Any help on how to do that in R would be greatly appreciated.
Here is one approach using the pracma package:
library(pracma)
trapz( c(data[1,2], tail(data[,2])), c(data[1,1],tail(data[,1])) ) -
trapz(data[,2], data[,1])
[1] 4276.685
The trapz function finds area under a set of points. The first trapz finds the area under the AB line, and subtracts by the second trapz, the area under the set of points.
A solution using the sf package. Assuming that dat is a data frame. If you have a matrix, please begin with the second step. The idea is to create a polygon and then calculate area.
library(sf)
# Convert to matrix
dat_m <- as.matrix(dat)
# Repeat the first row
dat_m <- rbind(dat_m, dat_m[1, ])
# Convert to polygon
dat_pl <- st_polygon(list(dat_m))
# Calculate the area
st_area(dat_pl)
# [1] 4874
By the way, here is how the polygon looks like.
plot(dat_pl)
DATA
dat <- read.table(text = "-1416.7 214.7
-1418.4 216.8
-1420.3 219.2
-1422.2 221.8
-1424.2 224.5
-1426.3 227.5
-1428.4 230.6
-1430.3 233.9
-1432.2 237.3
-1434 241
-1435.6 244.8
-1437 248.7
-1438.4 252.8
-1439.5 257.1
-1440.5 261.4
-1441.2 265.8
-1441.8 270.4
-1442.2 274.9
-1442.4 279.5
-1442.5 284.1
-1442.4 288.8
-1442.1 293.5
-1441.8 298.3
-1441.4 303.2
-1441 308.2
-1440.6 313.3
-1440.4 318.3
-1440.1 323.3
-1439.9 328.2
-1439.7 333.1
-1439.4 338
-1439.1 342.8
-1438.6 347.6
-1438.1 352.4
-1437.4 357.1
-1436.7 361.8
-1435.8 366.4
-1435 371
-1434 375.5
-1433 379.9
-1432 384.3
-1430.9 388.7
-1429.9 392.9
-1428.8 397.2
-1427.8 401.3
-1426.8 405.4
-1425.9 409.4
-1425.2 413.2
-1424.7 416.8
-1424.3 420.2
-1424 423.4
-1423.8 426.4
-1423.7 429.3
-1423.7 432
-1423.8 434.6
-1423.9 437.1
-1424 439.5
-1424.1 441.8
-1424.2 444
-1424.2 446.2
-1424 448.3
-1423.8 450.3
-1423.4 452.3
-1423 454.3
-1422.4 456.1
-1421.9 457.9
-1421.4 459.6
-1420.9 461.2
-1420.5 462.8
-1420.1 464.3
-1419.8 465.6
-1419.6 466.9
-1419.3 468.1
-1419 469.2
-1418.6 470.2
-1418.2 471.2
-1417.7 472.1
-1417.2 473
-1416.6 473.8
-1415.9 474.5
-1415.2 475.2
-1414.2 475.8
-1413.2 476.4
-1412.2 476.9
-1411.3 477.3")
You can do this without any packages.
Here is some sample data.
set.seed(2018)
x = sort(runif(150, 0,2))
y = sin(x) + sin(10*x)/20
We can get the area from the first point (x[ 1]) to the last (x[150]).
But the area between the curves is just the area under the upper curve minus the area under the line. You can use approxfun with your data to get a good approximation to the upper function. Then just do the integrals.
## Find the line
m = (y[150] - y[1]) / (x[150] - x[1])
b = y[1] - m * x[1]
## Get the functions and compute the integrals.
F1 = approxfun(x,y)
F2 = function(x) { m*x+b }
integrate(F1, x[1], x[150])$value - integrate(F2, x[1], x[150])$value
[1] 0.4539384
Here is an approach with sp:
library(sp)
Polygon(r)@area
#4874
data:
dput(r)
structure(list(V1 = c(-1416.7, -1418.4, -1420.3, -1422.2, -1424.2,
-1426.3, -1428.4, -1430.3, -1432.2, -1434, -1435.6, -1437, -1438.4,
-1439.5, -1440.5, -1441.2, -1441.8, -1442.2, -1442.4, -1442.5,
-1442.4, -1442.1, -1441.8, -1441.4, -1441, -1440.6, -1440.4,
-1440.1, -1439.9, -1439.7, -1439.4, -1439.1, -1438.6, -1438.1,
-1437.4, -1436.7, -1435.8, -1435, -1434, -1433, -1432, -1430.9,
-1429.9, -1428.8, -1427.8, -1426.8, -1425.9, -1425.2, -1424.7,
-1424.3, -1424, -1423.8, -1423.7, -1423.7, -1423.8, -1423.9,
-1424, -1424.1, -1424.2, -1424.2, -1424, -1423.8, -1423.4, -1423,
-1422.4, -1421.9, -1421.4, -1420.9, -1420.5, -1420.1, -1419.8,
-1419.6, -1419.3, -1419, -1418.6, -1418.2, -1417.7, -1417.2,
-1416.6, -1415.9, -1415.2, -1414.2, -1413.2, -1412.2, -1411.3
), V2 = c(214.7, 216.8, 219.2, 221.8, 224.5, 227.5, 230.6, 233.9,
237.3, 241, 244.8, 248.7, 252.8, 257.1, 261.4, 265.8, 270.4,
274.9, 279.5, 284.1, 288.8, 293.5, 298.3, 303.2, 308.2, 313.3,
318.3, 323.3, 328.2, 333.1, 338, 342.8, 347.6, 352.4, 357.1,
361.8, 366.4, 371, 375.5, 379.9, 384.3, 388.7, 392.9, 397.2,
401.3, 405.4, 409.4, 413.2, 416.8, 420.2, 423.4, 426.4, 429.3,
432, 434.6, 437.1, 439.5, 441.8, 444, 446.2, 448.3, 450.3, 452.3,
454.3, 456.1, 457.9, 459.6, 461.2, 462.8, 464.3, 465.6, 466.9,
468.1, 469.2, 470.2, 471.2, 472.1, 473, 473.8, 474.5, 475.2,
475.8, 476.4, 476.9, 477.3)), .Names = c("V1", "V2"), class = "data.frame", row.names = c(NA,
-85L))
