R: Converting cartesian coordinates to polar coordinates, and then calculating distance from origin

Question

I\'ve been looking for a solution to convert cartesian coordinates (lat, long) that I have to polar coordinates in order to facilitate a simulation that I want to run, but I hav

Answer 1

For x-y coordinates that are in the same units (e.g. meters rather than degrees of latitude and degrees of longitude), you can use this function to get a data.frame of jump sizes and turning angles (in degrees).

getSteps <- function(x,y) {
    d <- diff(complex(real = x, imaginary = y))
    data.frame(size = Mod(d), 
               angle = c(NA, diff(Arg(d)) %% (2*pi)) * 360/(2*pi))
}

## Try it out   
set.seed(1)
x <- rnorm(10)
y <- rnorm(10)
getSteps(x, y)
#        size     angle
# 1 1.3838360        NA
# 2 1.4356900 278.93771
# 3 2.9066189 101.98625
# 4 3.5714584 144.00231
# 5 1.6404354 114.73369
# 6 1.3082132 135.76778
# 7 0.9922699  74.09479
# 8 0.2036045 141.67541
# 9 0.9100189 337.43632

## A plot helps check that this works
plot(x, y, type = "n", asp = 1)
text(x, y, labels = 1:10)

Answer 2

Since it is fairly straight forward, you can write your own function. Matlab-like cart2pol function in R:

cart2pol <- function(x, y)
{
  r <- sqrt(x^2 + y^2)
  t <- atan(y/x)

  c(r,t)
}