Coordinate Transformations
Transforms between cartesian, spherical, polar, and cylindrical coordinate systems in two and three dimensions.
cart2sph(xyz) sph2cart(tpr) cart2pol(xyz) pol2cart(prz)
xyz |
cartesian coordinates x, y, z as vector or matrix. |
tpr |
spherical coordinates theta, phi, and r as vector or matrix. |
prz |
polar coordinates phi, r or cylindrical coordinates phi, r, z as vector or matrix. |
cart2sph returns spherical coordinates as (theta, phi, r), and
sph2cart expects them in this sequence.
cart2pol returns polar coordinates (phi, r) if length(xyz)==2
and cylindrical coordinates (phi, r, z) else. pol2cart needs them in
this sequence and length.
To go from cylindrical to cartesian coordinates, transform to cartesian coordinates first — or write your own function, see the examples.
All transformation functions are vectorized.
All functions return a (2- or 3-dimensional) vector representing a point in the requested coordinate system, or a matrix with 2 or 3 named columns where is row represents a point. The columns are named accordingly.
In Matlab these functions accept two or three variables and return two or three values. In R it did not appear appropriate to return coordinates as a list.
These functions should be vectorized in the sense that they accept will accept matrices with number of rows or columns equal to 2 or 3.
x <- 0.5*cos(pi/6); y <- 0.5*sin(pi/6); z <- sqrt(1 - x^2 - y^2) (s <-cart2sph(c(x, y, z))) # 0.5235988 1.0471976 1.0000000 sph2cart(s) # 0.4330127 0.2500000 0.8660254 cart2pol(c(1,1)) # 0.7853982 1.4142136 cart2pol(c(1,1,0)) # 0.7853982 1.4142136 0.0000000 pol2cart(c(pi/2, 1)) # 6.123234e-17 1.000000e+00 pol2cart(c(pi/4, 1, 1)) # 0.7071068 0.7071068 1.0000000 ## Transform spherical to cylindrical coordinates and vice versa sph2cyl <- function(th.ph.r) cart2pol(sph2cart(th.ph.r)) cyl2sph <- function(phi.r.z) cart2sph(pol2cart(phi.r.z))
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