pracma (version 1.8.8)

cart2sph: Coordinate Transformations

Description

Transforms between cartesian, spherical, polar, and cylindrical coordinate systems in two and three dimensions.

Usage

cart2sph(xyz)
sph2cart(tpr)
cart2pol(xyz)
pol2cart(prz)

Arguments

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.

Value

• 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.

Details

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.

Examples

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))