Transform Cartesian to Polar/Spherical Coordinates and Vice Versa

Transform cartesian into polar coordinates, resp. to spherical coordinates and vice versa.

CartToPol(x, y)
PolToCart(r, theta)

CartToSph(x, y, z, up = TRUE)
SphToCart(r, theta, phi, up = TRUE)

Arguments

x, y, z

vectors with the xy-coordianates to be transformed.

r

a vector with the radius of the points.

theta

a vector with the angle(s) of the points.

phi

a vector with the angle(s) of the points.

up

logical. If set to TRUE (default) theta is measured from x-y plane, else theta is measured from the z-axis.

Details

Angles are in radians, not degrees (i.e., a right angle is pi/2). Use DegToRad to convert, if you don't wanna do it by yourself.
All parameters are recycled if necessary.

Value

PolToCart returns a list of x and y coordinates of the points.

CartToPol returns a list of r for the radius and theta for the angles of the given points.

Author

Andri Signorell <andri@signorell.net>, Christian W. Hoffmann <christian@echoffmann.ch>

Examples

CartToPol(x=1, y=1)
#> $r
#> [1] 1.414214
#> 
#> $theta
#> [1] 0.7853982
#> 
CartToPol(x=c(1,2,3), y=c(1,1,1))
#> $r
#> [1] 1.414214 2.236068 3.162278
#> 
#> $theta
#> [1] 0.7853982 0.4636476 0.3217506
#> 
CartToPol(x=c(1,2,3), y=1)
#> $r
#> [1] 1.414214 2.236068 3.162278
#> 
#> $theta
#> [1] 0.7853982 0.4636476 0.3217506
#> 


PolToCart(r=1, theta=pi/2)
#> $x
#> [1] 6.123234e-17
#> 
#> $y
#> [1] 1
#> 
PolToCart(r=c(1,2,3), theta=pi/2)
#> $x
#> [1] 6.123234e-17 1.224647e-16 1.836970e-16
#> 
#> $y
#> [1] 1 2 3
#> 

CartToSph(x=1, y=2, z=3)   # r=3.741657, theta=0.930274, phi=1.107149
#> $r
#> [1] 3.741657
#> 
#> $theta
#> [1] 0.930274
#> 
#> $phi
#> [1] 1.107149
#>