Coordinate Transformations Cartesian/Polar/Spherical

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

Usage

polToCart(r, theta)

cartToPol(x, y)

cartToSph(x, y, z, up = TRUE)

sphToCart(r, theta, phi, up = TRUE)

Arguments

r

a vector with the radius of the points.

theta

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

x, y, z

vectors with the xy-coordianates to be transformed.

up

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

phi

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

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.

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.

Note

Based on code by Christian W. Hoffmann

See also

Other geometry.conversion: degree-radians-conversion

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
#> 

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
#>