## Coordinate Systems

With this you may transform three-dimensional cartesian coordinates into three-dimensional polar coordinates or cylindrical coordinates and vice versa.

Cartesian coordinates

In a *cartesian coordinate system* (x|y|z) a point is located by its distance from
each of three mutually perpendicular intersecting lines with the same unit of length.

Polar coordinates

In a *polar coordinate system* (r|φ|Θ) a point is located by its radius vector,
the angle of rotation φ (phi) on the equatorial plane and the angle of elevation Θ (Theta) from the
equatorial plane.

Cylindrical coordinates

In a *cylindrical coordinate system* (ρ|φ|z) a point is located by its distance
ρ (rho) from the cylinder axis, the angle of rotation φ (phi) around the axis and the altitude z above the origin.

### Example:

cartesian polar cylindrical x = 1 r = 1.7320508 ρ = 1.4142136 y = 1 φ = 45° φ = 45° z = 1 Θ = 35,26439° z = 1