Geometry 3D

Coordinate Systems

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

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.

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

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

Example:

  cartesian     polar                cylindrical
  x = 1            r = 1,7320508     rho = 1,4142136   
  y = 1          phi = 45°           phi = 45°         
  z = 1         Theta= 35,26439°       z = 1 

See also:

Wikipedia: Coordinate system
eng.matheass.eu