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           ρ  =  1.4142136
   y  =  1             φ  =  45°                      φ  =  45°  
   z  =  1             Θ =  35,26439°            z  =  1      
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