Change a generic point in polar coordinates to Cartesian coordinates:

Change a specific point in Cartesian coordinates to polar coordinates:

Give the {x,y,z} values for a point expressed in spherical coordinates:

Change a point in prolate spheroidal to spherical coordinates, specifying a parameter for prolate spheroidal coordinates:

The same transformation, expressed more verbosely:

Transform coordinates on the sphere of radius r to corresponding values in the stereographic projection:

Transform several points at once from cylindrical to Cartesian coordinates:

Transform a matrix of points from Cartesian to spherical coordinates:

Convert a curve in non-Cartesian coordinates to a corresponding Cartesian expression for purposes of visualization:

This curve is approximately 11.2 radii in length:

CoordinateTransformData[ent,"Mapping",pt] is effectively CoordinateTransform[ent,pt]:

CoordinateTransform checks that inputs obey the coordinate range assumptions of charts:

This point violates the coordinate range assumption on the polar angle :

Extract the symbolic transform from CoordinateTransformData to apply it to singular points:

The reverse mapping is not well-defined at this point:

CoordinateTransform preserves the shape of arrays:

This includes empty arrays:

CoordinateTransform changes the coordinate values of points:

TransformedField changes the coordinate expressions for fields:

ToPolarCoordinates is a special case of CoordinateTransform:

FromSphericalCoordinates is a special case of CoordinateTransform:

ToSphericalCoordinates is a special case of CoordinateTransform: