# FromPolarCoordinates

FromPolarCoordinates[{r,θ}]

gives the {x,y} Cartesian coordinates corresponding to the polar coordinates {r,θ}.

FromPolarCoordinates[{r,θ1,,θn-2,ϕ}]

gives the coordinates corresponding to the hyperspherical coordinates {r,θ1,,θn-2,ϕ}

# Details • FromPolarCoordinates converts points in the standard range , in two dimensions and , , in higher dimensions.
• FromPolarCoordinates automatically threads over arrays of coordinate lists.

# Examples

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## Basic Examples(3)

Convert a general point in polar coordinates:

A specific point:

A conversion in dimension 3:

## Scope(3)

Convert several points:

A matrix of points:

Five-dimensional hyperspherical coordinates:

## Properties & Relations(6)

FromPolarCoordinates checks that inputs obey the normal restrictions of polar coordinates: This point violates the condition on the angle :

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

FromPolarCoordinates preserves the shape of arrays:

This includes empty arrays:

is a special case of CoordinateTransform:

FromPolarCoordinates[{x,y,z}] uses spherical coordinates about the axis:

FromSphericalCoordinates[{x,y,z}] uses spherical coordinates about the axis:

FromPolarCoordinates changes the coordinate values of points:

TransformedField changes the coordinate expressions for fields:

Introduced in 2015
(10.1)