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
open all close allBasic Examples (3)
Scope (3)
Properties & Relations (6)
FromPolarCoordinates checks that inputs obey the normal restrictions of polar coordinates:
FromPolarCoordinates[{1, 3Pi}]
This point violates the condition on the angle 
:
CoordinateChartData["Polar", "CoordinateRangeAssumptions", {r, θ}]Extract the symbolic transform from CoordinateTransformData to apply it to singular points:
transform = CoordinateTransformData["Polar" -> "Cartesian", "Mapping"];
transform[{1, 3Pi}]FromPolarCoordinates preserves the shape of arrays:
FromPolarCoordinates[{{{1, -Pi / 4}}}]FromPolarCoordinates[{{} , {}}]FromPolarCoordinates[pt] is a special case of CoordinateTransform:
CoordinateTransform["Polar" -> "Cartesian", {r, θ}] == FromPolarCoordinates[{r, θ}]CoordinateTransform["Hyperspherical" -> "Cartesian", {r, θ, φ}] == FromPolarCoordinates[{r, θ, φ}]FromPolarCoordinates inverts ToPolarCoordinates:
FromPolarCoordinates[ToPolarCoordinates[{x, y}]]Simplify[FromPolarCoordinates[ToPolarCoordinates[{x, y, z}]], (x | y | z)∈Reals]FromPolarCoordinates[{x,y,z}] uses spherical coordinates about the 
axis:
FromPolarCoordinates[{r, θ, φ}]FromSphericalCoordinates[{x,y,z}] uses spherical coordinates about the 
axis:
FromSphericalCoordinates[{r, θ, φ}]FromPolarCoordinates changes the coordinate values of points:
FromPolarCoordinates[{r, θ}]TransformedField changes the coordinate expressions for fields:
TransformedField["Polar" -> "Cartesian", {r, θ}, {r, θ} -> {x, y}]//SimplifyText
Wolfram Research (2015), FromPolarCoordinates, Wolfram Language function, https://reference.wolfram.com/language/ref/FromPolarCoordinates.html.
CMS
Wolfram Language. 2015. "FromPolarCoordinates." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FromPolarCoordinates.html.
APA
Wolfram Language. (2015). FromPolarCoordinates. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FromPolarCoordinates.html