## org.apache.commons.math3.geometry.euclidean.threed Class SphericalCoordinates

```java.lang.Object
org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates
```
All Implemented Interfaces:
Serializable

`public class SphericalCoordinatesextends Objectimplements Serializable`

This class provides conversions related to spherical coordinates.

The conventions used here are the mathematical ones, i.e. spherical coordinates are related to Cartesian coordinates as follows:

• x = r cos(θ) sin(Φ)
• y = r sin(θ) sin(Φ)
• z = r cos(Φ)
• r = √(x2+y2+z2)
• θ = atan2(y, x)
• Φ = acos(z/r)

r is the radius, θ is the azimuthal angle in the x-y plane and Φ is the polar (co-latitude) angle. These conventions are different from the conventions used in physics (and in particular in spherical harmonics) where the meanings of θ and Φ are reversed.

This class provides conversion of coordinates and also of gradient and Hessian between spherical and Cartesian coordinates.

Since:
3.2
Version:
\$Id: SphericalCoordinates.html 860130 2013-04-27 21:11:39Z luc \$
See Also:
Serialized Form

Constructor Summary
```SphericalCoordinates(double r, double theta, double phi)```
Build a spherical coordinates transformer from spherical coordinates.
`SphericalCoordinates(Vector3D v)`
Build a spherical coordinates transformer from Cartesian coordinates.

Method Summary
` Vector3D` `getCartesian()`
Get the Cartesian coordinates.
` double` `getPhi()`
Get the polar (co-latitude) angle.
` double` `getR()`
Get the radius.
` double` `getTheta()`
Get the azimuthal angle in x-y plane.
` double[]` `toCartesianGradient(double[] sGradient)`
Convert a gradient with respect to spherical coordinates into a gradient with respect to Cartesian coordinates.
` double[][]` ```toCartesianHessian(double[][] sHessian, double[] sGradient)```
Convert a Hessian with respect to spherical coordinates into a Hessian with respect to Cartesian coordinates.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### SphericalCoordinates

`public SphericalCoordinates(Vector3D v)`
Build a spherical coordinates transformer from Cartesian coordinates.

Parameters:
`v` - Cartesian coordinates

### SphericalCoordinates

```public SphericalCoordinates(double r,
double theta,
double phi)```
Build a spherical coordinates transformer from spherical coordinates.

Parameters:
`r` - radius
`theta` - azimuthal angle in x-y plane
`phi` - polar (co-latitude) angle
Method Detail

### getCartesian

`public Vector3D getCartesian()`
Get the Cartesian coordinates.

Returns:
Cartesian coordinates

### getR

`public double getR()`
Get the radius.

Returns:
radius r
See Also:
`getTheta()`, `getPhi()`

### getTheta

`public double getTheta()`
Get the azimuthal angle in x-y plane.

Returns:
azimuthal angle in x-y plane θ
See Also:
`getR()`, `getPhi()`

### getPhi

`public double getPhi()`
Get the polar (co-latitude) angle.

Returns:
polar (co-latitude) angle Φ
See Also:
`getR()`, `getTheta()`

### toCartesianGradient

`public double[] toCartesianGradient(double[] sGradient)`
Convert a gradient with respect to spherical coordinates into a gradient with respect to Cartesian coordinates.

Parameters:
`sGradient` - gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ}
Returns:
gradient with respect to Cartesian coordinates {df/dx, df/dy, df/dz}

### toCartesianHessian

```public double[][] toCartesianHessian(double[][] sHessian,
double[] sGradient)```
Convert a Hessian with respect to spherical coordinates into a Hessian with respect to Cartesian coordinates.

As Hessian are always symmetric, we use only the lower left part of the provided spherical Hessian, so the upper part may not be initialized. However, we still do fill up the complete array we create, with guaranteed symmetry.

Parameters:
`sHessian` - Hessian with respect to spherical coordinates {{d2f/dr2, d2f/drdθ, d2f/drdΦ}, {d2f/drdθ, d2f/dθ2, d2f/dθdΦ}, {d2f/drdΦ, d2f/dθdΦ, d2f/dΦ2}
`sGradient` - gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ}
Returns:
Hessian with respect to Cartesian coordinates {{d2f/dx2, d2f/dxdy, d2f/dxdz}, {d2f/dxdy, d2f/dy2, d2f/dydz}, {d2f/dxdz, d2f/dydz, d2f/dz2}}

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