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.

Nested and Inner Type Summary

Modifier and Type	Class and Description
private static class	SphericalCoordinates.DataTransferObject Internal class used only for serialization.

Field Summary

Modifier and Type	Field and Description
private double[][]	jacobian Jacobian of (r, θ Φ).
private final double	phi Polar angle (co-latitude) Φ.
private double[][]	phiHessian Hessian of polar (co-latitude) angle Φ.
private final double	r Radius.
private double[][]	rHessian Hessian of radius.
private static final long	serialVersionUID Serializable UID.
private final double	theta Azimuthal angle in the x-y plane θ.
private double[][]	thetaHessian Hessian of azimuthal angle in the x-y plane θ.
private final Vector3D	v Cartesian coordinates.

Constructor Summary

Access	Constructor and Description
public	SphericalCoordinates(final Vector3D Cartesian coordinates v) Build a spherical coordinates transformer from Cartesian coordinates.
public	SphericalCoordinates(final double radius r, final double azimuthal angle in x-y plane theta, final double polar (co-latitude) angle phi) Build a spherical coordinates transformer from spherical coordinates.

Method Summary

Modifier and Type	Method and Description
private void	computeHessians() Lazy evaluation of Hessians.
private void	computeJacobian() Lazy evaluation of (r, θ, φ) Jacobian.
public Vector3D	Returns: Cartesian coordinates getCartesian() Get the Cartesian coordinates.
public double	Returns: polar (co-latitude) angle Φ getPhi() Get the polar (co-latitude) angle.
public double	Returns: radius r getR() Get the radius.
public double	Returns: azimuthal angle in x-y plane θ getTheta() Get the azimuthal angle in x-y plane.
public double[]	Returns: gradient with respect to Cartesian coordinates {df/dx, df/dy, df/dz} toCartesianGradient(final double[] gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ} sGradient) Convert a gradient with respect to spherical coordinates into a gradient with respect to Cartesian coordinates.
public double[][]	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}} toCartesianHessian(final double[][] Hessian with respect to spherical coordinates {{d²f/dr², d²f/drdθ, d²f/drdΦ}, {d²f/drdθ, d²f/dθ², d²f/dθdΦ}, {d²f/drdΦ, d²f/dθdΦ, d²f/dΦ²} sHessian, final double[] gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ} sGradient) Convert a Hessian with respect to spherical coordinates into a Hessian with respect to Cartesian coordinates.
private Object	Returns: data transfer object that will be serialized writeReplace() Replace the instance with a data transfer object for serialization.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

jacobian	back to summary
private double[][] jacobian Jacobian of (r, θ &Phi).

phi	back to summary
private final double phi Polar angle (co-latitude) Φ.

phiHessian	back to summary
private double[][] phiHessian Hessian of polar (co-latitude) angle Φ.

r	back to summary
private final double r Radius.

rHessian	back to summary
private double[][] rHessian Hessian of radius.

serialVersionUID	back to summary
private static final long serialVersionUID Serializable UID.

theta	back to summary
private final double theta Azimuthal angle in the x-y plane θ.

thetaHessian	back to summary
private double[][] thetaHessian Hessian of azimuthal angle in the x-y plane θ.

v	back to summary
private final Vector3D v Cartesian coordinates.

Constructor Detail

SphericalCoordinates	back to summary
public SphericalCoordinates(final Vector3D v) Build a spherical coordinates transformer from Cartesian coordinates. Parameters v:Vector3D Cartesian coordinates

SphericalCoordinates

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public SphericalCoordinates(final Vector3D v)

Build a spherical coordinates transformer from Cartesian coordinates.

Parameters

v:Vector3D: Cartesian coordinates

SphericalCoordinates	back to summary
public SphericalCoordinates(final double r, final double theta, final double phi) Build a spherical coordinates transformer from spherical coordinates. Parameters r:double radius theta:double azimuthal angle in x-y plane phi:double polar (co-latitude) angle

SphericalCoordinates

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public SphericalCoordinates(final double r, final double theta, final double phi)

Build a spherical coordinates transformer from spherical coordinates.

Parameters

r:double: radius
theta:double: azimuthal angle in x-y plane
phi:double: polar (co-latitude) angle

Method Detail

computeHessians	back to summary
private void computeHessians() Lazy evaluation of Hessians.

computeJacobian	back to summary
private void computeJacobian() Lazy evaluation of (r, θ, φ) Jacobian.

getCartesian	back to summary
public Vector3D getCartesian() Get the Cartesian coordinates. Returns:Vector3D Cartesian coordinates

getCartesian

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public Vector3D getCartesian()

Get the Cartesian coordinates.

Returns:Vector3D: Cartesian coordinates

getPhi back to summary

getPhi	back to summary
public double getPhi() Get the polar (co-latitude) angle. Returns:double polar (co-latitude) angle Φ See Also `getR()`, `getTheta()`

public double getPhi()

Get the polar (co-latitude) angle.

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

getR back to summary

getR	back to summary
public double getR() Get the radius. Returns:double radius r See Also `getTheta()`, `getPhi()`

public double getR()

Get the radius.

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

getTheta back to summary

getTheta	back to summary
public double getTheta() Get the azimuthal angle in x-y plane. Returns:double azimuthal angle in x-y plane θ See Also `getR()`, `getPhi()`

public double getTheta()

Get the azimuthal angle in x-y plane.

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

toCartesianGradient	back to summary
public double[] toCartesianGradient(final double[] sGradient) Convert a gradient with respect to spherical coordinates into a gradient with respect to Cartesian coordinates. Parameters sGradient:double[] gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ} Returns:double[] gradient with respect to Cartesian coordinates {df/dx, df/dy, df/dz}

toCartesianGradient

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public double[] toCartesianGradient(final double[] sGradient)

Convert a gradient with respect to spherical coordinates into a gradient with respect to Cartesian coordinates.

Parameters

sGradient:double[]: gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ}

Returns:double[]

gradient with respect to Cartesian coordinates {df/dx, df/dy, df/dz}

toCartesianHessian	back to summary
public double[][] toCartesianHessian(final double[][] sHessian, final 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:double[][] 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:double[] gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ} Returns:double[][] Hessian with respect to Cartesian coordinates {{d²f/dx², d²f/dxdy, d²f/dxdz}, {d²f/dxdy, d²f/dy², d²f/dydz}, {d²f/dxdz, d²f/dydz, d²f/dz²}}

toCartesianHessian

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public double[][] toCartesianHessian(final double[][] sHessian, final 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:double[][]: 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:double[]: gradient with respect to spherical coordinates {df/dr, df/dθ, df/dΦ}

Returns:double[][]

Hessian with respect to Cartesian coordinates {{d²f/dx², d²f/dxdy, d²f/dxdz}, {d²f/dxdy, d²f/dy², d²f/dydz}, {d²f/dxdz, d²f/dydz, d²f/dz²}}

writeReplace	back to summary
private Object writeReplace() Replace the instance with a data transfer object for serialization. Returns:Object data transfer object that will be serialized

writeReplace

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private Object writeReplace()

Replace the instance with a data transfer object for serialization.

Returns:Object: data transfer object that will be serialized

org.apache.commons.math3.geometry.euclidean.threed back to summary

private Class SphericalCoordinates.DataTransferObject

Class Inheritance

extends Object
implements Serializable

java.lang.Object
org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates.DataTransferObject

All Implemented Interfaces

java.io.Serializable

Internal class used only for serialization.

Field Summary

Modifier and Type	Field and Description
private static final long	serialVersionUID Serializable UID.
private final double	x Abscissa.
private final double	y Ordinate.
private final double	z Height.

Constructor Summary

Access	Constructor and Description
pack-priv	DataTransferObject(final double abscissa x, final double ordinate y, final double height z) Simple constructor.

Method Summary

Modifier and Type	Method and Description
private Object	Returns: replacement `SphericalCoordinates` readResolve() Replace the deserialized data transfer object with a `SphericalCoordinates`.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

serialVersionUID	back to summary
private static final long serialVersionUID Serializable UID.

x	back to summary
private final double x Abscissa.

y	back to summary
private final double y Ordinate.

z	back to summary
private final double z Height.

Constructor Detail

DataTransferObject	back to summary
pack-priv DataTransferObject(final double x, final double y, final double z) Simple constructor. Parameters x:double abscissa y:double ordinate z:double height

DataTransferObject

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pack-priv DataTransferObject(final double x, final double y, final double z)

Simple constructor.

Parameters

x:double: abscissa
y:double: ordinate
z:double: height

Method Detail

readResolve back to summary

readResolve	back to summary
private Object readResolve() Replace the deserialized data transfer object with a `SphericalCoordinates`. Returns:Object replacement `SphericalCoordinates`

private Object readResolve()

Replace the deserialized data transfer object with a SphericalCoordinates.

Returns:Object: replacement SphericalCoordinates

public Class SphericalCoordinates

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

private Class SphericalCoordinates.DataTransferObject

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail