Class SphericalCoordinates
- All Implemented Interfaces:
Serializable
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.
- See Also:
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Constructor Summary
ConstructorDescriptionSphericalCoordinates
(double r, double theta, double phi) Build a spherical coordinates transformer from spherical coordinates.Build a spherical coordinates transformer from Cartesian coordinates. -
Method Summary
Modifier and TypeMethodDescriptionGet 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.
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Constructor Details
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SphericalCoordinates
Build a spherical coordinates transformer from Cartesian coordinates.- Parameters:
v
- Cartesian coordinates
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SphericalCoordinates
public SphericalCoordinates(double r, double theta, double phi) Build a spherical coordinates transformer from spherical coordinates.- Parameters:
r
- radiustheta
- azimuthal angle in x-y planephi
- polar (co-latitude) angle
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Method Details
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getCartesian
Get the Cartesian coordinates.- Returns:
- Cartesian coordinates
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getR
public double getR()Get the radius.- Returns:
- radius r
- See Also:
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getTheta
public double getTheta()Get the azimuthal angle in x-y plane. -
getPhi
public double getPhi()Get the polar (co-latitude) angle.- Returns:
- polar (co-latitude) angle Φ
- See Also:
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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}
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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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