Class SphericalCoordinates

java.lang.Object
org.hipparchus.geometry.euclidean.threed.SphericalCoordinates
All Implemented Interfaces:
Serializable

public class SphericalCoordinates extends Object implements 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.

See Also:
  • Constructor Summary

    Constructors
    Constructor
    Description
    SphericalCoordinates(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 Type
    Method
    Description
    Get the Cartesian coordinates.
    double
    Get the polar (co-latitude) angle.
    double
    Get the radius.
    double
    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 Details

    • 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 Details

    • getCartesian

      public Vector3D getCartesian()
      Get the Cartesian coordinates.
      Returns:
      Cartesian coordinates
    • getR

      public double getR()
      Get the radius.
      Returns:
      radius r
      See Also:
    • getTheta

      public double getTheta()
      Get the azimuthal angle in x-y plane.
      Returns:
      azimuthal angle in x-y plane θ
      See Also:
    • getPhi

      public double getPhi()
      Get the polar (co-latitude) angle.
      Returns:
      polar (co-latitude) angle Φ
      See Also:
    • 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}}