Class SphericalCoordinates

java.lang.Object
org.apache.commons.geometry.euclidean.threed.SphericalCoordinates
All Implemented Interfaces:
Spatial
public final class SphericalCoordinates extends Object implements Spatial
Class representing spherical coordinates in 3 dimensional Euclidean space.

Spherical coordinates for a point are defined by three values:

  1. Radius - The distance from the point to a fixed referenced point.
  2. Azimuth angle - The angle measured from a fixed reference direction in a plane to the orthogonal projection of the point on that plane.
  3. Polar angle - The angle measured from a fixed zenith direction to the point. The zenith direction must be orthogonal to the reference plane.
This class follows the convention of using the origin as the reference point; the positive x-axis as the reference direction for the azimuth angle, measured in the x-y plane with positive angles moving counter-clockwise toward the positive y-axis; and the positive z-axis as the zenith direction. 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 = √(x^2 + y^2 + z^2)
 θ = atan2(y, x)
 Φ = acos(z/r)
where r is the radius, θ is the azimuth angle, and Φ is the polar angle of the spherical coordinates.

There are numerous, competing conventions for the symbols used to represent spherical coordinate values. For example, the mathematical convention is to use (r, θ, Φ) to represent radius, azimuth angle, and polar angle, whereas the physics convention flips the angle values and uses (r, Φ, θ). As such, this class avoids the use of these symbols altogether in favor of the less ambiguous formal names of the values, e.g. radius, azimuth, and polar.

In order to ensure the uniqueness of coordinate sets, coordinate values are normalized so that radius is in the range [0, +Infinity), azimuth is in the range [0, 2pi), and polar is in the range [0, pi].

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private final double
    azimuth
    Azimuth angle in radians.
    private final double
    polar
    Polar angle in radians.
    private final double
    radius
    Radius value.

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    SphericalCoordinates(double radius, double azimuth, double polar)
    Simple constructor.

  • Method Summary

    Modifier and Type
    Method
    Description
    boolean
    equals(Object other)
    Test for the equality of two sets of spherical coordinates.
    static SphericalCoordinates
    fromCartesian(double x, double y, double z)
    Convert the given set of Cartesian coordinates to spherical coordinates.
    static SphericalCoordinates
    fromCartesian(Vector3D vec)
    Convert the given set of Cartesian coordinates to spherical coordinates.
    double
    getAzimuth()
    Return the azimuth angle in radians.
    int
    getDimension()
    Returns the number of dimensions in the space that this element belongs to.
    double
    getPolar()
    Return the polar angle in radians.
    double
    getRadius()
    Return the radius value.
    int
    hashCode()
    Get a hashCode for this set of spherical coordinates.
    boolean
    isFinite()
    Returns true if all values in this element are finite, meaning they are not NaN or infinite.
    boolean
    isInfinite()
    Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.
    boolean
    isNaN()
    Returns true if any value in this element is NaN; otherwise returns false.
    static double
    normalizeAzimuth(double azimuth)
    Normalize an azimuth value to be within the range [0, 2pi).
    static double
    normalizePolar(double polar)
    Normalize a polar value to be within the range [0, +pi].
    static SphericalCoordinates
    of(double radius, double azimuth, double polar)
    Return a new instance with the given spherical coordinate values.
    static SphericalCoordinates
    parse(String input)
    Parse the given string and return a new SphericalCoordinates instance.
    static Vector3D
    toCartesian(double radius, double azimuth, double polar)
    Convert the given set of spherical coordinates to Cartesian coordinates.
    String
    toString()
    Vector3D
    toVector()
    Convert this set of spherical coordinates to a Cartesian form.

    Methods inherited from class Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Field Details

    • radius

      private final double radius
      Radius value.

    • azimuth

      private final double azimuth
      Azimuth angle in radians.

    • polar

      private final double polar
      Polar angle in radians.

  • Constructor Details

    • SphericalCoordinates

      private SphericalCoordinates(double radius, double azimuth, double polar)
      Simple constructor. The given inputs are normalized.
      Parameters:
      radius - Radius value.
      azimuth - Azimuth angle in radians.
      polar - Polar angle in radians.

  • Method Details

    • getRadius

      public double getRadius()
      Return the radius value. The value is in the range [0, +Infinity).
      Returns:
      the radius value

    • getAzimuth

      public double getAzimuth()
      Return the azimuth angle in radians. This is the angle in the x-y plane measured counter-clockwise from the positive x axis. The angle is in the range [0, 2pi).
      Returns:
      the azimuth angle in radians

    • getPolar

      public double getPolar()
      Return the polar angle in radians. This is the angle the coordinate ray makes with the positive z axis. The angle is in the range [0, pi].
      Returns:
      the polar angle in radians

    • getDimension

      public int getDimension()
      Returns the number of dimensions in the space that this element belongs to.
      Specified by:
      getDimension in interface Spatial
      Returns:
      the number of dimensions in the element's space

    • isNaN

      public boolean isNaN()
      Returns true if any value in this element is NaN; otherwise returns false.
      Specified by:
      isNaN in interface Spatial
      Returns:
      true if any value in this element is NaN

    • isInfinite

      public boolean isInfinite()
      Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.
      Specified by:
      isInfinite in interface Spatial
      Returns:
      true if any value in this element is infinite and none are NaN

    • isFinite

      public boolean isFinite()
      Returns true if all values in this element are finite, meaning they are not NaN or infinite.
      Specified by:
      isFinite in interface Spatial
      Returns:
      true if all values in this element are finite

    • toVector

      public Vector3D toVector()
      Convert this set of spherical coordinates to a Cartesian form.
      Returns:
      A 3-dimensional vector with an equivalent set of Cartesian coordinates.

    • hashCode

      public int hashCode()
      Get a hashCode for this set of spherical coordinates.

      All NaN values have the same hash code.

      Overrides:
      hashCode in class Object
      Returns:
      a hash code value for this object

    • equals

      public boolean equals(Object other)
      Test for the equality of two sets of spherical coordinates.

      If all values of two sets of coordinates are exactly the same, and none are Double.NaN, the two sets are considered to be equal.

      NaN values are considered to globally affect the coordinates and be equal to each other - i.e, if any (or all) values of the coordinate set are equal to Double.NaN, the set as a whole is considered to equal NaN.

      Overrides:
      equals in class Object
      Parameters:
      other - Object to test for equality to this
      Returns:
      true if two SphericalCoordinates objects are equal, false if object is null, not an instance of SphericalCoordinates, or not equal to this SphericalCoordinates instance

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • of

      public static SphericalCoordinates of(double radius, double azimuth, double polar)
      Return a new instance with the given spherical coordinate values. The values are normalized so that radius lies in the range [0, +Infinity), azimuth lies in the range [0, 2pi), and polar lies in the range [0, +pi].
      Parameters:
      radius - the length of the line segment from the origin to the coordinate point.
      azimuth - the angle in the x-y plane, measured in radians counter-clockwise from the positive x-axis.
      polar - the angle in radians between the positive z-axis and the ray from the origin to the coordinate point.
      Returns:
      a new SphericalCoordinates instance representing the same point as the given set of spherical coordinates.

    • fromCartesian

      public static SphericalCoordinates fromCartesian(double x, double y, double z)
      Convert the given set of Cartesian coordinates to spherical coordinates.
      Parameters:
      x - X coordinate value
      y - Y coordinate value
      z - Z coordinate value
      Returns:
      a set of spherical coordinates equivalent to the given Cartesian coordinates

    • fromCartesian

      public static SphericalCoordinates fromCartesian(Vector3D vec)
      Convert the given set of Cartesian coordinates to spherical coordinates.
      Parameters:
      vec - vector containing Cartesian coordinates to convert
      Returns:
      a set of spherical coordinates equivalent to the given Cartesian coordinates

    • toCartesian

      public static Vector3D toCartesian(double radius, double azimuth, double polar)
      Convert the given set of spherical coordinates to Cartesian coordinates.
      Parameters:
      radius - The spherical radius value.
      azimuth - The spherical azimuth angle in radians.
      polar - The spherical polar angle in radians.
      Returns:
      A 3-dimensional vector with an equivalent set of Cartesian coordinates.

    • parse

      public static SphericalCoordinates parse(String input)
      Parse the given string and return a new SphericalCoordinates instance. The parsed coordinate values are normalized as in the of(double, double, double) method. The expected string format is the same as that returned by toString().
      Parameters:
      input - the string to parse
      Returns:
      new SphericalCoordinates instance
      Throws:
      IllegalArgumentException - if the string format is invalid.

    • normalizeAzimuth

      public static double normalizeAzimuth(double azimuth)
      Normalize an azimuth value to be within the range [0, 2pi). This is exactly equivalent to PolarCoordinates.normalizeAzimuth(double).
      Parameters:
      azimuth - azimuth value in radians
      Returns:
      equivalent azimuth value in the range [0, 2pi).
      See Also:

    • normalizePolar

      public static double normalizePolar(double polar)
      Normalize a polar value to be within the range [0, +pi]. Since the polar angle is the angle between two vectors (the zenith direction and the point vector), the sign of the angle is not significant as in the azimuth angle. For example, a polar angle of -pi/2 and one of +pi/2 will both normalize to pi/2.
      Parameters:
      polar - polar value in radians
      Returns:
      equivalent polar value in the range [0, +pi]