# Class S2Point

java.lang.Object
org.hipparchus.geometry.spherical.twod.S2Point
All Implemented Interfaces:
Serializable, Point<Sphere2D>

public class S2Point extends Object implements Point<Sphere2D>
This class represents a point on the 2-sphere.

We use the mathematical convention to use the azimuthal angle $$\theta$$ in the x-y plane as the first coordinate, and the polar angle $$\varphi$$ as the second coordinate (see Spherical Coordinates in MathWorld).

Instances of this class are guaranteed to be immutable.

• ## Field Summary

Fields
Modifier and Type
Field
Description
static final S2Point
MINUS_I
-I (coordinates: $$\theta = \pi, \varphi = \pi/2$$).
static final S2Point
MINUS_J
-J (coordinates: $$\theta = 3\pi/2, \varphi = \pi/2$$).
static final S2Point
MINUS_K
-K (coordinates: $$\theta = any angle, \varphi = \pi$$).
static final S2Point
NaN
A vector with all coordinates set to NaN.
static final S2Point
PLUS_I
+I (coordinates: $$\theta = 0, \varphi = \pi/2$$).
static final S2Point
PLUS_J
+J (coordinates: $$\theta = \pi/2, \varphi = \pi/2$$)).
static final S2Point
PLUS_K
+K (coordinates: $$\theta = any angle, \varphi = 0$$).
• ## Constructor Summary

Constructors
Constructor
Description
S2Point(double theta, double phi)
Simple constructor.
S2Point(Vector3D vector)
Simple constructor.
• ## Method Summary

Modifier and Type
Method
Description
double
distance(Point<Sphere2D> point)
Compute the distance between the instance and another point.
static double
distance(S2Point p1, S2Point p2)
Compute the distance (angular separation) between two points.
boolean
equals(Object other)
Test for the equality of two points on the 2-sphere.
boolean
equalsIeee754(Object other)
Test for the equality of two points on the 2-sphere.
double
getPhi()
Get the polar angle $$\varphi$$.
Space
getSpace()
Get the space to which the point belongs.
double
getTheta()
Get the azimuthal angle $$\theta$$ in the x-y plane.
Vector3D
getVector()
Get the corresponding normalized vector in the 3D euclidean space.
int
hashCode()
Get a hashCode for the point.
boolean
isNaN()
Returns true if any coordinate of this point is NaN; false otherwise
S2Point
negate()
Get the opposite of the instance.
String
toString()

### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait
• ## Field Details

• ### PLUS_I

public static final S2Point PLUS_I
+I (coordinates: $$\theta = 0, \varphi = \pi/2$$).
• ### PLUS_J

public static final S2Point PLUS_J
+J (coordinates: $$\theta = \pi/2, \varphi = \pi/2$$)).
• ### PLUS_K

public static final S2Point PLUS_K
+K (coordinates: $$\theta = any angle, \varphi = 0$$).
• ### MINUS_I

public static final S2Point MINUS_I
-I (coordinates: $$\theta = \pi, \varphi = \pi/2$$).
• ### MINUS_J

public static final S2Point MINUS_J
-J (coordinates: $$\theta = 3\pi/2, \varphi = \pi/2$$).
• ### MINUS_K

public static final S2Point MINUS_K
-K (coordinates: $$\theta = any angle, \varphi = \pi$$).
• ### NaN

public static final S2Point NaN
A vector with all coordinates set to NaN.
• ## Constructor Details

• ### S2Point

public S2Point(double theta, double phi) throws MathIllegalArgumentException
Simple constructor. Build a vector from its spherical coordinates
Parameters:
theta - azimuthal angle $$\theta$$ in the x-y plane
phi - polar angle $$\varphi$$
Throws:
MathIllegalArgumentException - if $$\varphi$$ is not in the [$$0; \pi$$] range
• ### S2Point

public S2Point(Vector3D vector) throws MathRuntimeException
Simple constructor. Build a vector from its underlying 3D vector
Parameters:
vector - 3D vector
Throws:
MathRuntimeException - if vector norm is zero
• ## Method Details

• ### getTheta

public double getTheta()
Get the azimuthal angle $$\theta$$ in the x-y plane.
Returns:
azimuthal angle $$\theta$$ in the x-y plane
• ### getPhi

public double getPhi()
Get the polar angle $$\varphi$$.
Returns:
polar angle $$\varphi$$
• ### getVector

public Vector3D getVector()
Get the corresponding normalized vector in the 3D euclidean space.
Returns:
normalized vector
• ### getSpace

public Space getSpace()
Get the space to which the point belongs.
Specified by:
getSpace in interface Point<Sphere2D>
Returns:
containing space
• ### isNaN

public boolean isNaN()
Returns true if any coordinate of this point is NaN; false otherwise
Specified by:
isNaN in interface Point<Sphere2D>
Returns:
true if any coordinate of this point is NaN; false otherwise
• ### negate

public S2Point negate()
Get the opposite of the instance.
Returns:
a new vector which is opposite to the instance
• ### distance

public double distance(Point<Sphere2D> point)
Compute the distance between the instance and another point.
Specified by:
distance in interface Point<Sphere2D>
Parameters:
point - second point
Returns:
the distance between the instance and p
• ### distance

public static double distance(S2Point p1, S2Point p2)
Compute the distance (angular separation) between two points.
Parameters:
p1 - first vector
p2 - second vector
Returns:
the angular separation between p1 and p2
• ### equals

public boolean equals(Object other)
Test for the equality of two points on the 2-sphere.

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

NaN coordinates are considered to affect globally the point and be equals to each other - i.e, if either (or all) coordinates of the point are equal to Double.NaN, the point is equal to NaN.

Overrides:
equals in class Object
Parameters:
other - Object to test for equality to this
Returns:
true if two points on the 2-sphere objects are equal, false if object is null, not an instance of S2Point, or not equal to this S2Point instance
• ### equalsIeee754

public boolean equalsIeee754(Object other)
Test for the equality of two points on the 2-sphere.

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

In compliance with IEEE754 handling, if any coordinates of any of the two points are NaN, then the points are considered different. This implies that S2Point.NaN.equals(S2Point.NaN) returns false despite the instance is checked against itself.

Parameters:
other - Object to test for equality to this
Returns:
true if two points objects are equal, false if object is null, not an instance of S2Point, or not equal to this S2Point instance
Since:
2.1
• ### hashCode

public int hashCode()
Get a hashCode for the point.

All NaN values have the same hash code.

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

public String toString()
Overrides:
toString in class Object