Vector2D (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.geometry.euclidean.twod.Vector2D

All Implemented Interfaces:

Serializable, Point<Euclidean2D>, Vector<Euclidean2D>
```
public class Vector2D
extends Object
implements Vector<Euclidean2D>
```
This class represents a 2D vector.
Instances of this class are guaranteed to be immutable.

Since:

3.0

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static Vector2D`	`NaN` A vector with all coordinates set to NaN.
`static Vector2D`	`NEGATIVE_INFINITY` A vector with all coordinates set to negative infinity.
`static Vector2D`	`POSITIVE_INFINITY` A vector with all coordinates set to positive infinity.
`static Vector2D`	`ZERO` Origin (coordinates: 0, 0).

Constructor Summary

Constructors
Constructor and Description
`Vector2D(double[] v)` Simple constructor.
`Vector2D(double x, double y)` Simple constructor.
`Vector2D(double a, Vector2D u)` Multiplicative constructor Build a vector from another one and a scale factor.
`Vector2D(double a1, Vector2D u1, double a2, Vector2D u2)` Linear constructor Build a vector from two other ones and corresponding scale factors.
`Vector2D(double a1, Vector2D u1, double a2, Vector2D u2, double a3, Vector2D u3)` Linear constructor Build a vector from three other ones and corresponding scale factors.
`Vector2D(double a1, Vector2D u1, double a2, Vector2D u2, double a3, Vector2D u3, double a4, Vector2D u4)` Linear constructor Build a vector from four other ones and corresponding scale factors.

Method Summary

Methods
Modifier and Type	Method and Description
`Vector2D`	`add(double factor, Vector<Euclidean2D> v)` Add a scaled vector to the instance.
`Vector2D`	`add(Vector<Euclidean2D> v)` Add a vector to the instance.
`static double`	`angle(Vector2D v1, Vector2D v2)` Compute the angular separation between two vectors.
`double`	`crossProduct(Vector2D p1, Vector2D p2)` Compute the cross-product of the instance and the given points.
`double`	`distance(Point<Euclidean2D> p)` Compute the distance between the instance and another point.
`double`	`distance(Vector<Euclidean2D> p)` Compute the distance between the instance and another vector according to the L₂ norm.
`static double`	`distance(Vector2D p1, Vector2D p2)` Compute the distance between two vectors according to the L₂ norm.
`double`	`distance1(Vector<Euclidean2D> p)` Compute the distance between the instance and another vector according to the L₁ norm.
`double`	`distanceInf(Vector<Euclidean2D> p)` Compute the distance between the instance and another vector according to the L_∞ norm.
`static double`	`distanceInf(Vector2D p1, Vector2D p2)` Compute the distance between two vectors according to the L_∞ norm.
`double`	`distanceSq(Vector<Euclidean2D> p)` Compute the square of the distance between the instance and another vector.
`static double`	`distanceSq(Vector2D p1, Vector2D p2)` Compute the square of the distance between two vectors.
`double`	`dotProduct(Vector<Euclidean2D> v)` Compute the dot-product of the instance and another vector.
`boolean`	`equals(Object other)` Test for the equality of two 2D vectors.
`double`	`getNorm()` Get the L₂ norm for the vector.
`double`	`getNorm1()` Get the L₁ norm for the vector.
`double`	`getNormInf()` Get the L_∞ norm for the vector.
`double`	`getNormSq()` Get the square of the norm for the vector.
`Space`	`getSpace()` Get the space to which the point belongs.
`double`	`getX()` Get the abscissa of the vector.
`double`	`getY()` Get the ordinate of the vector.
`Vector2D`	`getZero()` Get the null vector of the vectorial space or origin point of the affine space.
`int`	`hashCode()` Get a hashCode for the 2D vector.
`boolean`	`isInfinite()` Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
`boolean`	`isNaN()` Returns true if any coordinate of this point is NaN; false otherwise
`Vector2D`	`negate()` Get the opposite of the instance.
`Vector2D`	`normalize()` Get a normalized vector aligned with the instance.
`Vector2D`	`scalarMultiply(double a)` Multiply the instance by a scalar.
`Vector2D`	`subtract(double factor, Vector<Euclidean2D> v)` Subtract a scaled vector from the instance.
`Vector2D`	`subtract(Vector<Euclidean2D> p)` Subtract a vector from the instance.
`double[]`	`toArray()` Get the vector coordinates as a dimension 2 array.
`String`	`toString()` Get a string representation of this vector.
`String`	`toString(NumberFormat format)` Get a string representation of this vector.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ZERO
```
public static final Vector2D ZERO
```
    Origin (coordinates: 0, 0).
  - NaN
```
public static final Vector2D NaN
```
    A vector with all coordinates set to NaN.
  - POSITIVE_INFINITY
```
public static final Vector2D POSITIVE_INFINITY
```
    A vector with all coordinates set to positive infinity.
  - NEGATIVE_INFINITY
```
public static final Vector2D NEGATIVE_INFINITY
```
    A vector with all coordinates set to negative infinity.
- Constructor Detail
  - Vector2D
```
public Vector2D(double x,
        double y)
```
    Simple constructor. Build a vector from its coordinates
    
    Parameters:
    x - abscissa
    y - ordinate
    See Also:
    getX(), getY()
  - Vector2D
```
public Vector2D(double[] v)
         throws DimensionMismatchException
```
    Simple constructor. Build a vector from its coordinates
    
    Parameters:
    v - coordinates array
    
    Throws:
    
    DimensionMismatchException - if array does not have 2 elements
    See Also:
    toArray()
  - Vector2D
```
public Vector2D(double a,
        Vector2D u)
```
    Multiplicative constructor Build a vector from another one and a scale factor. The vector built will be a * u
    
    Parameters:
    a - scale factor
    u - base (unscaled) vector
  - Vector2D
```
public Vector2D(double a1,
        Vector2D u1,
        double a2,
        Vector2D u2)
```
    Linear constructor Build a vector from two other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2
    
    Parameters:
    a1 - first scale factor
    u1 - first base (unscaled) vector
    a2 - second scale factor
    u2 - second base (unscaled) vector
  - Vector2D
```
public Vector2D(double a1,
        Vector2D u1,
        double a2,
        Vector2D u2,
        double a3,
        Vector2D u3)
```
    Linear constructor Build a vector from three other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3
    
    Parameters:
    a1 - first scale factor
    u1 - first base (unscaled) vector
    a2 - second scale factor
    u2 - second base (unscaled) vector
    a3 - third scale factor
    u3 - third base (unscaled) vector
  - Vector2D
```
public Vector2D(double a1,
        Vector2D u1,
        double a2,
        Vector2D u2,
        double a3,
        Vector2D u3,
        double a4,
        Vector2D u4)
```
    Linear constructor Build a vector from four other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4
    
    Parameters:
    a1 - first scale factor
    u1 - first base (unscaled) vector
    a2 - second scale factor
    u2 - second base (unscaled) vector
    a3 - third scale factor
    u3 - third base (unscaled) vector
    a4 - fourth scale factor
    u4 - fourth base (unscaled) vector
- Method Detail
  - getX
```
public double getX()
```
    Get the abscissa of the vector.
    
    Returns:
    abscissa of the vector
    See Also:
    Vector2D(double, double)
  - getY
```
public double getY()
```
    Get the ordinate of the vector.
    
    Returns:
    ordinate of the vector
    See Also:
    Vector2D(double, double)
  - toArray
```
public double[] toArray()
```
    Get the vector coordinates as a dimension 2 array.
    
    Returns:
    vector coordinates
    See Also:
    Vector2D(double[])
  - getSpace
```
public Space getSpace()
```
    Get the space to which the point belongs.
    
    Specified by:
    
    getSpace in interface Point<Euclidean2D>
    
    Returns:
    containing space
  - getZero
```
public Vector2D getZero()
```
    Get the null vector of the vectorial space or origin point of the affine space.
    
    Specified by:
    
    getZero in interface Vector<Euclidean2D>
    
    Returns:
    null vector of the vectorial space or origin point of the affine space
  - getNorm1
```
public double getNorm1()
```
    Get the L₁ norm for the vector.
    
    Specified by:
    
    getNorm1 in interface Vector<Euclidean2D>
    
    Returns:
    L₁ norm for the vector
  - getNorm
```
public double getNorm()
```
    Get the L₂ norm for the vector.
    
    Specified by:
    
    getNorm in interface Vector<Euclidean2D>
    
    Returns:
    Euclidean norm for the vector
  - getNormSq
```
public double getNormSq()
```
    Get the square of the norm for the vector.
    
    Specified by:
    
    getNormSq in interface Vector<Euclidean2D>
    
    Returns:
    square of the Euclidean norm for the vector
  - getNormInf
```
public double getNormInf()
```
    Get the L_∞ norm for the vector.
    
    Specified by:
    
    getNormInf in interface Vector<Euclidean2D>
    
    Returns:
    L_∞ norm for the vector
  - add
```
public Vector2D add(Vector<Euclidean2D> v)
```
    Add a vector to the instance.
    
    Specified by:
    
    add in interface Vector<Euclidean2D>
    
    Parameters:
    v - vector to add
    
    Returns:
    a new vector
  - add
```
public Vector2D add(double factor,
           Vector<Euclidean2D> v)
```
    Add a scaled vector to the instance.
    
    Specified by:
    
    add in interface Vector<Euclidean2D>
    
    Parameters:
    factor - scale factor to apply to v before adding it
    v - vector to add
    
    Returns:
    a new vector
  - subtract
```
public Vector2D subtract(Vector<Euclidean2D> p)
```
    Subtract a vector from the instance.
    
    Specified by:
    
    subtract in interface Vector<Euclidean2D>
    
    Parameters:
    p - vector to subtract
    
    Returns:
    a new vector
  - subtract
```
public Vector2D subtract(double factor,
                Vector<Euclidean2D> v)
```
    Subtract a scaled vector from the instance.
    
    Specified by:
    
    subtract in interface Vector<Euclidean2D>
    
    Parameters:
    factor - scale factor to apply to v before subtracting it
    v - vector to subtract
    
    Returns:
    a new vector
  - normalize
```
public Vector2D normalize()
                   throws MathArithmeticException
```
    Get a normalized vector aligned with the instance.
    
    Specified by:
    
    normalize in interface Vector<Euclidean2D>
    
    Returns:
    a new normalized vector
    
    Throws:
    
    MathArithmeticException - if the norm is zero
  - angle
```
public static double angle(Vector2D v1,
           Vector2D v2)
                    throws MathArithmeticException
```
    Compute the angular separation between two vectors.
    This method computes the angular separation between two vectors using the dot product for well separated vectors and the cross product for almost aligned vectors. This allows to have a good accuracy in all cases, even for vectors very close to each other.
    
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    angular separation between v1 and v2
    
    Throws:
    
    MathArithmeticException - if either vector has a null norm
  - negate
```
public Vector2D negate()
```
    Get the opposite of the instance.
    
    Specified by:
    
    negate in interface Vector<Euclidean2D>
    
    Returns:
    a new vector which is opposite to the instance
  - scalarMultiply
```
public Vector2D scalarMultiply(double a)
```
    Multiply the instance by a scalar.
    
    Specified by:
    
    scalarMultiply in interface Vector<Euclidean2D>
    
    Parameters:
    a - scalar
    
    Returns:
    a new vector
  - isNaN
```
public boolean isNaN()
```
    Returns true if any coordinate of this point is NaN; false otherwise
    
    Specified by:
    
    isNaN in interface Point<Euclidean2D>
    
    Returns:
    true if any coordinate of this point is NaN; false otherwise
  - isInfinite
```
public boolean isInfinite()
```
    Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
    
    Specified by:
    
    isInfinite in interface Vector<Euclidean2D>
    
    Returns:
    true if any coordinate of this vector is infinite and none are NaN; false otherwise
  - distance1
```
public double distance1(Vector<Euclidean2D> p)
```
    Compute the distance between the instance and another vector according to the L₁ norm.
    Calling this method is equivalent to calling: q.subtract(p).getNorm1() except that no intermediate vector is built
    
    Specified by:
    
    distance1 in interface Vector<Euclidean2D>
    
    Parameters:
    p - second vector
    
    Returns:
    the distance between the instance and p according to the L₁ norm
  - distance
```
public double distance(Vector<Euclidean2D> p)
```
    Compute the distance between the instance and another vector according to the L₂ norm.
    Calling this method is equivalent to calling: q.subtract(p).getNorm() except that no intermediate vector is built
    
    Specified by:
    
    distance in interface Vector<Euclidean2D>
    
    Parameters:
    p - second vector
    
    Returns:
    the distance between the instance and p according to the L₂ norm
  - distance
```
public double distance(Point<Euclidean2D> p)
```
    Compute the distance between the instance and another point.
    
    Specified by:
    
    distance in interface Point<Euclidean2D>
    
    Parameters:
    p - second point
    
    Returns:
    the distance between the instance and p
  - distanceInf
```
public double distanceInf(Vector<Euclidean2D> p)
```
    Compute the distance between the instance and another vector according to the L_∞ norm.
    Calling this method is equivalent to calling: q.subtract(p).getNormInf() except that no intermediate vector is built
    
    Specified by:
    
    distanceInf in interface Vector<Euclidean2D>
    
    Parameters:
    p - second vector
    
    Returns:
    the distance between the instance and p according to the L_∞ norm
  - distanceSq
```
public double distanceSq(Vector<Euclidean2D> p)
```
    Compute the square of the distance between the instance and another vector.
    Calling this method is equivalent to calling: q.subtract(p).getNormSq() except that no intermediate vector is built
    
    Specified by:
    
    distanceSq in interface Vector<Euclidean2D>
    
    Parameters:
    p - second vector
    
    Returns:
    the square of the distance between the instance and p
  - dotProduct
```
public double dotProduct(Vector<Euclidean2D> v)
```
    Compute the dot-product of the instance and another vector.
    
    Specified by:
    
    dotProduct in interface Vector<Euclidean2D>
    
    Parameters:
    v - second vector
    
    Returns:
    the dot product this.v
  - crossProduct
```
public double crossProduct(Vector2D p1,
                  Vector2D p2)
```
    Compute the cross-product of the instance and the given points.
    The cross product can be used to determine the location of a point with regard to the line formed by (p1, p2) and is calculated as: \[ P = (x_2 - x_1)(y_3 - y_1) - (y_2 - y_1)(x_3 - x_1) \] with \(p3 = (x_3, y_3)\) being this instance.
    If the result is 0, the points are collinear, i.e. lie on a single straight line L; if it is positive, this point lies to the left, otherwise to the right of the line formed by (p1, p2).
    
    Parameters:
    p1 - first point of the line
    p2 - second point of the line
    
    Returns:
    the cross-product
    See Also:
    Cross product (Wikipedia)
  - distance
```
public static double distance(Vector2D p1,
              Vector2D p2)
```
    Compute the distance between two vectors according to the L₂ norm.
    Calling this method is equivalent to calling: p1.subtract(p2).getNorm() except that no intermediate vector is built
    
    Parameters:
    p1 - first vector
    p2 - second vector
    
    Returns:
    the distance between p1 and p2 according to the L₂ norm
  - distanceInf
```
public static double distanceInf(Vector2D p1,
                 Vector2D p2)
```
    Compute the distance between two vectors according to the L_∞ norm.
    Calling this method is equivalent to calling: p1.subtract(p2).getNormInf() except that no intermediate vector is built
    
    Parameters:
    p1 - first vector
    p2 - second vector
    
    Returns:
    the distance between p1 and p2 according to the L_∞ norm
  - distanceSq
```
public static double distanceSq(Vector2D p1,
                Vector2D p2)
```
    Compute the square of the distance between two vectors.
    Calling this method is equivalent to calling: p1.subtract(p2).getNormSq() except that no intermediate vector is built
    
    Parameters:
    p1 - first vector
    p2 - second vector
    
    Returns:
    the square of the distance between p1 and p2
  - equals
```
public boolean equals(Object other)
```
    Test for the equality of two 2D vectors.
    If all coordinates of two 2D vectors are exactly the same, and none are Double.NaN, the two 2D vectors are considered to be equal.
    
    NaN coordinates are considered to affect globally the vector and be equals to each other - i.e, if either (or all) coordinates of the 2D vector are equal to Double.NaN, the 2D vector is equal to NaN.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    other - Object to test for equality to this
    
    Returns:
    true if two 2D vector objects are equal, false if object is null, not an instance of Vector2D, or not equal to this Vector2D instance
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the 2D vector.
    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()
```
    Get a string representation of this vector.
    
    Overrides:
    
    toString in class Object
    
    Returns:
    a string representation of this vector
  - toString
```
public String toString(NumberFormat format)
```
    Get a string representation of this vector.
    
    Specified by:
    
    toString in interface Vector<Euclidean2D>
    
    Parameters:
    format - the custom format for components
    
    Returns:
    a string representation of this vector

Class Vector2D

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ZERO

NaN

POSITIVE_INFINITY

NEGATIVE_INFINITY

Constructor Detail

Vector2D

Vector2D

Vector2D

Vector2D

Vector2D

Vector2D

Method Detail

getX

getY

toArray

getSpace

getZero

getNorm1

getNorm

getNormSq

getNormInf

add

add

subtract

subtract

normalize

angle

negate

scalarMultiply

isNaN

isInfinite

distance1

distance

distance

distanceInf

distanceSq

dotProduct

crossProduct

distance

distanceInf

distanceSq

equals

hashCode

toString

toString