org.apache.commons.math3.geometry.euclidean.twod

## Class Vector2D

- 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
  Version:
    $Id: Vector2D.java 1563684 2014-02-02 17:51:06Z tn $
  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

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