org.apache.commons.math3.geometry.euclidean.twod
Class Vector2D

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

All Implemented Interfaces:

Serializable, 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 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Serialized Form

Field Summary

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

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

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.
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 vector 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 vector 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 vector belongs.

Specified by:

getSpace in interface Vector<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

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 vector is NaN; false otherwise

Specified by:

isNaN in interface Vector<Euclidean2D>

Returns:

true if any coordinate of this vector 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

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

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