Package org.hipparchus.geometry.euclidean.twod

Class Vector2D

java.lang.Object

org.hipparchus.geometry.euclidean.twod.Vector2D

All Implemented Interfaces:

Serializable, Point<Euclidean2D>, Vector<Euclidean2D,Vector2D>, Blendable<Vector<Euclidean2D,Vector2D>>

public class Vector2D
extends Object
implements Vector<Euclidean2D,Vector2D>

This class represents a 2D vector.

Instances of this class are guaranteed to be immutable.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static Vector2D	MINUS_I	Opposite of the first canonical vector (coordinates: -1, 0).
static Vector2D	MINUS_J	Opposite of the second canonical vector (coordinates: 0, -1).
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	PLUS_I	First canonical vector (coordinates: 1, 0).
static Vector2D	PLUS_J	Second canonical vector (coordinates: 0, 1).
static Vector2D	POSITIVE_INFINITY	A vector with all coordinates set to positive infinity.
static Vector2D	ZERO	Origin (coordinates: 0, 0).

Constructor Summary

Constructors

Constructor	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

Modifier and Type	Method	Description
Vector2D	add(double factor, Vector<Euclidean2D,Vector2D> v)	Add a scaled vector to the instance.
Vector2D	add(Vector<Euclidean2D,Vector2D> 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.
static double	distance(Vector2D p1, Vector2D p2)	Compute the distance between two vectors according to the L2 norm.
double	distance(Point<Euclidean2D> p)	Compute the distance between the instance and another point.
static double	distance1(Vector2D p1, Vector2D p2)	Compute the distance between two vectors according to the L1 norm.
double	distance1(Vector<Euclidean2D,Vector2D> p)	Compute the distance between the instance and another vector according to the L1 norm.
static double	distanceInf(Vector2D p1, Vector2D p2)	Compute the distance between two vectors according to the L∞ norm.
double	distanceInf(Vector<Euclidean2D,Vector2D> p)	Compute the distance between the instance and another vector according to the L∞ norm.
static double	distanceSq(Vector2D p1, Vector2D p2)	Compute the square of the distance between two vectors.
double	distanceSq(Vector<Euclidean2D,Vector2D> p)	Compute the square of the distance between the instance and another vector.
double	dotProduct(Vector<Euclidean2D,Vector2D> v)	Compute the dot-product of the instance and another vector.
boolean	equals(Object other)	Test for the equality of two 2D vectors.
boolean	equalsIeee754(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.
static double	orientation(Vector2D p, Vector2D q, Vector2D r)	Compute the orientation of a triplet of points.
Vector2D	scalarMultiply(double a)	Multiply the instance by a scalar.
Vector2D	subtract(double factor, Vector<Euclidean2D,Vector2D> v)	Subtract a scaled vector from the instance.
Vector2D	subtract(Vector<Euclidean2D,Vector2D> 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

Methods inherited from interface org.hipparchus.geometry.Vector

blendArithmeticallyWith, normalize

Field Detail

ZERO

public static final Vector2D ZERO

Origin (coordinates: 0, 0).

PLUS_I

public static final Vector2D PLUS_I

First canonical vector (coordinates: 1, 0).

Since:

1.6

MINUS_I

public static final Vector2D MINUS_I

Opposite of the first canonical vector (coordinates: -1, 0).

Since:

1.6

PLUS_J

public static final Vector2D PLUS_J

Second canonical vector (coordinates: 0, 1).

Since:

1.6

MINUS_J

public static final Vector2D MINUS_J

Opposite of the second canonical vector (coordinates: 0, -1).

Since:

1.6

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 MathIllegalArgumentException

Simple constructor. Build a vector from its coordinates

Parameters:

v - coordinates array

Throws:

MathIllegalArgumentException - 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,Vector2D>

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,Vector2D>

Returns:

L₁ norm for the vector

getNorm

public double getNorm()

Get the L₂ norm for the vector.

Specified by:

getNorm in interface Vector<Euclidean2D,Vector2D>

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,Vector2D>

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,Vector2D>

Returns:

L_∞ norm for the vector

add

public Vector2D add(Vector<Euclidean2D,Vector2D> v)

Add a vector to the instance.

Specified by:

add in interface Vector<Euclidean2D,Vector2D>

Parameters:

v - vector to add

Returns:

a new vector

add

public Vector2D add(double factor,
                    Vector<Euclidean2D,Vector2D> v)

Add a scaled vector to the instance.

Specified by:

add in interface Vector<Euclidean2D,Vector2D>

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,Vector2D> p)

Subtract a vector from the instance.

Specified by:

subtract in interface Vector<Euclidean2D,Vector2D>

Parameters:

p - vector to subtract

Returns:

a new vector

subtract

public Vector2D subtract(double factor,
                         Vector<Euclidean2D,Vector2D> v)

Subtract a scaled vector from the instance.

Specified by:

subtract in interface Vector<Euclidean2D,Vector2D>

Parameters:

factor - scale factor to apply to v before subtracting it

v - vector to subtract

Returns:

a new vector

angle

public static double angle(Vector2D v1,
                           Vector2D v2)
                    throws MathRuntimeException

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:

MathRuntimeException - if either vector has a null norm

negate

public Vector2D negate()

Get the opposite of the instance.

Specified by:

negate in interface Vector<Euclidean2D,Vector2D>

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,Vector2D>

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,Vector2D>

Returns:

true if any coordinate of this vector is infinite and none are NaN; false otherwise

distance1

public double distance1(Vector<Euclidean2D,Vector2D> 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,Vector2D>

Parameters:

p - second vector

Returns:

the distance between the instance and p according to the L₁ 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,Vector2D> 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,Vector2D>

Parameters:

p - second vector

Returns:

the distance between the instance and p according to the L_∞ norm

distanceSq

public double distanceSq(Vector<Euclidean2D,Vector2D> 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,Vector2D>

Parameters:

p - second vector

Returns:

the square of the distance between the instance and p

dotProduct

public double dotProduct(Vector<Euclidean2D,Vector2D> v)

Compute the dot-product of the instance and another vector.

Specified by:

dotProduct in interface Vector<Euclidean2D,Vector2D>

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)

distance1

public static double distance1(Vector2D p1,
                               Vector2D p2)

Compute the distance between two vectors according to the L₁ norm.

Calling this method is equivalent to calling: p1.subtract(p2).getNorm1() except that no intermediate vector is built

Parameters:

p1 - first vector

p2 - second vector

Returns:

the distance between p1 and p2 according to the L₁ norm

Since:

1.6

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

orientation

public static double orientation(Vector2D p,
                                 Vector2D q,
                                 Vector2D r)

Compute the orientation of a triplet of points.

Parameters:

p - first vector of the triplet

q - second vector of the triplet

r - third vector of the triplet

Returns:

a positive value if (p, q, r) defines a counterclockwise oriented triangle, a negative value if (p, q, r) defines a clockwise oriented triangle, and 0 if (p, q, r) are collinear or some points are equal

Since:

1.2

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

equalsIeee754

public boolean equalsIeee754(Object other)

Test for the equality of two 2D vectors.

If all coordinates of two 2D vectors are exactly the same, and none are NaN, the two 2D vectors are considered to be equal.

In compliance with IEEE754 handling, if any coordinates of any of the two vectors are NaN, then the vectors are considered different. This implies that Vector2D.NaN.equals(Vector2D.NaN) returns false despite the instance is checked against itself.

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

Since:

2.1

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,Vector2D>

Parameters:

format - the custom format for components

Returns:

a string representation of this vector