org.hipparchus.geometry.euclidean.twod

## Class Vector2D

• ### Field Summary

Fields
Modifier and Type Field and 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 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

All 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.
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.
static double distance1(Vector2D p1, Vector2D p2)
Compute the distance between two vectors 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.
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> 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).
• #### 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
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
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

• #### toArray

public double[] toArray()
Get the vector coordinates as a dimension 2 array.
Returns:
vector coordinates
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

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

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 MathRuntimeException
Get a normalized vector aligned with the instance.
Specified by:
normalize in interface Vector<Euclidean2D>
Returns:
a new normalized vector
Throws:
MathRuntimeException - if the norm is zero
• #### 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>
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(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
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
• #### 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