Class Vector2D

java.lang.Object

org.episteme.core.mathematics.linearalgebra.vectors.GenericVector<Real>

org.episteme.core.mathematics.linearalgebra.vectors.DenseVector<Real>

org.episteme.core.mathematics.geometry.Vector2D

All Implemented Interfaces:

GeometricObject<Point2D>, Vector<Real>, AbelianGroup<Vector<Real>>, AbelianMonoid<Vector<Real>>, Group<Vector<Real>>, Magma<Vector<Real>>, Monoid<Vector<Real>>, Set<Vector<Real>>, Module<Vector<Real>, Real>, MetricSpace<Vector<Real>>, TopologicalSpace<Vector<Real>>

public final class Vector2D
extends DenseVector<Real>
implements GeometricObject<Point2D>, MetricSpace<Vector<Real>>

A 2D vector in Euclidean space. * @author Silvere Martin-Michiellot

Since:

1.0

Author:

Gemini AI (Google DeepMind)

Field Summary

Fields inherited from class GenericVector

provider, ring, storage

Constructor Summary

Constructors

Constructor	Description
Vector2D(double x, double y)
Vector2D(Real x, Real y)

Method Summary

Modifier and Type	Method	Description
Vector2D	add(Vector2D other)
int	ambientDimension()	Returns the dimension of the ambient space containing this object.
boolean	contains(Vector<Real> p)	Tests whether this set contains the specified element.
boolean	containsPoint(Point2D p)	Checks if a point lies at the same position as this vector (interpreted as position vector).
boolean	containsPoint(Vector<Real> p)	Checks if this space contains the given point.
String	description()	Returns a human-readable description of this set.
Vector2D	direction()
Real	distance(Vector<Real> a, Vector<Real> b)	Computes the distance between two points.
Real	dot(Vector2D other)
Real	getX()
Real	getY()
boolean	isClosed()	Checks if this set is closed in the topology.
boolean	isEmpty()	Returns true if this set contains no elements.
boolean	isOpen()	Checks if this set is open in the topology.
Real	magnitude()
Vector2D	minus(Vector2D other)
Vector2D	multiply(Real scalar)	Returns the scalar product of this vector.
Vector2D	negate()	Returns the negation of this vector (-this).
Vector2D	normalize()	Returns the normalized vector (unit vector).
Real	normSquared()
static Vector2D	of(double x, double y)
static Vector2D	of(Real x, Real y)
Vector2D	plus(Vector2D other)
Vector2D	scale(Real scalar)	Convenience scalar multiplication (r × this).
Vector2D	subtract(Vector2D other)
Vector2D	times(Real scalar)
String	toString()

Methods inherited from class DenseVector

getDenseStorage, of, valueOf, zeros

Methods inherited from class GenericVector

add, angle, cross, dimension, dot, get, getField, getProvider, getScalarRing, getStorage, inverse, norm, operate, projection, scale, set, subtract, toMatrix, toTensor, withProvider

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface AbelianGroup

isCommutative, negate, subtract

Methods inherited from interface AbelianMonoid

add, identity, zero

Methods inherited from interface GeometricObject

dimension

Methods inherited from interface Monoid

isAssociative

Methods inherited from interface Vector

map

Constructor Details

Vector2D

public Vector2D(double x,
 double y)

Vector2D

public Vector2D(Real x,
 Real y)

Method Details

of

public static Vector2D of(double x,
 double y)

of

public static Vector2D of(Real x,
 Real y)

getX

public Real getX()

getY

public Real getY()

add

public Vector2D add(Vector2D other)

subtract

public Vector2D subtract(Vector2D other)

multiply

public Vector2D multiply(Real scalar)

Description copied from interface: Vector

Returns the scalar product of this vector.

Specified by:

multiply in interface Vector<Real>

Overrides:

multiply in class GenericVector<Real>

Parameters:

scalar - the scalar multiplier

Returns:

this * scalar

negate

public Vector2D negate()

Description copied from interface: Vector

Returns the negation of this vector (-this).

Specified by:

negate in interface Vector<Real>

Overrides:

negate in class GenericVector<Real>

Returns:

-this

normalize

public Vector2D normalize()

Description copied from interface: Vector

Returns the normalized vector (unit vector).

Specified by:

normalize in interface Vector<Real>

Overrides:

normalize in class GenericVector<Real>

Returns:

this / norm()

dot

public Real dot(Vector2D other)

scale

public Vector2D scale(Real scalar)

Description copied from interface: Module

Convenience scalar multiplication (r × this).

Specified by:

scale in interface Module<Vector<Real>, Real>

Overrides:

scale in class GenericVector<Real>

Parameters:

scalar - the scalar r ∈ R

Returns:

r × this

distance

public Real distance(Vector<Real> a,
 Vector<Real> b)

Description copied from interface: MetricSpace

Computes the distance between two points.

Specified by:

distance in interface MetricSpace<Vector<Real>>

Parameters:

a - the first point

b - the second point

Returns:

the distance between a and b

isEmpty

public boolean isEmpty()

Description copied from interface: Set

Returns true if this set contains no elements.

The empty set (∅) is a fundamental concept in set theory. It is the unique set containing no elements.

Specified by:

isEmpty in interface Set<Vector<Real>>

Overrides:

isEmpty in class GenericVector<Real>

Returns:

true if this set is empty

isOpen

public boolean isOpen()

Description copied from interface: TopologicalSpace

Checks if this set is open in the topology.

Specified by:

isOpen in interface TopologicalSpace<Vector<Real>>

Returns:

true if this is an open set

isClosed

public boolean isClosed()

Description copied from interface: TopologicalSpace

Checks if this set is closed in the topology.

Specified by:

isClosed in interface TopologicalSpace<Vector<Real>>

Returns:

true if this is a closed set

toString

public String toString()

Overrides:

toString in class DenseVector<Real>

ambientDimension

public int ambientDimension()

Description copied from interface: GeometricObject

Returns the dimension of the ambient space containing this object.

For example, a 2D plane in 3D space has dimension=2 but ambientDimension=3.

Specified by:

ambientDimension in interface GeometricObject<Point2D>

Returns:

the ambient space dimension

containsPoint

public boolean containsPoint(Point2D p)

Checks if a point lies at the same position as this vector (interpreted as position vector).

containsPoint

public boolean containsPoint(Vector<Real> p)

Description copied from interface: TopologicalSpace

Checks if this space contains the given point.

Named containsPoint to avoid erasure conflict with Set.contains.

Specified by:

containsPoint in interface TopologicalSpace<Vector<Real>>

Parameters:

p - the point to check

Returns:

true if the point is in this space

contains

public boolean contains(Vector<Real> p)

Description copied from interface: Set

Tests whether this set contains the specified element.

This is the fundamental operation of a set - membership testing.

Specified by:

contains in interface Set<Vector<Real>>

Overrides:

contains in class GenericVector<Real>

Parameters:

p - the element to test for membership

Returns:

true if this set contains the element, false otherwise

See Also:

• Set.isEmpty()
• invalid reference

  #size()

description

public String description()

Description copied from interface: Set

Returns a human-readable description of this set.

Examples:

• "ℝ (Real Numbers)"
• "ℤ/12ℤ (Integers modulo 12)"
• "{1, 2, 3, 4, 5}"

Specified by:

description in interface GeometricObject<Point2D>

Specified by:

description in interface Set<Vector<Real>>

Overrides:

description in class GenericVector<Real>

Returns:

a description of this set

plus

public Vector2D plus(Vector2D other)

times

public Vector2D times(Real scalar)

minus

public Vector2D minus(Vector2D other)

direction

public Vector2D direction()

normSquared

public Real normSquared()

magnitude

public Real magnitude()