All Implemented Interfaces:
Point<Vector2D>, Spatial, Vector<Vector2D>
Direct Known Subclasses:
Vector2D.Unit

public class Vector2D extends MultiDimensionalEuclideanVector<Vector2D>
This class represents vectors and points in two-dimensional Euclidean space. Instances of this class are guaranteed to be immutable.
  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static final class 
    Class used to create high-accuracy sums of vectors.
    static final class 
    Represents unit vectors.
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final Comparator<Vector2D>
    Comparator that sorts vectors in component-wise ascending order.
    static final Vector2D
    A vector with all coordinates set to NaN.
    static final Vector2D
    A vector with all coordinates set to negative infinity.
    static final Vector2D
    A vector with all coordinates set to positive infinity.
    private final double
    Abscissa (first coordinate).
    private final double
    Ordinate (second coordinate).
    static final Vector2D
    Zero vector (coordinates: 0, 0).
  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    Vector2D(double x, double y)
    Simple constructor.
  • Method Summary

    Modifier and Type
    Method
    Description
    add(double factor, Vector2D v)
    Add a scaled vector to the instance.
    Add a vector to the instance.
    double
    Compute the angular separation between two vectors in radians.
    static Vector2D
    Compute the centroid of the given points.
    static Vector2D
    centroid(Vector2D first, Vector2D... more)
    Compute the centroid of the given points.
    private static Vector2D
    computeCentroid(Vector2D first, Iterator<? extends Vector2D> more)
    Internal method for computing the centroid of a set of points.
    private static Vector2D
    computeMax(Vector2D first, Iterator<? extends Vector2D> more)
    Internal method for computing a max vector.
    private static Vector2D
    computeMin(Vector2D first, Iterator<? extends Vector2D> more)
    Internal method for computing a min vector.
    Return the unit vector representing the direction of displacement from this vector to the given vector.
    double
    Compute the distance between the instance and another vector.
    double
    Compute the square of the distance between the instance and another vector.
    double
    Compute the dot-product of the instance and another vector.
    boolean
    eq(Vector2D vec, org.apache.commons.numbers.core.Precision.DoubleEquivalence precision)
    Return true if the current instance and given vector are considered equal as evaluated by the given precision context.
    boolean
    equals(Object other)
    Test for the equality of two vector instances.
    private <T extends Vector2D>
    T
    getComponent(Vector2D base, boolean reject, DoubleFunction2N<T> factory)
    Returns a component of the current instance relative to the given base vector.
    int
    Returns the number of dimensions in the space that this element belongs to.
    double
    Returns the abscissa (first coordinate value) of the instance.
    double
    Returns the ordinate (second coordinate value) of the instance.
    Get the zero (null) vector of the space.
    int
    Get a hashCode for the 2D coordinates.
    boolean
    Returns true if all values in this element are finite, meaning they are not NaN or infinite.
    boolean
    Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.
    boolean
    Returns true if any value in this element is NaN; otherwise returns false.
    lerp(Vector2D p, double t)
    Get a vector constructed by linearly interpolating between this vector and the given vector.
    static Vector2D
    Return a vector containing the maximum component values from all input vectors.
    static Vector2D
    max(Vector2D first, Vector2D... more)
    Return a vector containing the maximum component values from all input vectors.
    static Vector2D
    Return a vector containing the minimum component values from all input vectors.
    static Vector2D
    min(Vector2D first, Vector2D... more)
    Return a vector containing the minimum component values from all input vectors.
    multiply(double a)
    Multiply the instance by a scalar.
    Get the negation of the instance.
    double
    Get the L2 norm (commonly known as the Euclidean norm) for the vector.
    Get a normalized vector aligned with the instance.
    Attempt to compute a normalized vector aligned with the instance, returning null if such a vector cannot be computed.
    double
    Get the square of the L2 norm (also known as the Euclidean norm) for the vector.
    static Vector2D
    of(double[] v)
    Creates a vector from the coordinates in the given 2-element array.
    static Vector2D
    of(double x, double y)
    Returns a vector with the given coordinate values.
    Get a unit vector orthogonal to the instance.
    Get a unit vector orthogonal to the current vector and pointing in the direction of dir.
    static Vector2D
    Parses the given string and returns a new vector instance.
    Get the projection of the instance onto the given base vector.
    Get the rejection of the instance from the given base vector.
    double
    Compute the signed area of the parallelogram with sides formed by this instance and the given vector.
    subtract(double factor, Vector2D v)
    Subtract a scaled vector from the instance.
    Subtract a vector from the instance.
    double[]
    Get the coordinates for this instance as a dimension 2 array.
    Convenience method to apply a function to this vector.
    Return the vector representing the displacement from this vector to the given vector.
    withNorm(double magnitude)
    Returns a vector with the same direction but with the given norm.

    Methods inherited from class org.apache.commons.geometry.euclidean.EuclideanVector

    getCheckedNorm, isZero

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait
  • Field Details

    • ZERO

      public static final Vector2D ZERO
      Zero vector (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.
    • COORDINATE_ASCENDING_ORDER

      public static final Comparator<Vector2D> COORDINATE_ASCENDING_ORDER
      Comparator that sorts vectors in component-wise ascending order. Vectors are only considered equal if their coordinates match exactly. Null arguments are evaluated as being greater than non-null arguments.
    • x

      private final double x
      Abscissa (first coordinate).
    • y

      private final double y
      Ordinate (second coordinate).
  • Constructor Details

    • Vector2D

      private Vector2D(double x, double y)
      Simple constructor.
      Parameters:
      x - abscissa (first coordinate)
      y - ordinate (second coordinate)
  • Method Details

    • getX

      public double getX()
      Returns the abscissa (first coordinate value) of the instance.
      Returns:
      the abscissa
    • getY

      public double getY()
      Returns the ordinate (second coordinate value) of the instance.
      Returns:
      the ordinate
    • toArray

      public double[] toArray()
      Get the coordinates for this instance as a dimension 2 array.
      Returns:
      coordinates for this instance
    • getDimension

      public int getDimension()
      Returns the number of dimensions in the space that this element belongs to.
      Returns:
      the number of dimensions in the element's space
    • isNaN

      public boolean isNaN()
      Returns true if any value in this element is NaN; otherwise returns false.
      Returns:
      true if any value in this element is NaN
    • isInfinite

      public boolean isInfinite()
      Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.
      Returns:
      true if any value in this element is infinite and none are NaN
    • isFinite

      public boolean isFinite()
      Returns true if all values in this element are finite, meaning they are not NaN or infinite.
      Returns:
      true if all values in this element are finite
    • vectorTo

      public Vector2D vectorTo(Vector2D v)
      Return the vector representing the displacement from this vector to the given vector. This is exactly equivalent to v.subtract(thisVector) but with a method name that is much easier to visualize.
      Specified by:
      vectorTo in class EuclideanVector<Vector2D>
      Parameters:
      v - the vector that the returned vector will be directed toward
      Returns:
      vector representing the displacement from this vector to the given vector
    • directionTo

      public Vector2D.Unit directionTo(Vector2D v)
      Return the unit vector representing the direction of displacement from this vector to the given vector. This is exactly equivalent to v.subtract(thisVector).normalize() but without the intermediate vector instance.
      Specified by:
      directionTo in class EuclideanVector<Vector2D>
      Parameters:
      v - the vector that the returned vector will be directed toward
      Returns:
      unit vector representing the direction of displacement from this vector to the given vector
    • lerp

      public Vector2D lerp(Vector2D p, double t)
      Get a vector constructed by linearly interpolating between this vector and the given vector. The vector coordinates are generated by the equation V = (1 - t)*A + t*B, where A is the current vector and B is the given vector. This means that if t = 0, a vector equal to the current vector will be returned. If t = 1, a vector equal to the argument will be returned. The t parameter is not constrained to the range [0, 1], meaning that linear extrapolation can also be performed with this method.
      Specified by:
      lerp in class EuclideanVector<Vector2D>
      Parameters:
      p - other vector
      t - interpolation parameter
      Returns:
      interpolated or extrapolated vector
    • getZero

      public Vector2D getZero()
      Get the zero (null) vector of the space.
      Returns:
      zero vector of the space
    • norm

      public double norm()
      Get the L2 norm (commonly known as the Euclidean norm) for the vector. This corresponds to the common notion of vector magnitude or length and is defined as the square root of the sum of the squares of all vector components.
      Returns:
      L2 norm for the vector
      See Also:
    • normSq

      public double normSq()
      Get the square of the L2 norm (also known as the Euclidean norm) for the vector. This is equal to the sum of the squares of all vector components.
      Returns:
      square of the L2 norm for the vector
      See Also:
    • withNorm

      public Vector2D withNorm(double magnitude)
      Returns a vector with the same direction but with the given norm. This is equivalent to calling vec.normalize().scalarMultiply(mag) but without the intermediate vector.
      Parameters:
      magnitude - The vector norm
      Returns:
      a vector with the same direction as the current instance but the given norm
    • add

      public Vector2D add(Vector2D v)
      Add a vector to the instance.
      Parameters:
      v - vector to add
      Returns:
      a new vector
    • add

      public Vector2D add(double factor, Vector2D v)
      Add a scaled vector to the instance.
      Parameters:
      factor - scale factor to apply to v before adding it
      v - vector to add
      Returns:
      a new vector
    • subtract

      public Vector2D subtract(Vector2D v)
      Subtract a vector from the instance.
      Parameters:
      v - vector to subtract
      Returns:
      a new vector
    • subtract

      public Vector2D subtract(double factor, Vector2D v)
      Subtract a scaled vector from the instance.
      Parameters:
      factor - scale factor to apply to v before subtracting it
      v - vector to subtract
      Returns:
      a new vector
    • negate

      public Vector2D negate()
      Get the negation of the instance.
      Returns:
      a new vector which is the negation of the instance
    • normalize

      public Vector2D.Unit normalize()
      Get a normalized vector aligned with the instance. The returned vector has a magnitude of 1.
      Returns:
      normalized vector
      See Also:
    • normalizeOrNull

      public Vector2D.Unit normalizeOrNull()
      Attempt to compute a normalized vector aligned with the instance, returning null if such a vector cannot be computed. This method is equivalent to Vector.normalize() but returns null instead of throwing an exception on failure.
      Returns:
      normalized vector or null if such a vector cannot be computed, i.e. if the norm is zero, NaN, or infinite
      See Also:
    • multiply

      public Vector2D multiply(double a)
      Multiply the instance by a scalar.
      Parameters:
      a - scalar
      Returns:
      a new vector
    • distance

      public double distance(Vector2D v)
      Compute the distance between the instance and another vector.
      Parameters:
      v - second vector
      Returns:
      the distance between the instance and v
    • distanceSq

      public double distanceSq(Vector2D v)
      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

      Parameters:
      v - second vector
      Returns:
      the square of the distance between the instance and p
      See Also:
    • dot

      public double dot(Vector2D v)
      Compute the dot-product of the instance and another vector.
      Parameters:
      v - second vector
      Returns:
      the dot product (this · v)
    • angle

      public double angle(Vector2D v)
      Compute the angular separation between two vectors in radians.

      This method computes the angular separation between the 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:
      v - other vector
      Returns:
      angular separation between this instance and v in radians
    • project

      public Vector2D project(Vector2D base)
      Get the projection of the instance onto the given base vector. The returned vector is parallel to base. Vector projection and rejection onto a given base are related by the equation v = vprojection + vrejection
      Specified by:
      project in class MultiDimensionalEuclideanVector<Vector2D>
      Parameters:
      base - base vector
      Returns:
      the vector projection of the instance onto base
      See Also:
    • reject

      public Vector2D reject(Vector2D base)
      Get the rejection of the instance from the given base vector. The returned vector is orthogonal to base. This operation can be interpreted as returning the orthogonal projection of the instance onto the hyperplane orthogonal to base. Vector projection and rejection onto a given base are related by the equation v = vprojection + vrejection
      Specified by:
      reject in class MultiDimensionalEuclideanVector<Vector2D>
      Parameters:
      base - base vector
      Returns:
      the vector rejection of the instance from base
      See Also:
    • orthogonal

      public Vector2D.Unit orthogonal()
      Get a unit vector orthogonal to the instance. The returned vector is computed by rotating the current instance pi/2 radians counterclockwise around the origin and normalizing. For example, if this method is called on a vector pointing along the positive x-axis, then a unit vector representing the positive y-axis is returned.
      Specified by:
      orthogonal in class MultiDimensionalEuclideanVector<Vector2D>
      Returns:
      a unit vector orthogonal to the current instance
      Throws:
      IllegalArgumentException - if the norm of the current instance is zero, NaN, or infinite
    • orthogonal

      public Vector2D.Unit orthogonal(Vector2D dir)
      Get a unit vector orthogonal to the current vector and pointing in the direction of dir. This method is equivalent to calling dir.reject(vec).normalize() except that no intermediate vector object is produced.
      Specified by:
      orthogonal in class MultiDimensionalEuclideanVector<Vector2D>
      Parameters:
      dir - the direction to use for generating the orthogonal vector
      Returns:
      unit vector orthogonal to the current vector and pointing in the direction of dir that does not lie along the current vector
    • signedArea

      public double signedArea(Vector2D v)
      Compute the signed area of the parallelogram with sides formed by this instance and the given vector.

      The parallelogram in question can be visualized by taking the current instance as the first side and placing v at the end of it to create the second. The other sides are formed by lines parallel to these two vectors. If v points to the left of the current instance (ie, the parallelogram is wound counter-clockwise), then the returned area is positive. If v points to the right of the current instance, (ie, the parallelogram is wound clockwise), then the returned area is negative. If the vectors are collinear (ie, they lie on the same line), then 0 is returned. The area of the triangle formed by the two vectors is exactly half of the returned value.

      Parameters:
      v - vector representing the second side of the constructed parallelogram
      Returns:
      the signed area of the parallelogram formed by this instance and the given vector
    • transform

      public Vector2D transform(UnaryOperator<Vector2D> fn)
      Convenience method to apply a function to this vector. This can be used to transform the vector inline with other methods.
      Parameters:
      fn - the function to apply
      Returns:
      the transformed vector
    • eq

      public boolean eq(Vector2D vec, org.apache.commons.numbers.core.Precision.DoubleEquivalence precision)
      Return true if the current instance and given vector are considered equal as evaluated by the given precision context.

      Equality is determined by comparing each pair of components in turn from the two vectors. If all components evaluate as equal, then the vectors are considered equal. If any are not equal, then the vectors are not considered equal. Note that this approach means that the calculated distance between two "equal" vectors may be as much as √(n * eps2), where n is the number of components in the vector and eps is the maximum epsilon value allowed by the precision context.

      Specified by:
      eq in class EuclideanVector<Vector2D>
      Parameters:
      vec - vector to check for equality
      precision - precision context used to determine floating point equality
      Returns:
      true if the current instance is considered equal to the given vector when using the given precision context; otherwise false
    • hashCode

      public int hashCode()
      Get a hashCode for the 2D coordinates.

      All NaN values have the same hash code.

      Overrides:
      hashCode in class Object
      Returns:
      a hash code value for this object
    • equals

      public boolean equals(Object other)
      Test for the equality of two vector instances.

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

      NaN coordinates are considered to globally affect the vector and be equal to each other - i.e, if either (or all) coordinates of the vector are equal to Double.NaN, the vector is equal to NaN.

      Overrides:
      equals in class Object
      Parameters:
      other - Object to test for equality to this
      Returns:
      true if two Vector2D objects are equal, false if object is null, not an instance of Vector2D, or not equal to this Vector2D instance
    • toString

      public String toString()
      Overrides:
      toString in class Object
    • getComponent

      private <T extends Vector2D> T getComponent(Vector2D base, boolean reject, DoubleFunction2N<T> factory)
      Returns a component of the current instance relative to the given base vector. If reject is true, the vector rejection is returned; otherwise, the projection is returned.
      Type Parameters:
      T - Vector implementation type
      Parameters:
      base - The base vector
      reject - If true, the rejection of this instance from base is returned. If false, the projection of this instance onto base is returned.
      factory - factory function used to build the final vector
      Returns:
      The projection or rejection of this instance relative to base, depending on the value of reject.
      Throws:
      IllegalArgumentException - if base has a zero, NaN, or infinite norm
    • of

      public static Vector2D of(double x, double y)
      Returns a vector with the given coordinate values.
      Parameters:
      x - abscissa (first coordinate value)
      y - abscissa (second coordinate value)
      Returns:
      vector instance
    • of

      public static Vector2D of(double[] v)
      Creates a vector from the coordinates in the given 2-element array.
      Parameters:
      v - coordinates array
      Returns:
      new vector
      Throws:
      IllegalArgumentException - if the array does not have 2 elements
    • parse

      public static Vector2D parse(String str)
      Parses the given string and returns a new vector instance. The expected string format is the same as that returned by toString().
      Parameters:
      str - the string to parse
      Returns:
      vector instance represented by the string
      Throws:
      IllegalArgumentException - if the given string has an invalid format
    • max

      public static Vector2D max(Vector2D first, Vector2D... more)
      Return a vector containing the maximum component values from all input vectors.
      Parameters:
      first - first vector
      more - additional vectors
      Returns:
      a vector containing the maximum component values from all input vectors
    • max

      public static Vector2D max(Iterable<Vector2D> vecs)
      Return a vector containing the maximum component values from all input vectors.
      Parameters:
      vecs - input vectors
      Returns:
      a vector containing the maximum component values from all input vectors
      Throws:
      IllegalArgumentException - if the argument does not contain any vectors
    • computeMax

      private static Vector2D computeMax(Vector2D first, Iterator<? extends Vector2D> more)
      Internal method for computing a max vector.
      Parameters:
      first - first vector
      more - iterator with additional vectors
      Returns:
      vector containing the maximum component values of all input vectors
    • min

      public static Vector2D min(Vector2D first, Vector2D... more)
      Return a vector containing the minimum component values from all input vectors.
      Parameters:
      first - first vector
      more - more vectors
      Returns:
      a vector containing the minimum component values from all input vectors
    • min

      public static Vector2D min(Iterable<Vector2D> vecs)
      Return a vector containing the minimum component values from all input vectors.
      Parameters:
      vecs - input vectors
      Returns:
      a vector containing the minimum component values from all input vectors
      Throws:
      IllegalArgumentException - if the argument does not contain any vectors
    • computeMin

      private static Vector2D computeMin(Vector2D first, Iterator<? extends Vector2D> more)
      Internal method for computing a min vector.
      Parameters:
      first - first vector
      more - iterator with additional vectors
      Returns:
      vector containing the minimum component values of all input vectors
    • centroid

      public static Vector2D centroid(Vector2D first, Vector2D... more)
      Compute the centroid of the given points. The centroid is the arithmetic mean position of a set of points.
      Parameters:
      first - first point
      more - additional points
      Returns:
      the centroid of the given points
    • centroid

      public static Vector2D centroid(Iterable<Vector2D> pts)
      Compute the centroid of the given points. The centroid is the arithmetic mean position of a set of points.
      Parameters:
      pts - the points to compute the centroid of
      Returns:
      the centroid of the given points
      Throws:
      IllegalArgumentException - if the argument contains no points
    • computeCentroid

      private static Vector2D computeCentroid(Vector2D first, Iterator<? extends Vector2D> more)
      Internal method for computing the centroid of a set of points.
      Parameters:
      first - first point
      more - iterator with additional points
      Returns:
      the centroid of the point set