Class Vector2D

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description
      static class  Vector2D.Sum
      Class used to create high-accuracy sums of vectors.
      static class  Vector2D.Unit
      Represents unit vectors.
    • Field Summary

      Fields 
      Modifier and Type Field Description
      static java.util.Comparator<Vector2D> COORDINATE_ASCENDING_ORDER
      Comparator that sorts vectors in component-wise ascending order.
      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.
      private double x
      Abscissa (first coordinate).
      private double y
      Ordinate (second coordinate).
      static Vector2D ZERO
      Zero vector (coordinates: 0, 0).
    • Constructor Summary

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

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      Vector2D add​(double factor, Vector2D v)
      Add a scaled vector to the instance.
      Vector2D add​(Vector2D v)
      Add a vector to the instance.
      double angle​(Vector2D v)
      Compute the angular separation between two vectors in radians.
      static Vector2D centroid​(java.lang.Iterable<Vector2D> pts)
      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, java.util.Iterator<? extends Vector2D> more)
      Internal method for computing the centroid of a set of points.
      private static Vector2D computeMax​(Vector2D first, java.util.Iterator<? extends Vector2D> more)
      Internal method for computing a max vector.
      private static Vector2D computeMin​(Vector2D first, java.util.Iterator<? extends Vector2D> more)
      Internal method for computing a min vector.
      Vector2D.Unit directionTo​(Vector2D v)
      Return the unit vector representing the direction of displacement from this vector to the given vector.
      double distance​(Vector2D v)
      Compute the distance between the instance and another vector.
      double distanceSq​(Vector2D v)
      Compute the square of the distance between the instance and another vector.
      double dot​(Vector2D v)
      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​(java.lang.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 getDimension()
      Returns the number of dimensions in the space that this element belongs to.
      double getX()
      Returns the abscissa (first coordinate value) of the instance.
      double getY()
      Returns the ordinate (second coordinate value) of the instance.
      Vector2D getZero()
      Get the zero (null) vector of the space.
      int hashCode()
      Get a hashCode for the 2D coordinates.
      boolean isFinite()
      Returns true if all values in this element are finite, meaning they are not NaN or infinite.
      boolean isInfinite()
      Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.
      boolean isNaN()
      Returns true if any value in this element is NaN; otherwise returns false.
      Vector2D lerp​(Vector2D p, double t)
      Get a vector constructed by linearly interpolating between this vector and the given vector.
      static Vector2D max​(java.lang.Iterable<Vector2D> vecs)
      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 min​(java.lang.Iterable<Vector2D> vecs)
      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.
      Vector2D multiply​(double a)
      Multiply the instance by a scalar.
      Vector2D negate()
      Get the negation of the instance.
      double norm()
      Get the L2 norm (commonly known as the Euclidean norm) for the vector.
      Vector2D.Unit normalize()
      Get a normalized vector aligned with the instance.
      Vector2D.Unit normalizeOrNull()
      Attempt to compute a normalized vector aligned with the instance, returning null if such a vector cannot be computed.
      double normSq()
      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.
      Vector2D.Unit orthogonal()
      Get a unit vector orthogonal to the instance.
      Vector2D.Unit orthogonal​(Vector2D dir)
      Get a unit vector orthogonal to the current vector and pointing in the direction of dir.
      static Vector2D parse​(java.lang.String str)
      Parses the given string and returns a new vector instance.
      Vector2D project​(Vector2D base)
      Get the projection of the instance onto the given base vector.
      Vector2D reject​(Vector2D base)
      Get the rejection of the instance from the given base vector.
      double signedArea​(Vector2D v)
      Compute the signed area of the parallelogram with sides formed by this instance and the given vector.
      Vector2D subtract​(double factor, Vector2D v)
      Subtract a scaled vector from the instance.
      Vector2D subtract​(Vector2D v)
      Subtract a vector from the instance.
      double[] toArray()
      Get the coordinates for this instance as a dimension 2 array.
      java.lang.String toString()
      Vector2D transform​(java.util.function.UnaryOperator<Vector2D> fn)
      Convenience method to apply a function to this vector.
      Vector2D vectorTo​(Vector2D v)
      Return the vector representing the displacement from this vector to the given vector.
      Vector2D withNorm​(double magnitude)
      Returns a vector with the same direction but with the given norm.
      • Methods inherited from class java.lang.Object

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

      • 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 java.util.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 Detail

      • Vector2D

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

      • 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:
        L2 Norm
      • 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:
        Vector.norm()
      • 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:
        Vector.normalizeOrNull()
      • 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:
        Vector.normalize()
      • 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:
        Vector.normSq()
      • 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
      • 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:
        java.lang.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​(java.util.function.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 java.lang.Object
        Returns:
        a hash code value for this object
      • equals

        public boolean equals​(java.lang.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 java.lang.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 java.lang.String toString()
        Overrides:
        toString in class java.lang.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:
        java.lang.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:
        java.lang.IllegalArgumentException - if the array does not have 2 elements
      • parse

        public static Vector2D parse​(java.lang.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:
        java.lang.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​(java.lang.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:
        java.lang.IllegalArgumentException - if the argument does not contain any vectors
      • computeMax

        private static Vector2D computeMax​(Vector2D first,
                                           java.util.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​(java.lang.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:
        java.lang.IllegalArgumentException - if the argument does not contain any vectors
      • computeMin

        private static Vector2D computeMin​(Vector2D first,
                                           java.util.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​(java.lang.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:
        java.lang.IllegalArgumentException - if the argument contains no points
      • computeCentroid

        private static Vector2D computeCentroid​(Vector2D first,
                                                java.util.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