Package org.hipparchus.geometry.euclidean.twod

Class FieldVector2D<T extends CalculusFieldElement<T>>

  • Type Parameters:
    T - the type of the field elements
    public class FieldVector2D<T extends CalculusFieldElement<T>>
extends Object
    This class is a re-implementation of Vector2D using CalculusFieldElement.

    Instance of this class are guaranteed to be immutable.

    Since:
    1.6

    • Constructor Detail

      • FieldVector2D

        public FieldVector2D​(T x,
                     T y)
        Simple constructor. Build a vector from its coordinates
        Parameters:
        x - abscissa
        y - ordinate
        See Also:
        getX(), getY()

      • FieldVector2D

        public FieldVector2D​(T a,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T 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

      • FieldVector2D

        public FieldVector2D​(double a,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     FieldVector2D<T> u1,
                     T a2,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     Vector2D u1,
                     T 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

      • FieldVector2D

        public FieldVector2D​(double a1,
                     FieldVector2D<T> u1,
                     double a2,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     FieldVector2D<T> u1,
                     T a2,
                     FieldVector2D<T> u2,
                     T a3,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     Vector2D u1,
                     T a2,
                     Vector2D u2,
                     T 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

      • FieldVector2D

        public FieldVector2D​(double a1,
                     FieldVector2D<T> u1,
                     double a2,
                     FieldVector2D<T> u2,
                     double a3,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     FieldVector2D<T> u1,
                     T a2,
                     FieldVector2D<T> u2,
                     T a3,
                     FieldVector2D<T> u3,
                     T a4,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(T a1,
                     Vector2D u1,
                     T a2,
                     Vector2D u2,
                     T a3,
                     Vector2D u3,
                     T 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

      • FieldVector2D

        public FieldVector2D​(double a1,
                     FieldVector2D<T> u1,
                     double a2,
                     FieldVector2D<T> u2,
                     double a3,
                     FieldVector2D<T> u3,
                     double a4,
                     FieldVector2D<T> 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

      • FieldVector2D

        public FieldVector2D​(Field<T> field,
                     Vector2D v)
        Build a FieldVector2D from a Vector2D.
        Parameters:
        field - field for the components
        v - vector to convert

    • Method Detail

      • getZero

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getZero​(Field<T> field)
        Get null vector (coordinates: 0, 0).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getPlusI

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getPlusI​(Field<T> field)
        Get first canonical vector (coordinates: 1, 0).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getMinusI

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getMinusI​(Field<T> field)
        Get opposite of the first canonical vector (coordinates: -1).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getPlusJ

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getPlusJ​(Field<T> field)
        Get second canonical vector (coordinates: 0, 1).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getMinusJ

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getMinusJ​(Field<T> field)
        Get opposite of the second canonical vector (coordinates: 0, -1).
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getNaN

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getNaN​(Field<T> field)
        Get a vector with all coordinates set to NaN.
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getPositiveInfinity

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getPositiveInfinity​(Field<T> field)
        Get a vector with all coordinates set to positive infinity.
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • getNegativeInfinity

        public static <T extends CalculusFieldElement<T>> FieldVector2D<T> getNegativeInfinity​(Field<T> field)
        Get a vector with all coordinates set to negative infinity.
        Type Parameters:
        T - the type of the field elements
        Parameters:
        field - field for the components
        Returns:
        a new vector

      • toVector2D

        public Vector2D toVector2D()
        Convert to a constant vector without extra field parts.
        Returns:
        a constant vector

      • getNorm1

        public T getNorm1()
        Get the L1 norm for the vector.
        Returns:
        L1 norm for the vector

      • getNorm

        public T getNorm()
        Get the L2 norm for the vector.
        Returns:
        Euclidean norm for the vector

      • getNormSq

        public T getNormSq()
        Get the square of the norm for the vector.
        Returns:
        square of the Euclidean norm for the vector

      • getNormInf

        public T getNormInf()
        Get the L∞ norm for the vector.
        Returns:
        L∞ norm for the vector

      • add

        public FieldVector2D<T> add​(FieldVector2D<T> v)
        Add a vector to the instance.
        Parameters:
        v - vector to add
        Returns:
        a new vector

      • add

        public FieldVector2D<T> add​(Vector2D v)
        Add a vector to the instance.
        Parameters:
        v - vector to add
        Returns:
        a new vector

      • add

        public FieldVector2D<T> add​(T factor,
                            FieldVector2D<T> 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

      • add

        public FieldVector2D<T> add​(T 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

      • add

        public FieldVector2D<T> add​(double factor,
                            FieldVector2D<T> 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

      • add

        public FieldVector2D<T> 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 FieldVector2D<T> subtract​(FieldVector2D<T> v)
        Subtract a vector from the instance.
        Parameters:
        v - vector to subtract
        Returns:
        a new vector

      • subtract

        public FieldVector2D<T> subtract​(Vector2D v)
        Subtract a vector from the instance.
        Parameters:
        v - vector to subtract
        Returns:
        a new vector

      • subtract

        public FieldVector2D<T> subtract​(T factor,
                                 FieldVector2D<T> 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

      • subtract

        public FieldVector2D<T> subtract​(T 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

      • subtract

        public FieldVector2D<T> subtract​(double factor,
                                 FieldVector2D<T> 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

      • subtract

        public FieldVector2D<T> 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

      • angle

        public static <T extends CalculusFieldElement<T>> T angle​(FieldVector2D<T> v1,
                                                          FieldVector2D<T> 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.

        Type Parameters:
        T - the type of the field elements
        Parameters:
        v1 - first vector
        v2 - second vector
        Returns:
        angular separation between v1 and v2
        Throws:
        MathRuntimeException - if either vector has a null norm

      • angle

        public static <T extends CalculusFieldElement<T>> T angle​(FieldVector2D<T> 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.

        Type Parameters:
        T - the type of the field elements
        Parameters:
        v1 - first vector
        v2 - second vector
        Returns:
        angular separation between v1 and v2
        Throws:
        MathRuntimeException - if either vector has a null norm

      • angle

        public static <T extends CalculusFieldElement<T>> T angle​(Vector2D v1,
                                                          FieldVector2D<T> 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.

        Type Parameters:
        T - the type of the field elements
        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 FieldVector2D<T> negate()
        Get the opposite of the instance.
        Returns:
        a new vector which is opposite to the instance

      • scalarMultiply

        public FieldVector2D<T> scalarMultiply​(T a)
        Multiply the instance by a scalar.
        Parameters:
        a - scalar
        Returns:
        a new vector

      • scalarMultiply

        public FieldVector2D<T> scalarMultiply​(double a)
        Multiply the instance by a scalar.
        Parameters:
        a - scalar
        Returns:
        a new vector

      • isNaN

        public boolean isNaN()
        Returns true if any coordinate of this vector is NaN; false otherwise
        Returns:
        true if any coordinate of this vector is NaN; false otherwise

      • isInfinite

        public boolean isInfinite()
        Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
        Returns:
        true if any coordinate of this vector is infinite and none are NaN; false otherwise

      • 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 of their real part are 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) real part of the coordinates of the 3D vector are NaN, the 2D vector is 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 FieldVector2D, or not equal to this FieldVector2D instance

      • hashCode

        public int hashCode()
        Get a hashCode for the 3D vector.

        All NaN values have the same hash code.

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

      • distance1

        public T distance1​(FieldVector2D<T> v)
        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

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L1 norm

      • distance1

        public T distance1​(Vector2D v)
        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

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L1 norm

      • distance

        public T distance​(FieldVector2D<T> v)
        Compute the distance between the instance and another vector according to the L2 norm.

        Calling this method is equivalent to calling: q.subtract(p).getNorm() except that no intermediate vector is built

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L2 norm

      • distance

        public T distance​(Vector2D v)
        Compute the distance between the instance and another vector according to the L2 norm.

        Calling this method is equivalent to calling: q.subtract(p).getNorm() except that no intermediate vector is built

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L2 norm

      • distanceInf

        public T distanceInf​(FieldVector2D<T> v)
        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

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L∞ norm

      • distanceInf

        public T distanceInf​(Vector2D v)
        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

        Parameters:
        v - second vector
        Returns:
        the distance between the instance and p according to the L∞ norm

      • distanceSq

        public T distanceSq​(FieldVector2D<T> 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

      • distanceSq

        public T 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

      • dotProduct

        public T dotProduct​(FieldVector2D<T> v)
        Compute the dot-product of the instance and another vector.

        The implementation uses specific multiplication and addition algorithms to preserve accuracy and reduce cancellation effects. It should be very accurate even for nearly orthogonal vectors.

        Parameters:
        v - second vector
        Returns:
        the dot product this.v
        See Also:
        MathArrays.linearCombination(double, double, double, double, double, double)

      • dotProduct

        public T dotProduct​(Vector2D v)
        Compute the dot-product of the instance and another vector.

        The implementation uses specific multiplication and addition algorithms to preserve accuracy and reduce cancellation effects. It should be very accurate even for nearly orthogonal vectors.

        Parameters:
        v - second vector
        Returns:
        the dot product this.v
        See Also:
        MathArrays.linearCombination(double, double, double, double, double, double)

      • crossProduct

        public T crossProduct​(FieldVector2D<T> p1,
                      FieldVector2D<T> 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)

      • crossProduct

        public T 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 <T extends CalculusFieldElement<T>> T distance1​(FieldVector2D<T> p1,
                                                              FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distance1

        public static <T extends CalculusFieldElement<T>> T distance1​(FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distance1

        public static <T extends CalculusFieldElement<T>> T distance1​(Vector2D p1,
                                                              FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distance

        public static <T extends CalculusFieldElement<T>> T distance​(FieldVector2D<T> p1,
                                                             FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distance

        public static <T extends CalculusFieldElement<T>> T distance​(FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distance

        public static <T extends CalculusFieldElement<T>> T distance​(Vector2D p1,
                                                             FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L2 norm

      • distanceInf

        public static <T extends CalculusFieldElement<T>> T distanceInf​(FieldVector2D<T> p1,
                                                                FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L∞ norm

      • distanceInf

        public static <T extends CalculusFieldElement<T>> T distanceInf​(FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L∞ norm

      • distanceInf

        public static <T extends CalculusFieldElement<T>> T distanceInf​(Vector2D p1,
                                                                FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the distance between p1 and p2 according to the L∞ norm

      • distanceSq

        public static <T extends CalculusFieldElement<T>> T distanceSq​(FieldVector2D<T> p1,
                                                               FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the square of the distance between p1 and p2

      • distanceSq

        public static <T extends CalculusFieldElement<T>> T distanceSq​(FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the square of the distance between p1 and p2

      • distanceSq

        public static <T extends CalculusFieldElement<T>> T distanceSq​(Vector2D p1,
                                                               FieldVector2D<T> 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

        Type Parameters:
        T - the type of the field elements
        Parameters:
        p1 - first vector
        p2 - second vector
        Returns:
        the square of the distance between p1 and p2

      • orientation

        public static <T extends CalculusFieldElement<T>> T orientation​(FieldVector2D<T> p,
                                                                FieldVector2D<T> q,
                                                                FieldVector2D<T> r)
        Compute the orientation of a triplet of points.
        Type Parameters:
        T - the type of the field elements
        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

      • 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.
        Parameters:
        format - the custom format for components
        Returns:
        a string representation of this vector