Package org.hipparchus.geometry.euclidean.twod

Class FieldVector2D<T extends CalculusFieldElement<T>>

java.lang.Object
org.hipparchus.geometry.euclidean.twod.FieldVector2D<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 Details

    • FieldVector2D

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

    • FieldVector2D

      public FieldVector2D(T[] v) throws MathIllegalArgumentException
      Simple constructor. Build a vector from its coordinates
      Parameters:
      v - coordinates array
      Throws:
      MathIllegalArgumentException - if array does not have 2 elements
      See Also:

    • 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 Details

    • 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

    • getX

      public T getX()
      Get the abscissa of the vector.
      Returns:
      abscissa of the vector
      See Also:

    • getY

      public T getY()
      Get the ordinate of the vector.
      Returns:
      ordinate of the vector
      See Also:

    • toArray

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

    • 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

    • normalize

      public FieldVector2D<T> normalize() throws MathRuntimeException
      Get a normalized vector aligned with the instance.
      Returns:
      a new normalized vector
      Throws:
      MathRuntimeException - if the norm is zero

    • 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:

    • 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:

    • 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:

    • 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:

    • 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