FieldVector3D (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.geometry.euclidean.threed.FieldVector3D<T>

Type Parameters:
T - the type of the field elements

All Implemented Interfaces:

Serializable
```
public class FieldVector3D<T extends RealFieldElement<T>>
extends Object
implements Serializable
```
This class is a re-implementation of Vector3D using RealFieldElement.
Instance of this class are guaranteed to be immutable.

Since:

3.2

See Also:
Serialized Form

Constructor Summary

Constructors
Constructor and Description
`FieldVector3D(double a, FieldVector3D<T> u)` Multiplicative constructor Build a vector from another one and a scale factor.
`FieldVector3D(double a1, FieldVector3D<T> u1, double a2, FieldVector3D<T> u2)` Linear constructor Build a vector from two other ones and corresponding scale factors.
`FieldVector3D(double a1, FieldVector3D<T> u1, double a2, FieldVector3D<T> u2, double a3, FieldVector3D<T> u3)` Linear constructor Build a vector from three other ones and corresponding scale factors.
`FieldVector3D(double a1, FieldVector3D<T> u1, double a2, FieldVector3D<T> u2, double a3, FieldVector3D<T> u3, double a4, FieldVector3D<T> u4)` Linear constructor Build a vector from four other ones and corresponding scale factors.
`FieldVector3D(T[] v)` Simple constructor.
`FieldVector3D(T a, FieldVector3D<T> u)` Multiplicative constructor Build a vector from another one and a scale factor.
`FieldVector3D(T a1, FieldVector3D<T> u1, T a2, FieldVector3D<T> u2)` Linear constructor Build a vector from two other ones and corresponding scale factors.
`FieldVector3D(T a1, FieldVector3D<T> u1, T a2, FieldVector3D<T> u2, T a3, FieldVector3D<T> u3)` Linear constructor Build a vector from three other ones and corresponding scale factors.
`FieldVector3D(T a1, FieldVector3D<T> u1, T a2, FieldVector3D<T> u2, T a3, FieldVector3D<T> u3, T a4, FieldVector3D<T> u4)` Linear constructor Build a vector from four other ones and corresponding scale factors.
`FieldVector3D(T alpha, T delta)` Simple constructor.
`FieldVector3D(T x, T y, T z)` Simple constructor.
`FieldVector3D(T a, Vector3D u)` Multiplicative constructor Build a vector from another one and a scale factor.
`FieldVector3D(T a1, Vector3D u1, T a2, Vector3D u2)` Linear constructor Build a vector from two other ones and corresponding scale factors.
`FieldVector3D(T a1, Vector3D u1, T a2, Vector3D u2, T a3, Vector3D u3)` Linear constructor Build a vector from three other ones and corresponding scale factors.
`FieldVector3D(T a1, Vector3D u1, T a2, Vector3D u2, T a3, Vector3D u3, T a4, Vector3D u4)` Linear constructor Build a vector from four other ones and corresponding scale factors.

Method Summary

Methods
Modifier and Type	Method and Description
`FieldVector3D<T>`	`add(double factor, FieldVector3D<T> v)` Add a scaled vector to the instance.
`FieldVector3D<T>`	`add(double factor, Vector3D v)` Add a scaled vector to the instance.
`FieldVector3D<T>`	`add(FieldVector3D<T> v)` Add a vector to the instance.
`FieldVector3D<T>`	`add(T factor, FieldVector3D<T> v)` Add a scaled vector to the instance.
`FieldVector3D<T>`	`add(T factor, Vector3D v)` Add a scaled vector to the instance.
`FieldVector3D<T>`	`add(Vector3D v)` Add a vector to the instance.
`static <T extends RealFieldElement<T>> T`	`angle(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the angular separation between two vectors.
`static <T extends RealFieldElement<T>> T`	`angle(FieldVector3D<T> v1, Vector3D v2)` Compute the angular separation between two vectors.
`static <T extends RealFieldElement<T>> T`	`angle(Vector3D v1, FieldVector3D<T> v2)` Compute the angular separation between two vectors.
`FieldVector3D<T>`	`crossProduct(FieldVector3D<T> v)` Compute the cross-product of the instance with another vector.
`static <T extends RealFieldElement<T>> FieldVector3D<T>`	`crossProduct(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the cross-product of two vectors.
`static <T extends RealFieldElement<T>> FieldVector3D<T>`	`crossProduct(FieldVector3D<T> v1, Vector3D v2)` Compute the cross-product of two vectors.
`FieldVector3D<T>`	`crossProduct(Vector3D v)` Compute the cross-product of the instance with another vector.
`static <T extends RealFieldElement<T>> FieldVector3D<T>`	`crossProduct(Vector3D v1, FieldVector3D<T> v2)` Compute the cross-product of two vectors.
`T`	`distance(FieldVector3D<T> v)` Compute the distance between the instance and another vector according to the L₂ norm.
`static <T extends RealFieldElement<T>> T`	`distance(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L₂ norm.
`static <T extends RealFieldElement<T>> T`	`distance(FieldVector3D<T> v1, Vector3D v2)` Compute the distance between two vectors according to the L₂ norm.
`T`	`distance(Vector3D v)` Compute the distance between the instance and another vector according to the L₂ norm.
`static <T extends RealFieldElement<T>> T`	`distance(Vector3D v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L₂ norm.
`T`	`distance1(FieldVector3D<T> v)` Compute the distance between the instance and another vector according to the L₁ norm.
`static <T extends RealFieldElement<T>> T`	`distance1(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L₁ norm.
`static <T extends RealFieldElement<T>> T`	`distance1(FieldVector3D<T> v1, Vector3D v2)` Compute the distance between two vectors according to the L₁ norm.
`T`	`distance1(Vector3D v)` Compute the distance between the instance and another vector according to the L₁ norm.
`static <T extends RealFieldElement<T>> T`	`distance1(Vector3D v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L₁ norm.
`T`	`distanceInf(FieldVector3D<T> v)` Compute the distance between the instance and another vector according to the L_∞ norm.
`static <T extends RealFieldElement<T>> T`	`distanceInf(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L_∞ norm.
`static <T extends RealFieldElement<T>> T`	`distanceInf(FieldVector3D<T> v1, Vector3D v2)` Compute the distance between two vectors according to the L_∞ norm.
`T`	`distanceInf(Vector3D v)` Compute the distance between the instance and another vector according to the L_∞ norm.
`static <T extends RealFieldElement<T>> T`	`distanceInf(Vector3D v1, FieldVector3D<T> v2)` Compute the distance between two vectors according to the L_∞ norm.
`T`	`distanceSq(FieldVector3D<T> v)` Compute the square of the distance between the instance and another vector.
`static <T extends RealFieldElement<T>> T`	`distanceSq(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the square of the distance between two vectors.
`static <T extends RealFieldElement<T>> T`	`distanceSq(FieldVector3D<T> v1, Vector3D v2)` Compute the square of the distance between two vectors.
`T`	`distanceSq(Vector3D v)` Compute the square of the distance between the instance and another vector.
`static <T extends RealFieldElement<T>> T`	`distanceSq(Vector3D v1, FieldVector3D<T> v2)` Compute the square of the distance between two vectors.
`T`	`dotProduct(FieldVector3D<T> v)` Compute the dot-product of the instance and another vector.
`static <T extends RealFieldElement<T>> T`	`dotProduct(FieldVector3D<T> v1, FieldVector3D<T> v2)` Compute the dot-product of two vectors.
`static <T extends RealFieldElement<T>> T`	`dotProduct(FieldVector3D<T> v1, Vector3D v2)` Compute the dot-product of two vectors.
`T`	`dotProduct(Vector3D v)` Compute the dot-product of the instance and another vector.
`static <T extends RealFieldElement<T>> T`	`dotProduct(Vector3D v1, FieldVector3D<T> v2)` Compute the dot-product of two vectors.
`boolean`	`equals(Object other)` Test for the equality of two 3D vectors.
`T`	`getAlpha()` Get the azimuth of the vector.
`T`	`getDelta()` Get the elevation of the vector.
`T`	`getNorm()` Get the L₂ norm for the vector.
`T`	`getNorm1()` Get the L₁ norm for the vector.
`T`	`getNormInf()` Get the L_∞ norm for the vector.
`T`	`getNormSq()` Get the square of the norm for the vector.
`T`	`getX()` Get the abscissa of the vector.
`T`	`getY()` Get the ordinate of the vector.
`T`	`getZ()` Get the height of the vector.
`int`	`hashCode()` Get a hashCode for the 3D vector.
`boolean`	`isInfinite()` Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
`boolean`	`isNaN()` Returns true if any coordinate of this vector is NaN; false otherwise
`FieldVector3D<T>`	`negate()` Get the opposite of the instance.
`FieldVector3D<T>`	`normalize()` Get a normalized vector aligned with the instance.
`FieldVector3D<T>`	`orthogonal()` Get a vector orthogonal to the instance.
`FieldVector3D<T>`	`scalarMultiply(double a)` Multiply the instance by a scalar.
`FieldVector3D<T>`	`scalarMultiply(T a)` Multiply the instance by a scalar.
`FieldVector3D<T>`	`subtract(double factor, FieldVector3D<T> v)` Subtract a scaled vector from the instance.
`FieldVector3D<T>`	`subtract(double factor, Vector3D v)` Subtract a scaled vector from the instance.
`FieldVector3D<T>`	`subtract(FieldVector3D<T> v)` Subtract a vector from the instance.
`FieldVector3D<T>`	`subtract(T factor, FieldVector3D<T> v)` Subtract a scaled vector from the instance.
`FieldVector3D<T>`	`subtract(T factor, Vector3D v)` Subtract a scaled vector from the instance.
`FieldVector3D<T>`	`subtract(Vector3D v)` Subtract a vector from the instance.
`T[]`	`toArray()` Get the vector coordinates as a dimension 3 array.
`String`	`toString()` Get a string representation of this vector.
`String`	`toString(NumberFormat format)` Get a string representation of this vector.
`Vector3D`	`toVector3D()` Convert to a constant vector without derivatives.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - FieldVector3D
```
public FieldVector3D(T x,
             T y,
             T z)
```
    Simple constructor. Build a vector from its coordinates
    
    Parameters:
    x - abscissa
    y - ordinate
    z - height
    See Also:
    getX(), getY(), getZ()
  - FieldVector3D
```
public FieldVector3D(T[] v)
              throws DimensionMismatchException
```
    Simple constructor. Build a vector from its coordinates
    
    Parameters:
    v - coordinates array
    
    Throws:
    
    DimensionMismatchException - if array does not have 3 elements
    See Also:
    toArray()
  - FieldVector3D
```
public FieldVector3D(T alpha,
             T delta)
```
    Simple constructor. Build a vector from its azimuthal coordinates
    
    Parameters:
    alpha - azimuth (α) around Z (0 is +X, π/2 is +Y, π is -X and 3π/2 is -Y)
    delta - elevation (δ) above (XY) plane, from -π/2 to +π/2
    See Also:
    getAlpha(), getDelta()
  - FieldVector3D
```
public FieldVector3D(T a,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a,
             Vector3D 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
  - FieldVector3D
```
public FieldVector3D(double a,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             FieldVector3D<T> u1,
             T a2,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             Vector3D u1,
             T a2,
             Vector3D 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
  - FieldVector3D
```
public FieldVector3D(double a1,
             FieldVector3D<T> u1,
             double a2,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             FieldVector3D<T> u1,
             T a2,
             FieldVector3D<T> u2,
             T a3,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             Vector3D u1,
             T a2,
             Vector3D u2,
             T a3,
             Vector3D 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
  - FieldVector3D
```
public FieldVector3D(double a1,
             FieldVector3D<T> u1,
             double a2,
             FieldVector3D<T> u2,
             double a3,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             FieldVector3D<T> u1,
             T a2,
             FieldVector3D<T> u2,
             T a3,
             FieldVector3D<T> u3,
             T a4,
             FieldVector3D<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
  - FieldVector3D
```
public FieldVector3D(T a1,
             Vector3D u1,
             T a2,
             Vector3D u2,
             T a3,
             Vector3D u3,
             T a4,
             Vector3D 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
  - FieldVector3D
```
public FieldVector3D(double a1,
             FieldVector3D<T> u1,
             double a2,
             FieldVector3D<T> u2,
             double a3,
             FieldVector3D<T> u3,
             double a4,
             FieldVector3D<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
- Method Detail
  - getX
```
public T getX()
```
    Get the abscissa of the vector.
    
    Returns:
    abscissa of the vector
    See Also:
    FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
  - getY
```
public T getY()
```
    Get the ordinate of the vector.
    
    Returns:
    ordinate of the vector
    See Also:
    FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
  - getZ
```
public T getZ()
```
    Get the height of the vector.
    
    Returns:
    height of the vector
    See Also:
    FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
  - toArray
```
public T[] toArray()
```
    Get the vector coordinates as a dimension 3 array.
    
    Returns:
    vector coordinates
    See Also:
    FieldVector3D(RealFieldElement[])
  - toVector3D
```
public Vector3D toVector3D()
```
    Convert to a constant vector without derivatives.
    
    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
  - getAlpha
```
public T getAlpha()
```
    Get the azimuth of the vector.
    
    Returns:
    azimuth (α) of the vector, between -π and +π
    See Also:
    FieldVector3D(RealFieldElement, RealFieldElement)
  - getDelta
```
public T getDelta()
```
    Get the elevation of the vector.
    
    Returns:
    elevation (δ) of the vector, between -π/2 and +π/2
    See Also:
    FieldVector3D(RealFieldElement, RealFieldElement)
  - add
```
public FieldVector3D<T> add(FieldVector3D<T> v)
```
    Add a vector to the instance.
    
    Parameters:
    v - vector to add
    
    Returns:
    a new vector
  - add
```
public FieldVector3D<T> add(Vector3D v)
```
    Add a vector to the instance.
    
    Parameters:
    v - vector to add
    
    Returns:
    a new vector
  - add
```
public FieldVector3D<T> add(T factor,
                   FieldVector3D<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 FieldVector3D<T> add(T factor,
                   Vector3D 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 FieldVector3D<T> add(double factor,
                   FieldVector3D<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 FieldVector3D<T> add(double factor,
                   Vector3D 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 FieldVector3D<T> subtract(FieldVector3D<T> v)
```
    Subtract a vector from the instance.
    
    Parameters:
    v - vector to subtract
    
    Returns:
    a new vector
  - subtract
```
public FieldVector3D<T> subtract(Vector3D v)
```
    Subtract a vector from the instance.
    
    Parameters:
    v - vector to subtract
    
    Returns:
    a new vector
  - subtract
```
public FieldVector3D<T> subtract(T factor,
                        FieldVector3D<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 FieldVector3D<T> subtract(T factor,
                        Vector3D 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 FieldVector3D<T> subtract(double factor,
                        FieldVector3D<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 FieldVector3D<T> subtract(double factor,
                        Vector3D 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 FieldVector3D<T> normalize()
                                                       throws MathArithmeticException
```
    Get a normalized vector aligned with the instance.
    
    Returns:
    a new normalized vector
    
    Throws:
    
    MathArithmeticException - if the norm is zero
  - orthogonal
```
public FieldVector3D<T> orthogonal()
                                                        throws MathArithmeticException
```
    Get a vector orthogonal to the instance.
    There are an infinite number of normalized vectors orthogonal to the instance. This method picks up one of them almost arbitrarily. It is useful when one needs to compute a reference frame with one of the axes in a predefined direction. The following example shows how to build a frame having the k axis aligned with the known vector u :
```
   Vector3D k = u.normalize();
   Vector3D i = k.orthogonal();
   Vector3D j = Vector3D.crossProduct(k, i);
 
```
    Returns:
    a new normalized vector orthogonal to the instance
    
    Throws:
    
    MathArithmeticException - if the norm of the instance is null
  - angle
```
public static <T extends RealFieldElement<T>> T angle(FieldVector3D<T> v1,
                                      FieldVector3D<T> v2)
                                        throws MathArithmeticException
```
    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:
    
    MathArithmeticException - if either vector has a null norm
  - angle
```
public static <T extends RealFieldElement<T>> T angle(FieldVector3D<T> v1,
                                      Vector3D v2)
                                        throws MathArithmeticException
```
    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:
    
    MathArithmeticException - if either vector has a null norm
  - angle
```
public static <T extends RealFieldElement<T>> T angle(Vector3D v1,
                                      FieldVector3D<T> v2)
                                        throws MathArithmeticException
```
    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:
    
    MathArithmeticException - if either vector has a null norm
  - negate
```
public FieldVector3D<T> negate()
```
    Get the opposite of the instance.
    
    Returns:
    a new vector which is opposite to the instance
  - scalarMultiply
```
public FieldVector3D<T> scalarMultiply(T a)
```
    Multiply the instance by a scalar.
    
    Parameters:
    a - scalar
    
    Returns:
    a new vector
  - scalarMultiply
```
public FieldVector3D<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 3D vectors.
    If all coordinates of two 3D vectors are exactly the same, and none of their real part are NaN, the two 3D 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 3D vector is NaN.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    other - Object to test for equality to this
    
    Returns:
    true if two 3D vector objects are equal, false if object is null, not an instance of Vector3D, or not equal to this Vector3D 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
  - dotProduct
```
public T dotProduct(FieldVector3D<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(Vector3D 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 FieldVector3D<T> crossProduct(FieldVector3D<T> v)
```
    Compute the cross-product of the instance with another vector.
    
    Parameters:
    v - other vector
    
    Returns:
    the cross product this ^ v as a new Vector3D
  - crossProduct
```
public FieldVector3D<T> crossProduct(Vector3D v)
```
    Compute the cross-product of the instance with another vector.
    
    Parameters:
    v - other vector
    
    Returns:
    the cross product this ^ v as a new Vector3D
  - distance1
```
public T distance1(FieldVector3D<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(Vector3D 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(FieldVector3D<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(Vector3D 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(FieldVector3D<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(Vector3D 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(FieldVector3D<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(Vector3D 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 static <T extends RealFieldElement<T>> T dotProduct(FieldVector3D<T> v1,
                                           FieldVector3D<T> v2)
```
    Compute the dot-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the dot product v1.v2
  - dotProduct
```
public static <T extends RealFieldElement<T>> T dotProduct(FieldVector3D<T> v1,
                                           Vector3D v2)
```
    Compute the dot-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the dot product v1.v2
  - dotProduct
```
public static <T extends RealFieldElement<T>> T dotProduct(Vector3D v1,
                                           FieldVector3D<T> v2)
```
    Compute the dot-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the dot product v1.v2
  - crossProduct
```
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(FieldVector3D<T> v1,
                                                            FieldVector3D<T> v2)
```
    Compute the cross-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the cross product v1 ^ v2 as a new Vector
  - crossProduct
```
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(FieldVector3D<T> v1,
                                                            Vector3D v2)
```
    Compute the cross-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the cross product v1 ^ v2 as a new Vector
  - crossProduct
```
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(Vector3D v1,
                                                            FieldVector3D<T> v2)
```
    Compute the cross-product of two vectors.
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the cross product v1 ^ v2 as a new Vector
  - distance1
```
public static <T extends RealFieldElement<T>> T distance1(FieldVector3D<T> v1,
                                          FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L₁ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm1() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₁ norm
  - distance1
```
public static <T extends RealFieldElement<T>> T distance1(FieldVector3D<T> v1,
                                          Vector3D v2)
```
    Compute the distance between two vectors according to the L₁ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm1() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₁ norm
  - distance1
```
public static <T extends RealFieldElement<T>> T distance1(Vector3D v1,
                                          FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L₁ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm1() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₁ norm
  - distance
```
public static <T extends RealFieldElement<T>> T distance(FieldVector3D<T> v1,
                                         FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L₂ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₂ norm
  - distance
```
public static <T extends RealFieldElement<T>> T distance(FieldVector3D<T> v1,
                                         Vector3D v2)
```
    Compute the distance between two vectors according to the L₂ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₂ norm
  - distance
```
public static <T extends RealFieldElement<T>> T distance(Vector3D v1,
                                         FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L₂ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNorm() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L₂ norm
  - distanceInf
```
public static <T extends RealFieldElement<T>> T distanceInf(FieldVector3D<T> v1,
                                            FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L_∞ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormInf() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L_∞ norm
  - distanceInf
```
public static <T extends RealFieldElement<T>> T distanceInf(FieldVector3D<T> v1,
                                            Vector3D v2)
```
    Compute the distance between two vectors according to the L_∞ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormInf() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L_∞ norm
  - distanceInf
```
public static <T extends RealFieldElement<T>> T distanceInf(Vector3D v1,
                                            FieldVector3D<T> v2)
```
    Compute the distance between two vectors according to the L_∞ norm.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormInf() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the distance between v1 and v2 according to the L_∞ norm
  - distanceSq
```
public static <T extends RealFieldElement<T>> T distanceSq(FieldVector3D<T> v1,
                                           FieldVector3D<T> v2)
```
    Compute the square of the distance between two vectors.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormSq() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the square of the distance between v1 and v2
  - distanceSq
```
public static <T extends RealFieldElement<T>> T distanceSq(FieldVector3D<T> v1,
                                           Vector3D v2)
```
    Compute the square of the distance between two vectors.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormSq() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the square of the distance between v1 and v2
  - distanceSq
```
public static <T extends RealFieldElement<T>> T distanceSq(Vector3D v1,
                                           FieldVector3D<T> v2)
```
    Compute the square of the distance between two vectors.
    Calling this method is equivalent to calling: v1.subtract(v2).getNormSq() except that no intermediate vector is built
    
    Type Parameters:
    T - the type of the field elements
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the square of the distance between v1 and v2
  - 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

Class FieldVector3D<T extends RealFieldElement<T>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

FieldVector3D

Method Detail

getX

getY

getZ

toArray

toVector3D

getNorm1

getNorm

getNormSq

getNormInf

getAlpha

getDelta

add

add

add

add

add

add

subtract

subtract

subtract

subtract

subtract

subtract

normalize

orthogonal

angle

angle

angle

negate

scalarMultiply

scalarMultiply

isNaN

isInfinite

equals

hashCode

dotProduct

dotProduct

crossProduct

crossProduct

distance1

distance1

distance

distance

distanceInf

distanceInf

distanceSq

distanceSq

dotProduct

dotProduct

dotProduct

crossProduct

crossProduct

crossProduct

distance1

distance1

distance1

distance

distance

distance