Vector3D ("The Adobe AEM Quickstart and Web Application.")

java.lang.Object
- org.apache.commons.math.geometry.Vector3D

All Implemented Interfaces:

java.io.Serializable
```
public class Vector3D
extends java.lang.Object
implements java.io.Serializable
```
This class implements vectors in a three-dimensional space.
Instance of this class are guaranteed to be immutable.

Since:

1.2

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static Vector3D`	`MINUS_I` Opposite of the first canonical vector (coordinates: -1, 0, 0).
`static Vector3D`	`MINUS_J` Opposite of the second canonical vector (coordinates: 0, -1, 0).
`static Vector3D`	`MINUS_K` Opposite of the third canonical vector (coordinates: 0, 0, -1).
`static Vector3D`	`NaN` A vector with all coordinates set to NaN.
`static Vector3D`	`NEGATIVE_INFINITY` A vector with all coordinates set to negative infinity.
`static Vector3D`	`PLUS_I` First canonical vector (coordinates: 1, 0, 0).
`static Vector3D`	`PLUS_J` Second canonical vector (coordinates: 0, 1, 0).
`static Vector3D`	`PLUS_K` Third canonical vector (coordinates: 0, 0, 1).
`static Vector3D`	`POSITIVE_INFINITY` A vector with all coordinates set to positive infinity.
`static Vector3D`	`ZERO` Null vector (coordinates: 0, 0, 0).

Constructor Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Vector3D`	`add(double factor, Vector3D v)` Add a scaled vector to the instance.
`Vector3D`	`add(Vector3D v)` Add a vector to the instance.
`static double`	`angle(Vector3D v1, Vector3D v2)` Compute the angular separation between two vectors.
`static Vector3D`	`crossProduct(Vector3D v1, Vector3D v2)` Compute the cross-product of two vectors.
`static double`	`distance(Vector3D v1, Vector3D v2)` Compute the distance between two vectors according to the L₂ norm.
`static double`	`distance1(Vector3D v1, Vector3D v2)` Compute the distance between two vectors according to the L₁ norm.
`static double`	`distanceInf(Vector3D v1, Vector3D v2)` Compute the distance between two vectors according to the L_∞ norm.
`static double`	`distanceSq(Vector3D v1, Vector3D v2)` Compute the square of the distance between two vectors.
`static double`	`dotProduct(Vector3D v1, Vector3D v2)` Compute the dot-product of two vectors.
`boolean`	`equals(java.lang.Object other)` Test for the equality of two 3D vectors.
`double`	`getAlpha()` Get the azimuth of the vector.
`double`	`getDelta()` Get the elevation of the vector.
`double`	`getNorm()` Get the L₂ norm for the vector.
`double`	`getNorm1()` Get the L₁ norm for the vector.
`double`	`getNormInf()` Get the L_∞ norm for the vector.
`double`	`getNormSq()` Get the square of the norm for the vector.
`double`	`getX()` Get the abscissa of the vector.
`double`	`getY()` Get the ordinate of the vector.
`double`	`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
`Vector3D`	`negate()` Get the opposite of the instance.
`Vector3D`	`normalize()` Get a normalized vector aligned with the instance.
`Vector3D`	`orthogonal()` Get a vector orthogonal to the instance.
`Vector3D`	`scalarMultiply(double a)` Multiply the instance by a scalar
`Vector3D`	`subtract(double factor, Vector3D v)` Subtract a scaled vector from the instance.
`Vector3D`	`subtract(Vector3D v)` Subtract a vector from the instance.
`java.lang.String`	`toString()` Get a string representation of this vector.

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

- Field Detail
  - ZERO
```
public static final Vector3D ZERO
```
    Null vector (coordinates: 0, 0, 0).
  - PLUS_I
```
public static final Vector3D PLUS_I
```
    First canonical vector (coordinates: 1, 0, 0).
  - MINUS_I
```
public static final Vector3D MINUS_I
```
    Opposite of the first canonical vector (coordinates: -1, 0, 0).
  - PLUS_J
```
public static final Vector3D PLUS_J
```
    Second canonical vector (coordinates: 0, 1, 0).
  - MINUS_J
```
public static final Vector3D MINUS_J
```
    Opposite of the second canonical vector (coordinates: 0, -1, 0).
  - PLUS_K
```
public static final Vector3D PLUS_K
```
    Third canonical vector (coordinates: 0, 0, 1).
  - MINUS_K
```
public static final Vector3D MINUS_K
```
    Opposite of the third canonical vector (coordinates: 0, 0, -1).
  - NaN
```
public static final Vector3D NaN
```
    A vector with all coordinates set to NaN.
  - POSITIVE_INFINITY
```
public static final Vector3D POSITIVE_INFINITY
```
    A vector with all coordinates set to positive infinity.
  - NEGATIVE_INFINITY
```
public static final Vector3D NEGATIVE_INFINITY
```
    A vector with all coordinates set to negative infinity.
- Constructor Detail
  - Vector3D
```
public Vector3D(double x,
                double y,
                double z)
```
    Simple constructor. Build a vector from its coordinates
    
    Parameters:
    
    x - abscissa
    
    y - ordinate
    
    z - height
    
    See Also:
    
    getX(), getY(), getZ()
  - Vector3D
```
public Vector3D(double alpha,
                double 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()
  - Vector3D
```
public Vector3D(double 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
  - Vector3D
```
public Vector3D(double a1,
                Vector3D u1,
                double 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
  - Vector3D
```
public Vector3D(double a1,
                Vector3D u1,
                double a2,
                Vector3D u2,
                double 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
  - Vector3D
```
public Vector3D(double a1,
                Vector3D u1,
                double a2,
                Vector3D u2,
                double a3,
                Vector3D u3,
                double 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
- Method Detail
  - getX
```
public double getX()
```
    Get the abscissa of the vector.
    
    Returns:
    
    abscissa of the vector
    
    See Also:
    
    Vector3D(double, double, double)
  - getY
```
public double getY()
```
    Get the ordinate of the vector.
    
    Returns:
    
    ordinate of the vector
    
    See Also:
    
    Vector3D(double, double, double)
  - getZ
```
public double getZ()
```
    Get the height of the vector.
    
    Returns:
    
    height of the vector
    
    See Also:
    
    Vector3D(double, double, double)
  - getNorm1
```
public double getNorm1()
```
    Get the L₁ norm for the vector.
    
    Returns:
    
    L₁ norm for the vector
  - getNorm
```
public double getNorm()
```
    Get the L₂ norm for the vector.
    
    Returns:
    
    euclidian norm for the vector
  - getNormSq
```
public double getNormSq()
```
    Get the square of the norm for the vector.
    
    Returns:
    
    square of the euclidian norm for the vector
  - getNormInf
```
public double getNormInf()
```
    Get the L_∞ norm for the vector.
    
    Returns:
    
    L_∞ norm for the vector
  - getAlpha
```
public double getAlpha()
```
    Get the azimuth of the vector.
    
    Returns:
    
    azimuth (α) of the vector, between -π and +π
    
    See Also:
    
    Vector3D(double, double)
  - getDelta
```
public double getDelta()
```
    Get the elevation of the vector.
    
    Returns:
    
    elevation (δ) of the vector, between -π/2 and +π/2
    
    See Also:
    
    Vector3D(double, double)
  - add
```
public Vector3D add(Vector3D v)
```
    Add a vector to the instance.
    
    Parameters:
    
    v - vector to add
    
    Returns:
    
    a new vector
  - add
```
public Vector3D 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 Vector3D subtract(Vector3D v)
```
    Subtract a vector from the instance.
    
    Parameters:
    
    v - vector to subtract
    
    Returns:
    
    a new vector
  - subtract
```
public Vector3D 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 Vector3D normalize()
```
    Get a normalized vector aligned with the instance.
    
    Returns:
    
    a new normalized vector
    
    Throws:
    
    java.lang.ArithmeticException - if the norm is zero
  - orthogonal
```
public Vector3D orthogonal()
```
    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:
    
    java.lang.ArithmeticException - if the norm of the instance is null
  - angle
```
public static double angle(Vector3D v1,
                           Vector3D v2)
```
    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.
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    angular separation between v1 and v2
    
    Throws:
    
    java.lang.ArithmeticException - if either vector has a null norm
  - negate
```
public Vector3D negate()
```
    Get the opposite of the instance.
    
    Returns:
    
    a new vector which is opposite to the instance
  - scalarMultiply
```
public Vector3D 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(java.lang.Object other)
```
    Test for the equality of two 3D vectors.
    If all coordinates of two 3D vectors are exactly the same, and none are Double.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) coordinates of the 3D vector are equal to Double.NaN, the 3D vector is equal to NaN.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    other - Object to test for equality to this
    
    Returns:
    
    true if two 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 java.lang.Object
    
    Returns:
    
    a hash code value for this object
  - dotProduct
```
public static double dotProduct(Vector3D v1,
                                Vector3D v2)
```
    Compute the dot-product of two vectors.
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the dot product v1.v2
  - crossProduct
```
public static Vector3D crossProduct(Vector3D v1,
                                    Vector3D v2)
```
    Compute the cross-product of two vectors.
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the cross product v1 ^ v2 as a new Vector
  - distance1
```
public static double distance1(Vector3D 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
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the distance between v1 and v2 according to the L₁ norm
  - distance
```
public static double distance(Vector3D 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
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the distance between v1 and v2 according to the L₂ norm
  - distanceInf
```
public static double distanceInf(Vector3D 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
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the distance between v1 and v2 according to the L_∞ norm
  - distanceSq
```
public static double distanceSq(Vector3D 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
    
    Parameters:
    
    v1 - first vector
    
    v2 - second vector
    
    Returns:
    
    the square of the distance between v1 and v2
  - toString
```
public java.lang.String toString()
```
    Get a string representation of this vector.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a string representation of this vector

Class Vector3D

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ZERO

PLUS_I

MINUS_I

PLUS_J

MINUS_J

PLUS_K

MINUS_K

NaN

POSITIVE_INFINITY

NEGATIVE_INFINITY

Constructor Detail

Vector3D

Vector3D

Vector3D

Vector3D

Vector3D

Vector3D

Method Detail

getX

getY

getZ

getNorm1

getNorm

getNormSq

getNormInf

getAlpha

getDelta

add

add

subtract

subtract

normalize

orthogonal

angle

negate

scalarMultiply

isNaN

isInfinite

equals

hashCode

dotProduct

crossProduct

distance1

distance

distanceInf

distanceSq

toString