org.apache.commons.math.geometry
Class Vector3D

java.lang.Object
  extended by 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
Version:
$Revision: 627998 $ $Date: 2008-02-15 03:24:50 -0700 (Fri, 15 Feb 2008) $
See Also:
Serialized Form

Field Summary
static Vector3D minusI
          Opposite of the first canonical vector (coordinates: -1, 0, 0).
static Vector3D minusJ
          Opposite of the second canonical vector (coordinates: 0, -1, 0).
static Vector3D minusK
          Opposite of the third canonical vector (coordinates: 0, 0, -1).
static Vector3D plusI
          First canonical vector (coordinates: 1, 0, 0).
static Vector3D plusJ
          Second canonical vector (coordinates: 0, 1, 0).
static Vector3D plusK
          Third canonical vector (coordinates: 0, 0, 1).
private static long serialVersionUID
          Serializable version identifier
private  double x
          Abscissa.
private  double y
          Ordinate.
private  double z
          Height.
static Vector3D zero
          Null vector (coordinates: 0, 0, 0).
 
Constructor Summary
Vector3D()
          Simple constructor.
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
 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 dotProduct(Vector3D v1, Vector3D v2)
          Compute the dot-product of two vectors.
 double getAlpha()
          Get the azimuth of the vector.
 double getDelta()
          Get the elevation of the vector.
 double getNorm()
          Get 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.
 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.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

plusI

public static final Vector3D plusI
First canonical vector (coordinates: 1, 0, 0).


minusI

public static final Vector3D minusI
Opposite of the first canonical vector (coordinates: -1, 0, 0).


plusJ

public static final Vector3D plusJ
Second canonical vector (coordinates: 0, 1, 0).


minusJ

public static final Vector3D minusJ
Opposite of the second canonical vector (coordinates: 0, -1, 0).


plusK

public static final Vector3D plusK
Third canonical vector (coordinates: 0, 0, 1).


minusK

public static final Vector3D minusK
Opposite of the third canonical vector (coordinates: 0, 0, -1).


zero

public static final Vector3D zero
Null vector (coordinates: 0, 0, 0).


x

private final double x
Abscissa.


y

private final double y
Ordinate.


z

private final double z
Height.


serialVersionUID

private static final long serialVersionUID
Serializable version identifier

See Also:
Constant Field Values
Constructor Detail

Vector3D

public Vector3D()
Simple constructor. Build a null vector.


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)

getNorm

public double getNorm()
Get the norm for the vector.

Returns:
euclidian 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 allow 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

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