org.apache.commons.math3.geometry.euclidean.threed
Class Vector3D

java.lang.Object
  org.apache.commons.math3.geometry.euclidean.threed.Vector3D

All Implemented Interfaces:

Serializable, Vector<Euclidean3D>

public class Vector3D
extends Object
implements Serializable, Vector<Euclidean3D>

This class implements vectors in a three-dimensional space.

Instance of this class are guaranteed to be immutable.

Since:

1.2

Version:

$Id: Vector3D.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Serialized Form

Field Summary

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

Vector3D(double[] v)
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.

Vector3D(RealVector vector)
From a RealVector constructor Build a vector from a RealVector object.

Method Summary

Vector3D	add(double factor, Vector<Euclidean3D> v) Add a scaled vector to the instance.
Vector3D	add(Vector<Euclidean3D> v) Add a vector to the instance.
static double	angle(Vector3D v1, Vector3D v2) Compute the angular separation between two vectors.
Vector3D	crossProduct(Vector<Euclidean3D> v) Compute the cross-product of the instance with another vector.
static Vector3D	crossProduct(Vector3D v1, Vector3D v2) Compute the cross-product of two vectors.
double	distance(Vector<Euclidean3D> v) Compute the distance between the instance and another vector according to the L2 norm.
static double	distance(Vector3D v1, Vector3D v2) Compute the distance between two vectors according to the L2 norm.
double	distance1(Vector<Euclidean3D> v) Compute the distance between the instance and another vector according to the L1 norm.
static double	distance1(Vector3D v1, Vector3D v2) Compute the distance between two vectors according to the L1 norm.
double	distanceInf(Vector<Euclidean3D> v) Compute the distance between the instance and another vector according to the L∞ norm.
static double	distanceInf(Vector3D v1, Vector3D v2) Compute the distance between two vectors according to the L∞ norm.
double	distanceSq(Vector<Euclidean3D> v) Compute the square of the distance between the instance and another vector.
static double	distanceSq(Vector3D v1, Vector3D v2) Compute the square of the distance between two vectors.
double	dotProduct(Vector<Euclidean3D> v) Compute the dot-product of the instance and another vector.
static double	dotProduct(Vector3D v1, Vector3D v2) Compute the dot-product of two vectors.
boolean	equals(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.
RealVector	getRealVector() Get a RealVector with identical data.
Space	getSpace() Get the space to which the vector belongs.
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	getZero() Get the null vector of the vectorial space or origin point of the affine space.
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, Vector<Euclidean3D> v) Subtract a scaled vector from the instance.
Vector3D	subtract(Vector<Euclidean3D> v) Subtract a vector from the instance.
double[]	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.

Methods inherited from class java.lang.Object

clone, finalize, 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[] 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()

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

Vector3D

public Vector3D(RealVector vector)

From a RealVector constructor Build a vector from a RealVector object. The input RealVector dimension must be 3.

Parameters:

vector - The RealVector

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)

getRealVector

public RealVector getRealVector()

Get a RealVector with identical data.

Returns:

the RealVector

See Also:

RealVector

toArray

public double[] toArray()

Get the vector coordinates as a dimension 3 array.

Returns:

vector coordinates

See Also:

Vector3D(double[])

getSpace

public Space getSpace()

Get the space to which the vector belongs.

Specified by:

getSpace in interface Vector<Euclidean3D>

Returns:

containing space

getZero

public Vector3D getZero()

Get the null vector of the vectorial space or origin point of the affine space.

Specified by:

getZero in interface Vector<Euclidean3D>

Returns:

null vector of the vectorial space or origin point of the affine space

getNorm1

public double getNorm1()

Get the L₁ norm for the vector.

Specified by:

getNorm1 in interface Vector<Euclidean3D>

Returns:

L₁ norm for the vector

getNorm

public double getNorm()

Get the L₂ norm for the vector.

Specified by:

getNorm in interface Vector<Euclidean3D>

Returns:

Euclidean norm for the vector

getNormSq

public double getNormSq()

Get the square of the norm for the vector.

Specified by:

getNormSq in interface Vector<Euclidean3D>

Returns:

square of the Euclidean norm for the vector

getNormInf

public double getNormInf()

Get the L_∞ norm for the vector.

Specified by:

getNormInf in interface Vector<Euclidean3D>

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(Vector<Euclidean3D> v)

Add a vector to the instance.

Specified by:

add in interface Vector<Euclidean3D>

Parameters:

v - vector to add

Returns:

a new vector

add

public Vector3D add(double factor,
                    Vector<Euclidean3D> v)

Add a scaled vector to the instance.

Specified by:

add in interface Vector<Euclidean3D>

Parameters:

factor - scale factor to apply to v before adding it

v - vector to add

Returns:

a new vector

subtract

public Vector3D subtract(Vector<Euclidean3D> v)

Subtract a vector from the instance.

Specified by:

subtract in interface Vector<Euclidean3D>

Parameters:

v - vector to subtract

Returns:

a new vector

subtract

public Vector3D subtract(double factor,
                         Vector<Euclidean3D> v)

Subtract a scaled vector from the instance.

Specified by:

subtract in interface Vector<Euclidean3D>

Parameters:

factor - scale factor to apply to v before subtracting it

v - vector to subtract

Returns:

a new vector

normalize

public Vector3D normalize()
                   throws MathArithmeticException

Get a normalized vector aligned with the instance.

Specified by:

normalize in interface Vector<Euclidean3D>

Returns:

a new normalized vector

Throws:

MathArithmeticException - if the norm is zero

orthogonal

public Vector3D 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 double angle(Vector3D 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.

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 Vector3D negate()

Get the opposite of the instance.

Specified by:

negate in interface Vector<Euclidean3D>

Returns:

a new vector which is opposite to the instance

scalarMultiply

public Vector3D scalarMultiply(double a)

Multiply the instance by a scalar.

Specified by:

scalarMultiply in interface Vector<Euclidean3D>

Parameters:

a - scalar

Returns:

a new vector

isNaN

public boolean isNaN()

Returns true if any coordinate of this vector is NaN; false otherwise

Specified by:

isNaN in interface Vector<Euclidean3D>

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

Specified by:

isInfinite in interface Vector<Euclidean3D>

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 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 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 double dotProduct(Vector<Euclidean3D> 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.

Specified by:

dotProduct in interface Vector<Euclidean3D>

Parameters:

v - second vector

Returns:

the dot product this.v

See Also:

MathArrays.linearCombination(double, double, double, double, double, double)

crossProduct

public Vector3D crossProduct(Vector<Euclidean3D> 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 double distance1(Vector<Euclidean3D> 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

Specified by:

distance1 in interface Vector<Euclidean3D>

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L₁ norm

distance

public double distance(Vector<Euclidean3D> 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

Specified by:

distance in interface Vector<Euclidean3D>

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L₂ norm

distanceInf

public double distanceInf(Vector<Euclidean3D> 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

Specified by:

distanceInf in interface Vector<Euclidean3D>

Parameters:

v - second vector

Returns:

the distance between the instance and p according to the L_∞ norm

distanceSq

public double distanceSq(Vector<Euclidean3D> 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

Specified by:

distanceSq in interface Vector<Euclidean3D>

Parameters:

v - second vector

Returns:

the square of the distance between the instance and p

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 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.

Specified by:

toString in interface Vector<Euclidean3D>

Parameters:

format - the custom format for components

Returns:

a string representation of this vector