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

## Class Vector3D

• All Implemented Interfaces:
Serializable, Point<Euclidean3D>, 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
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[] 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.
• ### Method Summary

Methods
Modifier and Type Method and Description
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(Point<Euclidean3D> v)
Compute the distance between the instance and another point.
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.
Space getSpace()
Get the space to which the point 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 point 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
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
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
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

• #### toArray

public double[] toArray()
Get the vector coordinates as a dimension 3 array.
Returns:
vector coordinates
Vector3D(double[])
• #### getSpace

public Space getSpace()
Get the space to which the point belongs.
Specified by:
getSpace in interface Point<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
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
Vector3D(double, double)

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

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 point is NaN; false otherwise
Specified by:
isNaN in interface Point<Euclidean3D>
Returns:
true if any coordinate of this point 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
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
• #### distance

public double distance(Point<Euclidean3D> v)
Compute the distance between the instance and another point.
Specified by:
distance in interface Point<Euclidean3D>
Parameters:
v - second point
Returns:
the distance between the instance and p
• #### 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