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

Class FieldVector3D<T extends RealFieldElement<T>>

• java.lang.Object
• org.apache.commons.math3.geometry.euclidean.threed.FieldVector3D<T>
• 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
getX(), getY(), getZ()
• 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
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

• 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

Add a vector to the instance.
Parameters:
Returns:
a new vector

FieldVector3D<T> v)
Add a scaled vector to the instance.
Parameters:
factor - scale factor to apply to v before adding it
Returns:
a new vector

Vector3D v)
Add a scaled vector to the instance.
Parameters:
factor - scale factor to apply to v before adding it
Returns:
a new vector

FieldVector3D<T> v)
Add a scaled vector to the instance.
Parameters:
factor - scale factor to apply to v before adding it
Returns:
a new vector

Vector3D v)
Add a scaled vector to the instance.
Parameters:
factor - scale factor to apply to v before adding it
Returns:
a new vector
• subtract

public FieldVector3D<Tsubtract(Vector3D v)
Subtract a vector from the instance.
Parameters:
v - vector to subtract
Returns:
a new vector
• subtract

public FieldVector3D<Tsubtract(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<Tsubtract(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<Tsubtract(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<Tsubtract(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
• orthogonal

public FieldVector3D<Torthogonal()
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<Tnegate()
Get the opposite of the instance.
Returns:
a new vector which is opposite to the instance
• scalarMultiply

public FieldVector3D<TscalarMultiply(T a)
Multiply the instance by a scalar.
Parameters:
a - scalar
Returns:
a new vector
• scalarMultiply

public FieldVector3D<TscalarMultiply(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
• crossProduct

public FieldVector3D<TcrossProduct(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<TcrossProduct(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