Class Vector3D
- All Implemented Interfaces:
Serializable
,Point<Euclidean3D>
,Vector<Euclidean3D,
,Vector3D> Blendable<Vector<Euclidean3D,
Vector3D>>
Instance of this class are guaranteed to be immutable.
- See Also:
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Field Summary
Modifier and TypeFieldDescriptionstatic final Vector3D
Opposite of the first canonical vector (coordinates: -1, 0, 0).static final Vector3D
Opposite of the second canonical vector (coordinates: 0, -1, 0).static final Vector3D
Opposite of the third canonical vector (coordinates: 0, 0, -1).static final Vector3D
A vector with all coordinates set to NaN.static final Vector3D
A vector with all coordinates set to negative infinity.static final Vector3D
First canonical vector (coordinates: 1, 0, 0).static final Vector3D
Second canonical vector (coordinates: 0, 1, 0).static final Vector3D
Third canonical vector (coordinates: 0, 0, 1).static final Vector3D
A vector with all coordinates set to positive infinity.static final Vector3D
Null vector (coordinates: 0, 0, 0). -
Constructor Summary
ConstructorDescriptionVector3D
(double[] v) Simple constructor.Vector3D
(double alpha, double delta) Simple constructor.Vector3D
(double x, double y, double z) Simple constructor.Multiplicative constructor Build a vector from another one and a scale factor.Linear constructor Build a vector from two other ones and corresponding scale factors.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
Modifier and TypeMethodDescriptionadd
(double factor, Vector<Euclidean3D, Vector3D> v) Add a scaled vector to the instance.add
(Vector<Euclidean3D, Vector3D> v) Add a vector to the instance.static double
Compute the angular separation between two vectors.static Vector3D
crossProduct
(Vector3D v1, Vector3D v2) Compute the cross-product of two vectors.Compute the cross-product of the instance with another vector.static double
Compute the distance between two vectors according to the L2 norm.double
distance
(Point<Euclidean3D> v) Compute the distance between the instance and another point.static double
Compute the distance between two vectors according to the L1 norm.double
Compute the distance between the instance and another vector according to the L1 norm.static double
distanceInf
(Vector3D v1, Vector3D v2) Compute the distance between two vectors according to the L∞ norm.double
Compute the distance between the instance and another vector according to the L∞ norm.static double
distanceSq
(Vector3D v1, Vector3D v2) Compute the square of the distance between two vectors.double
Compute the square of the distance between the instance and another vector.static double
dotProduct
(Vector3D v1, Vector3D v2) Compute the dot-product of two vectors.double
Compute the dot-product of the instance and another vector.boolean
Test for the equality of two 3D vectors.boolean
equalsIeee754
(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
Get the L∞ norm for the vector.double
Get the square of the norm for the vector.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.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
Returns true if any coordinate of this vector is infinite and none are NaN; false otherwiseboolean
isNaN()
Returns true if any coordinate of this point is NaN; false otherwisenegate()
Get the opposite of the instance.Get a vector orthogonal to the instance.scalarMultiply
(double a) Multiply the instance by a scalar.subtract
(double factor, Vector<Euclidean3D, Vector3D> v) Subtract a scaled vector from the instance.Subtract a vector from the instance.double[]
toArray()
Get the vector coordinates as a dimension 3 array.toString()
Get a string representation of this vector.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
Methods inherited from interface org.hipparchus.geometry.Vector
blendArithmeticallyWith, normalize
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Field Details
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ZERO
Null vector (coordinates: 0, 0, 0). -
PLUS_I
First canonical vector (coordinates: 1, 0, 0). -
MINUS_I
Opposite of the first canonical vector (coordinates: -1, 0, 0). -
PLUS_J
Second canonical vector (coordinates: 0, 1, 0). -
MINUS_J
Opposite of the second canonical vector (coordinates: 0, -1, 0). -
PLUS_K
Third canonical vector (coordinates: 0, 0, 1). -
MINUS_K
Opposite of the third canonical vector (coordinates: 0, 0, -1). -
NaN
A vector with all coordinates set to NaN. -
POSITIVE_INFINITY
A vector with all coordinates set to positive infinity. -
NEGATIVE_INFINITY
A vector with all coordinates set to negative infinity.
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Constructor Details
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Vector3D
public Vector3D(double x, double y, double z) Simple constructor. Build a vector from its coordinates -
Vector3D
Simple constructor. Build a vector from its coordinates- Parameters:
v
- coordinates array- Throws:
MathIllegalArgumentException
- if array does not have 3 elements- See Also:
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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:
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Vector3D
Multiplicative constructor Build a vector from another one and a scale factor. The vector built will be a * u- Parameters:
a
- scale factoru
- base (unscaled) vector
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Vector3D
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 factoru1
- first base (unscaled) vectora2
- second scale factoru2
- second base (unscaled) vector
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Vector3D
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 factoru1
- first base (unscaled) vectora2
- second scale factoru2
- second base (unscaled) vectora3
- third scale factoru3
- third base (unscaled) vector
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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 factoru1
- first base (unscaled) vectora2
- second scale factoru2
- second base (unscaled) vectora3
- third scale factoru3
- third base (unscaled) vectora4
- fourth scale factoru4
- fourth base (unscaled) vector
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Method Details
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getX
public double getX()Get the abscissa of the vector.- Returns:
- abscissa of the vector
- See Also:
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getY
public double getY()Get the ordinate of the vector.- Returns:
- ordinate of the vector
- See Also:
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getZ
public double getZ()Get the height of the vector.- Returns:
- height of the vector
- See Also:
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toArray
public double[] toArray()Get the vector coordinates as a dimension 3 array.- Returns:
- vector coordinates
- See Also:
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getSpace
Get the space to which the point belongs.- Specified by:
getSpace
in interfacePoint<Euclidean3D>
- Returns:
- containing space
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getZero
Get the null vector of the vectorial space or origin point of the affine space.- Specified by:
getZero
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- null vector of the vectorial space or origin point of the affine space
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getNorm1
public double getNorm1()Get the L1 norm for the vector.- Specified by:
getNorm1
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- L1 norm for the vector
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getNorm
public double getNorm()Get the L2 norm for the vector.- Specified by:
getNorm
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- Euclidean norm for the vector
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getNormSq
public double getNormSq()Get the square of the norm for the vector.- Specified by:
getNormSq
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- square of the Euclidean norm for the vector
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getNormInf
public double getNormInf()Get the L∞ norm for the vector.- Specified by:
getNormInf
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- L∞ norm for the vector
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getAlpha
public double getAlpha()Get the azimuth of the vector.- Returns:
- azimuth (α) of the vector, between -π and +π
- See Also:
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getDelta
public double getDelta()Get the elevation of the vector.- Returns:
- elevation (δ) of the vector, between -π/2 and +π/2
- See Also:
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add
Add a vector to the instance.- Specified by:
add
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- vector to add- Returns:
- a new vector
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add
Add a scaled vector to the instance.- Specified by:
add
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
factor
- scale factor to apply to v before adding itv
- vector to add- Returns:
- a new vector
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subtract
Subtract a vector from the instance.- Specified by:
subtract
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- vector to subtract- Returns:
- a new vector
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subtract
Subtract a scaled vector from the instance.- Specified by:
subtract
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
factor
- scale factor to apply to v before subtracting itv
- vector to subtract- Returns:
- a new vector
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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:
MathRuntimeException
- if the norm of the instance is null
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angle
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 vectorv2
- second vector- Returns:
- angular separation between v1 and v2
- Throws:
MathRuntimeException
- if either vector has a null norm
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negate
Get the opposite of the instance.- Specified by:
negate
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- a new vector which is opposite to the instance
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scalarMultiply
Multiply the instance by a scalar.- Specified by:
scalarMultiply
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
a
- scalar- Returns:
- a new vector
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isNaN
public boolean isNaN()Returns true if any coordinate of this point is NaN; false otherwise- Specified by:
isNaN
in interfacePoint<Euclidean3D>
- Returns:
- true if any coordinate of this point is NaN; false otherwise
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isInfinite
public boolean isInfinite()Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise- Specified by:
isInfinite
in interfaceVector<Euclidean3D,
Vector3D> - Returns:
- true if any coordinate of this vector is infinite and none are NaN; false otherwise
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equals
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 toDouble.NaN
, the 3D vector is equal toNaN
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equalsIeee754
Test for the equality of two 3D vectors.If all coordinates of two 3D vectors are exactly the same, and none are
NaN
, the two 3D vectors are considered to be equal.In compliance with IEEE754 handling, if any coordinates of any of the two vectors are
NaN
, then the vectors are considered different. This implies thatVector3D.NaN
.equals(Vector3D.NaN
) returnsfalse
despite the instance is checked against itself.- 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
- Since:
- 2.1
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hashCode
public int hashCode()Get a hashCode for the 3D vector.All NaN values have the same hash code.
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dotProduct
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 interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- second vector- Returns:
- the dot product this.v
- See Also:
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crossProduct
Compute the cross-product of the instance with another vector.- Parameters:
v
- other vector- Returns:
- the cross product this ^ v as a new Vector3D
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distance1
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 interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- second vector- Returns:
- the distance between the instance and p according to the L1 norm
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distance
Compute the distance between the instance and another point.- Specified by:
distance
in interfacePoint<Euclidean3D>
- Parameters:
v
- second point- Returns:
- the distance between the instance and p
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distanceInf
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 interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- second vector- Returns:
- the distance between the instance and p according to the L∞ norm
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distanceSq
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 interfaceVector<Euclidean3D,
Vector3D> - Parameters:
v
- second vector- Returns:
- the square of the distance between the instance and p
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dotProduct
Compute the dot-product of two vectors.- Parameters:
v1
- first vectorv2
- second vector- Returns:
- the dot product v1.v2
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crossProduct
Compute the cross-product of two vectors.- Parameters:
v1
- first vectorv2
- second vector- Returns:
- the cross product v1 ^ v2 as a new Vector
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distance1
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 vectorv2
- second vector- Returns:
- the distance between v1 and v2 according to the L1 norm
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distance
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 vectorv2
- second vector- Returns:
- the distance between v1 and v2 according to the L2 norm
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distanceInf
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 vectorv2
- second vector- Returns:
- the distance between v1 and v2 according to the L∞ norm
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distanceSq
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 vectorv2
- second vector- Returns:
- the square of the distance between v1 and v2
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toString
Get a string representation of this vector. -
toString
Get a string representation of this vector.- Specified by:
toString
in interfaceVector<Euclidean3D,
Vector3D> - Parameters:
format
- the custom format for components- Returns:
- a string representation of this vector
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