Class Vector3D
- All Implemented Interfaces:
Serializable
Instance of this class are guaranteed to be immutable.
- Since:
- 1.2
- Version:
- $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
- See Also:
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Field Summary
FieldsModifier 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
ConstructorsConstructorDescriptionVector3D
(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 a scaled vector to the instance.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.static double
Compute the distance between two vectors according to the L2 norm.static double
Compute the distance between two vectors according to the L1 norm.static double
distanceInf
(Vector3D v1, Vector3D v2) Compute the distance between two vectors according to the L∞ norm.static double
distanceSq
(Vector3D v1, Vector3D v2) Compute the square of the distance between two vectors.static double
dotProduct
(Vector3D v1, Vector3D v2) Compute the dot-product of two vectors.boolean
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.double
getX()
Get the abscissa of the vector.double
getY()
Get the ordinate of the vector.double
getZ()
Get the height of the vector.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 vector is NaN; false otherwisenegate()
Get the opposite of the instance.Get a normalized vector aligned with the instance.Get a vector orthogonal to the instance.scalarMultiply
(double a) Multiply the instance by a scalarSubtract a scaled vector from the instance.Subtract a vector from the instance.toString()
Get a string representation of this vector.
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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- Parameters:
x
- abscissay
- ordinatez
- height- 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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getNorm1
public double getNorm1()Get the L1 norm for the vector.- Returns:
- L1 norm for the vector
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getNorm
public double getNorm()Get the L2 norm for the vector.- Returns:
- euclidian norm for the vector
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getNormSq
public double getNormSq()Get the square of the norm for the vector.- Returns:
- square of the euclidian norm for the vector
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getNormInf
public double getNormInf()Get the L∞ norm for the vector.- 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.- Parameters:
v
- vector to add- Returns:
- a new vector
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add
Add a scaled vector to the instance.- 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.- Parameters:
v
- vector to subtract- Returns:
- a new vector
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subtract
Subtract a scaled vector from the instance.- Parameters:
factor
- scale factor to apply to v before subtracting itv
- vector to subtract- Returns:
- a new vector
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normalize
Get a normalized vector aligned with the instance.- Returns:
- a new normalized vector
- Throws:
ArithmeticException
- if the norm is zero
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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:
ArithmeticException
- 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:
ArithmeticException
- if either vector has a null norm
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negate
Get the opposite of the instance.- Returns:
- a new vector which is opposite to the instance
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scalarMultiply
Multiply the instance by a scalar- Parameters:
a
- scalar- Returns:
- a new vector
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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
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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
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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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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 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.
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