Class Vector3D
- java.lang.Object
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- org.apache.commons.geometry.euclidean.EuclideanVector<V>
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- org.apache.commons.geometry.euclidean.MultiDimensionalEuclideanVector<Vector3D>
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- org.apache.commons.geometry.euclidean.threed.Vector3D
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- Direct Known Subclasses:
Vector3D.Unit
public class Vector3D extends MultiDimensionalEuclideanVector<Vector3D>
This class represents vectors and points in three-dimensional Euclidean space. Instances of this class are guaranteed to be immutable.
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Nested Class Summary
Nested Classes Modifier and Type Class Description static class
Vector3D.Sum
Class used to create high-accuracy sums of vectors.static class
Vector3D.Unit
Represents unit vectors.
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Field Summary
Fields Modifier and Type Field Description static java.util.Comparator<Vector3D>
COORDINATE_ASCENDING_ORDER
Comparator that sorts vectors in component-wise ascending order.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
POSITIVE_INFINITY
A vector with all coordinates set to positive infinity.private double
x
X coordinate value (abscissa).private double
y
Y coordinate value (ordinate).private double
z
Z coordinate value (height).static Vector3D
ZERO
Zero (null) vector (coordinates: 0, 0, 0).
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Constructor Summary
Constructors Modifier Constructor Description private
Vector3D(double x, double y, double z)
Simple constructor.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description Vector3D
add(double factor, Vector3D v)
Add a scaled vector to the instance.Vector3D
add(Vector3D v)
Add a vector to the instance.double
angle(Vector3D v)
Compute the angular separation between two vectors in radians.static Vector3D
centroid(java.lang.Iterable<Vector3D> pts)
Compute the centroid of the given points.static Vector3D
centroid(Vector3D first, Vector3D... more)
Compute the centroid of the given points.private static Vector3D
computeCentroid(Vector3D first, java.util.Iterator<? extends Vector3D> more)
Internal method for computing the centroid of a set of points.private static Vector3D
computeMax(Vector3D first, java.util.Iterator<? extends Vector3D> more)
Internal method for computing a max vector.private static Vector3D
computeMin(Vector3D first, java.util.Iterator<? extends Vector3D> more)
Internal method for computing a min vector.Vector3D
cross(Vector3D v)
Compute the cross-product of the instance with another vector.Vector3D.Unit
directionTo(Vector3D v)
Return the unit vector representing the direction of displacement from this vector to the given vector.double
distance(Vector3D v)
Compute the distance between the instance and another vector.double
distanceSq(Vector3D v)
Compute the square of the distance between the instance and another vector.double
dot(Vector3D v)
Compute the dot-product of the instance and another vector.boolean
eq(Vector3D vec, org.apache.commons.numbers.core.Precision.DoubleEquivalence precision)
Return true if the current instance and given vector are considered equal as evaluated by the given precision context.boolean
equals(java.lang.Object other)
d Test for the equality of two vector instances.private <V extends Vector3D>
VgetComponent(Vector3D base, boolean reject, DoubleFunction3N<V> factory)
Returns a component of the current instance relative to the given base vector.int
getDimension()
Returns the number of dimensions in the space that this element belongs to.double
getX()
Return the x coordinate value (abscissa) of the instance.double
getY()
Return the y coordinate value (ordinate) of the instance.double
getZ()
Returns the z coordinate value (height) of the instance.Vector3D
getZero()
Get the zero (null) vector of the space.int
hashCode()
Get a hashCode for the vector.boolean
isFinite()
Returns true if all values in this element are finite, meaning they are not NaN or infinite.boolean
isInfinite()
Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.boolean
isNaN()
Returns true if any value in this element is NaN; otherwise returns false.Vector3D
lerp(Vector3D p, double t)
Get a vector constructed by linearly interpolating between this vector and the given vector.static Vector3D
max(java.lang.Iterable<Vector3D> vecs)
Return a vector containing the maximum component values from all input vectors.static Vector3D
max(Vector3D first, Vector3D... more)
Return a vector containing the maximum component values from all input vectors.static Vector3D
min(java.lang.Iterable<Vector3D> vecs)
Return a vector containing the minimum component values from all input vectors.static Vector3D
min(Vector3D first, Vector3D... more)
Return a vector containing the minimum component values from all input vectors.Vector3D
multiply(double a)
Multiply the instance by a scalar.Vector3D
negate()
Get the negation of the instance.double
norm()
Get the L2 norm (commonly known as the Euclidean norm) for the vector.Vector3D.Unit
normalize()
Get a normalized vector aligned with the instance.Vector3D.Unit
normalizeOrNull()
Attempt to compute a normalized vector aligned with the instance, returning null if such a vector cannot be computed.double
normSq()
Get the square of the L2 norm (also known as the Euclidean norm) for the vector.static Vector3D
of(double[] v)
Creates a vector from the coordinates in the given 3-element array.static Vector3D
of(double x, double y, double z)
Returns a vector with the given coordinate values.Vector3D.Unit
orthogonal()
Get a unit vector orthogonal to the instance.Vector3D.Unit
orthogonal(Vector3D dir)
Get a unit vector orthogonal to the current vector and pointing in the direction ofdir
.static Vector3D
parse(java.lang.String str)
Parses the given string and returns a new vector instance.Vector3D
project(Vector3D base)
Get the projection of the instance onto the given base vector.Vector3D
reject(Vector3D base)
Get the rejection of the instance from the given base vector.Vector3D
subtract(double factor, Vector3D v)
Subtract a scaled vector from the instance.Vector3D
subtract(Vector3D v)
Subtract a vector from the instance.double[]
toArray()
Get the coordinates for this instance as a dimension 3 array.java.lang.String
toString()
Vector3D
transform(java.util.function.UnaryOperator<Vector3D> fn)
Convenience method to apply a function to this vector.Vector3D
vectorTo(Vector3D v)
Return the vector representing the displacement from this vector to the given vector.Vector3D
withNorm(double magnitude)
Returns a vector with the same direction but with the given norm.-
Methods inherited from class org.apache.commons.geometry.euclidean.EuclideanVector
getCheckedNorm, isZero
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Field Detail
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ZERO
public static final Vector3D ZERO
Zero (null) vector (coordinates: 0, 0, 0).
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NaN
public static final Vector3D NaN
A vector with all coordinates set to NaN.
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POSITIVE_INFINITY
public static final Vector3D POSITIVE_INFINITY
A vector with all coordinates set to positive infinity.
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NEGATIVE_INFINITY
public static final Vector3D NEGATIVE_INFINITY
A vector with all coordinates set to negative infinity.
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COORDINATE_ASCENDING_ORDER
public static final java.util.Comparator<Vector3D> COORDINATE_ASCENDING_ORDER
Comparator that sorts vectors in component-wise ascending order. Vectors are only considered equal if their coordinates match exactly. Null arguments are evaluated as being greater than non-null arguments.
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x
private final double x
X coordinate value (abscissa).
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y
private final double y
Y coordinate value (ordinate).
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z
private final double z
Z coordinate value (height).
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Method Detail
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getX
public double getX()
Return the x coordinate value (abscissa) of the instance.- Returns:
- the x coordinate value
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getY
public double getY()
Return the y coordinate value (ordinate) of the instance.- Returns:
- the y coordinate value
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getZ
public double getZ()
Returns the z coordinate value (height) of the instance.- Returns:
- the z coordinate value
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toArray
public double[] toArray()
Get the coordinates for this instance as a dimension 3 array.- Returns:
- the coordinates for this instance
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getDimension
public int getDimension()
Returns the number of dimensions in the space that this element belongs to.- Returns:
- the number of dimensions in the element's space
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isNaN
public boolean isNaN()
Returns true if any value in this element is NaN; otherwise returns false.- Returns:
- true if any value in this element is NaN
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isInfinite
public boolean isInfinite()
Returns true if any value in this element is infinite and none are NaN; otherwise, returns false.- Returns:
- true if any value in this element is infinite and none are NaN
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isFinite
public boolean isFinite()
Returns true if all values in this element are finite, meaning they are not NaN or infinite.- Returns:
- true if all values in this element are finite
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getZero
public Vector3D getZero()
Get the zero (null) vector of the space.- Returns:
- zero vector of the space
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vectorTo
public Vector3D vectorTo(Vector3D v)
Return the vector representing the displacement from this vector to the given vector. This is exactly equivalent tov.subtract(thisVector)
but with a method name that is much easier to visualize.- Specified by:
vectorTo
in classEuclideanVector<Vector3D>
- Parameters:
v
- the vector that the returned vector will be directed toward- Returns:
- vector representing the displacement from this vector to the given vector
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directionTo
public Vector3D.Unit directionTo(Vector3D v)
Return the unit vector representing the direction of displacement from this vector to the given vector. This is exactly equivalent tov.subtract(thisVector).normalize()
but without the intermediate vector instance.- Specified by:
directionTo
in classEuclideanVector<Vector3D>
- Parameters:
v
- the vector that the returned vector will be directed toward- Returns:
- unit vector representing the direction of displacement from this vector to the given vector
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lerp
public Vector3D lerp(Vector3D p, double t)
Get a vector constructed by linearly interpolating between this vector and the given vector. The vector coordinates are generated by the equationV = (1 - t)*A + t*B
, whereA
is the current vector andB
is the given vector. This means that ift = 0
, a vector equal to the current vector will be returned. Ift = 1
, a vector equal to the argument will be returned. Thet
parameter is not constrained to the range[0, 1]
, meaning that linear extrapolation can also be performed with this method.- Specified by:
lerp
in classEuclideanVector<Vector3D>
- Parameters:
p
- other vectort
- interpolation parameter- Returns:
- interpolated or extrapolated vector
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norm
public double norm()
Get the L2 norm (commonly known as the Euclidean norm) for the vector. This corresponds to the common notion of vector magnitude or length and is defined as the square root of the sum of the squares of all vector components.- Returns:
- L2 norm for the vector
- See Also:
- L2 Norm
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normSq
public double normSq()
Get the square of the L2 norm (also known as the Euclidean norm) for the vector. This is equal to the sum of the squares of all vector components.- Returns:
- square of the L2 norm for the vector
- See Also:
Vector.norm()
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withNorm
public Vector3D withNorm(double magnitude)
Returns a vector with the same direction but with the given norm. This is equivalent to callingvec.normalize().scalarMultiply(mag)
but without the intermediate vector.- Parameters:
magnitude
- The vector norm- Returns:
- a vector with the same direction as the current instance but the given norm
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add
public Vector3D add(Vector3D v)
Add a vector to the instance.- Parameters:
v
- vector to add- Returns:
- a new vector
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add
public Vector3D add(double factor, Vector3D v)
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
public Vector3D subtract(Vector3D v)
Subtract a vector from the instance.- Parameters:
v
- vector to subtract- Returns:
- a new vector
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subtract
public Vector3D subtract(double factor, Vector3D v)
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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negate
public Vector3D negate()
Get the negation of the instance.- Returns:
- a new vector which is the negation of the instance
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normalize
public Vector3D.Unit normalize()
Get a normalized vector aligned with the instance. The returned vector has a magnitude of 1.- Returns:
- normalized vector
- See Also:
Vector.normalizeOrNull()
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normalizeOrNull
public Vector3D.Unit normalizeOrNull()
Attempt to compute a normalized vector aligned with the instance, returning null if such a vector cannot be computed. This method is equivalent toVector.normalize()
but returns null instead of throwing an exception on failure.- Returns:
- normalized vector or null if such a vector cannot be computed, i.e. if the norm is zero, NaN, or infinite
- See Also:
Vector.normalize()
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multiply
public Vector3D multiply(double a)
Multiply the instance by a scalar.- Parameters:
a
- scalar- Returns:
- a new vector
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distance
public double distance(Vector3D v)
Compute the distance between the instance and another vector.- Parameters:
v
- second vector- Returns:
- the distance between the instance and v
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distanceSq
public double 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
- See Also:
Vector.normSq()
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dot
public double dot(Vector3D 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.
- Parameters:
v
- second vector- Returns:
- the dot product (this · v)
- See Also:
Sum
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angle
public double angle(Vector3D v)
Compute the angular separation between two vectors in radians.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:
v
- other vector- Returns:
- angular separation between this instance and v in radians
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project
public Vector3D project(Vector3D base)
Get the projection of the instance onto the given base vector. The returned vector is parallel tobase
. Vector projection and rejection onto a given base are related by the equationv = vprojection + vrejection
- Specified by:
project
in classMultiDimensionalEuclideanVector<Vector3D>
- Parameters:
base
- base vector- Returns:
- the vector projection of the instance onto
base
- See Also:
MultiDimensionalEuclideanVector.reject(MultiDimensionalEuclideanVector)
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reject
public Vector3D reject(Vector3D base)
Get the rejection of the instance from the given base vector. The returned vector is orthogonal tobase
. This operation can be interpreted as returning the orthogonal projection of the instance onto the hyperplane orthogonal tobase
. Vector projection and rejection onto a given base are related by the equationv = vprojection + vrejection
- Specified by:
reject
in classMultiDimensionalEuclideanVector<Vector3D>
- Parameters:
base
- base vector- Returns:
- the vector rejection of the instance from
base
- See Also:
MultiDimensionalEuclideanVector.project(MultiDimensionalEuclideanVector)
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orthogonal
public Vector3D.Unit orthogonal()
Get a unit 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 = k.cross(i);
- Specified by:
orthogonal
in classMultiDimensionalEuclideanVector<Vector3D>
- Returns:
- a unit vector orthogonal to the instance
- Throws:
java.lang.IllegalArgumentException
- if the norm of the instance is zero, NaN, or infinite
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orthogonal
public Vector3D.Unit orthogonal(Vector3D dir)
Get a unit vector orthogonal to the current vector and pointing in the direction ofdir
. This method is equivalent to callingdir.reject(vec).normalize()
except that no intermediate vector object is produced.- Specified by:
orthogonal
in classMultiDimensionalEuclideanVector<Vector3D>
- Parameters:
dir
- the direction to use for generating the orthogonal vector- Returns:
- unit vector orthogonal to the current vector and pointing in the direction of
dir
that does not lie along the current vector
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cross
public Vector3D cross(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
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transform
public Vector3D transform(java.util.function.UnaryOperator<Vector3D> fn)
Convenience method to apply a function to this vector. This can be used to transform the vector inline with other methods.- Parameters:
fn
- the function to apply- Returns:
- the transformed vector
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eq
public boolean eq(Vector3D vec, org.apache.commons.numbers.core.Precision.DoubleEquivalence precision)
Return true if the current instance and given vector are considered equal as evaluated by the given precision context.Equality is determined by comparing each pair of components in turn from the two vectors. If all components evaluate as equal, then the vectors are considered equal. If any are not equal, then the vectors are not considered equal. Note that this approach means that the calculated distance between two "equal" vectors may be as much as
√(n * eps2)
, wheren
is the number of components in the vector andeps
is the maximum epsilon value allowed by the precision context.- Specified by:
eq
in classEuclideanVector<Vector3D>
- Parameters:
vec
- vector to check for equalityprecision
- precision context used to determine floating point equality- Returns:
- true if the current instance is considered equal to the given vector when using the given precision context; otherwise false
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hashCode
public int hashCode()
Get a hashCode for the vector.All NaN values have the same hash code.
- Overrides:
hashCode
in classjava.lang.Object
- Returns:
- a hash code value for this object
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equals
public boolean equals(java.lang.Object other)
d Test for the equality of two vector instances.If all coordinates of two vectors are exactly the same, and none are
Double.NaN
, the two instances are considered to be equal.NaN
coordinates are considered to globally affect the vector and be equal to each other - i.e, if either (or all) coordinates of the vector are equal toDouble.NaN
, the vector is equal toNaN
.- Overrides:
equals
in classjava.lang.Object
- Parameters:
other
- Object to test for equality to this- Returns:
- true if two Vector3D objects are equal, false if object is null, not an instance of Vector3D, or not equal to this Vector3D instance
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toString
public java.lang.String toString()
- Overrides:
toString
in classjava.lang.Object
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getComponent
private <V extends Vector3D> V getComponent(Vector3D base, boolean reject, DoubleFunction3N<V> factory)
Returns a component of the current instance relative to the given base vector. Ifreject
is true, the vector rejection is returned; otherwise, the projection is returned.- Type Parameters:
V
- Vector implementation type- Parameters:
base
- The base vectorreject
- If true, the rejection of this instance frombase
is returned. If false, the projection of this instance ontobase
is returned.factory
- factory function used to build the final vector- Returns:
- The projection or rejection of this instance relative to
base
, depending on the value ofreject
. - Throws:
java.lang.IllegalArgumentException
- ifbase
has a zero, NaN, or infinite norm
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of
public static Vector3D of(double x, double y, double z)
Returns a vector with the given coordinate values.- Parameters:
x
- x coordinate valuey
- y coordinate valuez
- z coordinate value- Returns:
- vector instance
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of
public static Vector3D of(double[] v)
Creates a vector from the coordinates in the given 3-element array.- Parameters:
v
- coordinates array- Returns:
- new vector
- Throws:
java.lang.IllegalArgumentException
- if the array does not have 3 elements
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parse
public static Vector3D parse(java.lang.String str)
Parses the given string and returns a new vector instance. The expected string format is the same as that returned bytoString()
.- Parameters:
str
- the string to parse- Returns:
- vector instance represented by the string
- Throws:
java.lang.IllegalArgumentException
- if the given string has an invalid format
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max
public static Vector3D max(Vector3D first, Vector3D... more)
Return a vector containing the maximum component values from all input vectors.- Parameters:
first
- first vectormore
- additional vectors- Returns:
- a vector containing the maximum component values from all input vectors
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max
public static Vector3D max(java.lang.Iterable<Vector3D> vecs)
Return a vector containing the maximum component values from all input vectors.- Parameters:
vecs
- input vectors- Returns:
- a vector containing the maximum component values from all input vectors
- Throws:
java.lang.IllegalArgumentException
- if the argument does not contain any vectors
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computeMax
private static Vector3D computeMax(Vector3D first, java.util.Iterator<? extends Vector3D> more)
Internal method for computing a max vector.- Parameters:
first
- first vectormore
- iterator with additional vectors- Returns:
- vector containing the maximum component values of all input vectors
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min
public static Vector3D min(Vector3D first, Vector3D... more)
Return a vector containing the minimum component values from all input vectors.- Parameters:
first
- first vectormore
- additional vectors- Returns:
- a vector containing the minimum component values from all input vectors
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min
public static Vector3D min(java.lang.Iterable<Vector3D> vecs)
Return a vector containing the minimum component values from all input vectors.- Parameters:
vecs
- input vectors- Returns:
- a vector containing the minimum component values from all input vectors
- Throws:
java.lang.IllegalArgumentException
- if the argument does not contain any vectors
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computeMin
private static Vector3D computeMin(Vector3D first, java.util.Iterator<? extends Vector3D> more)
Internal method for computing a min vector.- Parameters:
first
- first vectormore
- iterator with additional vectors- Returns:
- vector containing the minimum component values of all input vectors
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centroid
public static Vector3D centroid(Vector3D first, Vector3D... more)
Compute the centroid of the given points. The centroid is the arithmetic mean position of a set of points.- Parameters:
first
- first pointmore
- additional points- Returns:
- the centroid of the given points
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centroid
public static Vector3D centroid(java.lang.Iterable<Vector3D> pts)
Compute the centroid of the given points. The centroid is the arithmetic mean position of a set of points.- Parameters:
pts
- the points to compute the centroid of- Returns:
- the centroid of the given points
- Throws:
java.lang.IllegalArgumentException
- if the argument contains no points
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