maspack.matrix
Class Vector3d

java.lang.Object
  maspack.matrix.VectorObject
      maspack.matrix.Vector3d

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

Point3d

public class Vector3d

extends VectorObject

implements java.io.Serializable

Implements a 3 element vector, along with its most commonly used operations.

The size of these vectors is fixed.

See Also:

Serialized Form

Field Summary

double	x First element
double	y Second element
double	z Third element

Constructor Summary

Vector3d()
Creates a 3-vector and initializes its elements to 0.

Vector3d(double[] values)
Creates a 3-vector with the supplied element values.

Vector3d(double x, double y, double z)
Creates a 3-vector with the supplied element values.

Vector3d(Vector3d v)
Creates a 3-vector by copying an existing one.

Method Summary

void	absolute() Sets the elements of this vector to their absolute values.
void	absolute(Vector3d v1) Sets the elements of this vector to the absolute value of v1.
void	add(Vector3d v1) Adds this vector to v1 and places the result in this vector.
void	add(Vector3d v1, Vector3d v2) Adds vector v1 to v2 and places the result in this vector.
double	angle(Vector3d v1) Returns the angle between this vector and v1.
void	combine(double s1, Vector3d v1, double s2, Vector3d v2) Computes s1 v1 + s2 v2 and places the result in this vector.
void	cross(Vector3d v1) Computes the cross product of this vector and v1, and places the result in this vector.
void	cross(Vector3d v1, Vector3d v2) Computes the cross product of v1 and v2 and places the result in this vector.
void	crossAdd(Vector3d v1, Vector3d v2, Vector3d v3) Computes the cross product of v1 and v2, adds this to v3, and places the result in this vector.
double	distance(Vector3d v) Returns the Euclidean distance between this vector and vector v.
double	distanceSquared(Vector3d v) Returns the squared of the Euclidean distance between this vector and vector v.
double	dot(Vector3d v1) Returns the dot product of this vector and v1.
boolean	epsilonEquals(Vector3d v1, double eps) Returns true if the elements of this vector equal those of vector v1within a prescribed tolerance epsilon.
boolean	equals(Vector3d v1) Returns true if the elements of this vector exactly equal those of vector v1.
void	get(double[] values) Copies the elements of this vector into an array of doubles.
double	get(int i) Gets a single element of this vector.
double	infinityNorm() Returns the infinity norm of this vector.
void	interpolate(double s, Vector3d v1) Computes the interpolation (1-s) this + s v1 and places the result in this vector.
void	interpolate(Vector3d v1, double s, Vector3d v2) Computes the interpolation (1-s) v1 + s v2 and places the result in this vector.
void	inverseTransform(AffineTransform3dObject X) Applies an inverse affine transformation to this vector, in place.
void	inverseTransform(AffineTransform3dObject X, Vector3d v1) Applies an inverse affine transformation to the vector v1, and places the result in this vector.
void	inverseTransform(RotationMatrix3d R) Applies an inverse rotational transformation to this vector, in place.
void	inverseTransform(RotationMatrix3d R, Vector3d v1) Applies an inverse rotational transformation to the vector v1, and stores the result in this vector.
int	maxAbsIndex() Returns the index (0, 1, or 2) of the element of this vector with the largest absolute value.
double	maxElement() Returns the maximum element value of this vector.
int	minAbsIndex() Returns the index (0, 1, or 2) of the element of this vector with the smallest absolute value.
double	minElement() Returns the minimum element value of this vector.
void	mul(Matrix3d X, Vector3d v1) Multiplies matrix X by vector v1 and places the result in this vector.
void	mulTranspose(Matrix3d X, Vector3d v1) Multiplies the transpose of matrix X by vector v1 and places the result in this vector.
void	negate() Negates this vector in place.
void	negate(Vector3d v1) Sets this vector to the negative of v1.
double	norm() Returns the 2 norm of this vector.
void	normalize() Normalizes this vector in place.
void	normalize(Vector3d v1) Computes a unit vector in the direction of v1 and places the result in this vector.
double	normSquared() Returns the square of the 2 norm of this vector.
double	oneNorm() Returns the 1 norm of this vector.
void	perpendicular(Vector3d v1) Sets this vector to one which is perpendicular to v1.
void	scale(double s) Scales the elements of this vector by s.
void	scale(double s, Vector3d v1) Scales the elements of vector v1 by s and places the results in this vector.
void	scaleAdd(double s, Vector3d v1) Computes s this + v1 and places the result in this vector.
void	scaleAdd(double s, Vector3d v1, Vector3d v2) Computes s v1 + v2 and places the result in this vector.
void	set(double[] values) Sets the elements of this vector from an array of doubles.
void	set(double x, double y, double z) Sets the elements of this vector to the prescribed values.
void	set(int i, double value) Sets a single element of this vector.
void	set(Vector3d v1) Sets the values of this vector to those of v1.
void	setFromHomogeneous(Vector4d v1) Sets the values of this vector from a homogeneous representation stored in the 4-vector v1.
void	setRandom() Sets the elements of this vector to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).
void	setRandom(double lower, double upper) Sets the elements of this vector to uniformly distributed random values in a specified range.
void	setRandom(double lower, double upper, java.util.Random generator) Sets the elements of this vector to uniformly distributed random values in a specified range, using a supplied random number generator.
void	setZero() Sets the elements of this vector to zero.
int	size() Returns the size of this vector (which is always 3)
void	sort() Sorts the contents of this vector by element value, with x being set to the largest value and z being set to the smallest value.
void	sort(Vector3d v1) Sorts the contents of vector v1 by element value, with x being set to the largest value and z being set to the smallest value, and places the results in this vector.
void	sortAbsolute() Sorts the contents of this vector by absolute element value, with x being set to the largest value and z being set to the smallest value.
void	sub(Vector3d v1) Subtracts v1 from this vector and places the result in this vector.
void	sub(Vector3d v1, Vector3d v2) Subtracts vector v1 from v2 and places the result in this vector.
void	transform(AffineTransform3dObject X) Applies a affine transformation to this vector, in place.
void	transform(AffineTransform3dObject X, Vector3d v1) Applies an affine transformation to the vector v1, and places the result in this vector.
void	transform(RotationMatrix3d R) Applies a rotational transformation to this vector, in place.
void	transform(RotationMatrix3d R, Vector3d v1) Applies a rotational transformation to the vector v1 and stores the result in this vector.

Methods inherited from class maspack.matrix.VectorObject

dot, epsilonEquals, equals, equals, get, isFixedSize, scan, set, setSize, toString, toString, toString

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

x

public double x

First element

y

public double y

Second element

z

public double z

Third element

Constructor Detail

Vector3d

public Vector3d()

Creates a 3-vector and initializes its elements to 0.

Vector3d

public Vector3d(Vector3d v)

Creates a 3-vector by copying an existing one.

Parameters:

v - vector to be copied

Vector3d

public Vector3d(double x,
                double y,
                double z)

Creates a 3-vector with the supplied element values.

Parameters:

x - first element

y - second element

z - third element

Vector3d

public Vector3d(double[] values)

Creates a 3-vector with the supplied element values.

Parameters:

values - element values

Method Detail

size

public int size()

Returns the size of this vector (which is always 3)

Specified by:

size in class VectorObject

Returns:

3

get

public double get(int i)

Gets a single element of this vector. Elements 0, 1, and 2 correspond to x, y, and z.

Specified by:

get in class VectorObject

Parameters:

i - element index

Returns:

element value throws ArrayIndexOutOfBoundsException if i is not in the range 0 to 2.

get

public void get(double[] values)

Copies the elements of this vector into an array of doubles.

Overrides:

get in class VectorObject

Parameters:

values - array into which values are copied

set

public void set(int i,
                double value)

Sets a single element of this vector. Elements 0, 1, and 2 correspond to x, y, and z.

Specified by:

set in class VectorObject

Parameters:

i - element index

value - element value

Returns:

element value throws ArrayIndexOutOfBoundsException if i is not in the range 0 to 2.

set

public void set(double[] values)

Sets the elements of this vector from an array of doubles.

Overrides:

set in class VectorObject

Parameters:

values - array from which values are copied

set

public void set(Vector3d v1)

Sets the values of this vector to those of v1.

Parameters:

v1 - vector whose values are copied

setFromHomogeneous

public void setFromHomogeneous(Vector4d v1)

Sets the values of this vector from a homogeneous representation stored in the 4-vector v1. This involves dividing the x, y, and z elements of v1 by its w element.

Parameters:

v1 - homogenous vector

add

public void add(Vector3d v1,
                Vector3d v2)

Adds vector v1 to v2 and places the result in this vector.

Parameters:

v1 - left-hand vector

v2 - right-hand vector

add

public void add(Vector3d v1)

Adds this vector to v1 and places the result in this vector.

Parameters:

v1 - right-hand vector

sub

public void sub(Vector3d v1,
                Vector3d v2)

Subtracts vector v1 from v2 and places the result in this vector.

Parameters:

v1 - left-hand vector

v2 - right-hand vector

sub

public void sub(Vector3d v1)

Subtracts v1 from this vector and places the result in this vector.

Parameters:

v1 - right-hand vector

negate

public void negate(Vector3d v1)

Sets this vector to the negative of v1.

Parameters:

v1 - vector to negate

negate

public void negate()

Negates this vector in place.

scale

public void scale(double s)

Scales the elements of this vector by s.

Parameters:

s - scaling factor

scale

public void scale(double s,
                  Vector3d v1)

Scales the elements of vector v1 by s and places the results in this vector.

Parameters:

s - scaling factor

v1 - vector to be scaled

interpolate

public void interpolate(Vector3d v1,
                        double s,
                        Vector3d v2)

Computes the interpolation (1-s) v1 + s v2 and places the result in this vector.

Parameters:

v1 - left-hand vector

s - interpolation factor

v2 - right-hand vector

interpolate

public void interpolate(double s,
                        Vector3d v1)

Computes the interpolation (1-s) this + s v1 and places the result in this vector.

Parameters:

s - interpolation factor

v1 - right-hand vector

scaleAdd

public void scaleAdd(double s,
                     Vector3d v1,
                     Vector3d v2)

Computes s v1 + v2 and places the result in this vector.

Parameters:

s - scaling factor

v1 - vector to be scaled

v2 - vector to be added

scaleAdd

public void scaleAdd(double s,
                     Vector3d v1)

Computes s this + v1 and places the result in this vector.

Parameters:

s - scaling factor

v1 - vector to be added

combine

public void combine(double s1,
                    Vector3d v1,
                    double s2,
                    Vector3d v2)

Computes s1 v1 + s2 v2 and places the result in this vector.

Parameters:

s1 - left-hand scaling factor

v1 - left-hand vector

s2 - right-hand scaling factor

v2 - right-hand vector

norm

public double norm()

Returns the 2 norm of this vector. This is the square root of the sum of the squares of the elements.

Overrides:

norm in class VectorObject

Returns:

vector 2 norm

normSquared

public double normSquared()

Returns the square of the 2 norm of this vector. This is the sum of the squares of the elements.

Overrides:

normSquared in class VectorObject

Returns:

square of the 2 norm

distance

public double distance(Vector3d v)

Returns the Euclidean distance between this vector and vector v.

Returns:

distance between this vector and v

distanceSquared

public double distanceSquared(Vector3d v)

Returns the squared of the Euclidean distance between this vector and vector v.

Returns:

squared distance between this vector and v

maxElement

public double maxElement()

Returns the maximum element value of this vector.

Overrides:

maxElement in class VectorObject

Returns:

maximal element

minElement

public double minElement()

Returns the minimum element value of this vector.

Overrides:

minElement in class VectorObject

Returns:

minimal element

infinityNorm

public double infinityNorm()

Returns the infinity norm of this vector. This is the maximum absolute value over all elements.

Overrides:

infinityNorm in class VectorObject

Returns:

vector infinity norm

oneNorm

public double oneNorm()

Returns the 1 norm of this vector. This is the sum of the absolute values of the elements.

Overrides:

oneNorm in class VectorObject

Returns:

vector 1 norm

dot

public double dot(Vector3d v1)

Returns the dot product of this vector and v1.

Parameters:

v1 - right-hand vector

Returns:

dot product

angle

public double angle(Vector3d v1)

Returns the angle between this vector and v1. The angle is defined as acos(c), where c is the dot product of unit vectors parallel to this vector and v1.

Parameters:

v1 - right-hand vector

Returns:

angle between vectors, in radians

normalize

public void normalize()

Normalizes this vector in place.

normalize

public void normalize(Vector3d v1)

Computes a unit vector in the direction of v1 and places the result in this vector.

Parameters:

v1 - vector to normalize

perpendicular

public void perpendicular(Vector3d v1)

Sets this vector to one which is perpendicular to v1. The resulting vector will not be normalized.

Parameters:

v1 - perpendicular reference vector

epsilonEquals

public boolean epsilonEquals(Vector3d v1,
                             double eps)

Returns true if the elements of this vector equal those of vector v1within a prescribed tolerance epsilon.

Parameters:

v1 - vector to compare with

eps - comparison tolerance

Returns:

false if the vectors are not equal within the specified tolerance

equals

public boolean equals(Vector3d v1)

Returns true if the elements of this vector exactly equal those of vector v1.

Parameters:

v1 - vector to compare with

Returns:

false if the vectors are not equal

setZero

public void setZero()

Sets the elements of this vector to zero.

set

public void set(double x,
                double y,
                double z)

Sets the elements of this vector to the prescribed values.

Parameters:

x - value for first element

y - value for second element

z - value for third element

absolute

public void absolute()

Sets the elements of this vector to their absolute values.

absolute

public void absolute(Vector3d v1)

Sets the elements of this vector to the absolute value of v1.

Parameters:

v1 - vector to take the absolute value of

sortAbsolute

public void sortAbsolute()

Sorts the contents of this vector by absolute element value, with x being set to the largest value and z being set to the smallest value.

maxAbsIndex

public int maxAbsIndex()

Returns the index (0, 1, or 2) of the element of this vector with the largest absolute value.

Returns:

index of largest absolute value

minAbsIndex

public int minAbsIndex()

Returns the index (0, 1, or 2) of the element of this vector with the smallest absolute value.

Returns:

index of smallest absolute value

sort

public void sort(Vector3d v1)

Sorts the contents of vector v1 by element value, with x being set to the largest value and z being set to the smallest value, and places the results in this vector.

Parameters:

v1 - vector to sort

sort

public void sort()

Sorts the contents of this vector by element value, with x being set to the largest value and z being set to the smallest value.

cross

public void cross(Vector3d v1,
                  Vector3d v2)

Computes the cross product of v1 and v2 and places the result in this vector.

Parameters:

v1 - left-hand vector

v2 - right-hand vector

cross

public void cross(Vector3d v1)

Computes the cross product of this vector and v1, and places the result in this vector.

Parameters:

v1 - right-hand vector

crossAdd

public void crossAdd(Vector3d v1,
                     Vector3d v2,
                     Vector3d v3)

Computes the cross product of v1 and v2, adds this to v3, and places the result in this vector.

Parameters:

v1 - left-hand vector for cross product

v2 - right-hand vector for cross product

v3 - vector to add

transform

public void transform(RotationMatrix3d R)

Applies a rotational transformation to this vector, in place. This is equivalent to multiplying the rotation matrix by this vector.

Parameters:

R - rotational transformation matrix

transform

public void transform(RotationMatrix3d R,
                      Vector3d v1)

Applies a rotational transformation to the vector v1 and stores the result in this vector. This is equivalent to multiplying the rotation matrix by v1.

Parameters:

R - rotational transformation matrix

v1 - vector to transform

inverseTransform

public void inverseTransform(RotationMatrix3d R)

Applies an inverse rotational transformation to this vector, in place. This is equivalent to multiplying the transpose (or inverse) of the rotation matrix by this vector.

Parameters:

R - rotational transformation matrix

inverseTransform

public void inverseTransform(RotationMatrix3d R,
                             Vector3d v1)

Applies an inverse rotational transformation to the vector v1, and stores the result in this vector. This is equivalent to multiplying the transpose (or inverse) of the rotation matrix by this v1.

Parameters:

R - rotational transformation matrix

v1 - vector to transform

transform

public void transform(AffineTransform3dObject X)

Applies a affine transformation to this vector, in place.

Parameters:

X - affine transformation

transform

public void transform(AffineTransform3dObject X,
                      Vector3d v1)

Applies an affine transformation to the vector v1, and places the result in this vector.

Parameters:

X - affine transformation

v1 - vector to be transformed

inverseTransform

public void inverseTransform(AffineTransform3dObject X)

Applies an inverse affine transformation to this vector, in place.

Parameters:

X - affine transformation

inverseTransform

public void inverseTransform(AffineTransform3dObject X,
                             Vector3d v1)

Applies an inverse affine transformation to the vector v1, and places the result in this vector.

Parameters:

X - affine transformation

v1 - vector to be transformed

mul

public void mul(Matrix3d X,
                Vector3d v1)

Multiplies matrix X by vector v1 and places the result in this vector.

Parameters:

X - matrix

v1 - vector

mulTranspose

public void mulTranspose(Matrix3d X,
                         Vector3d v1)

Multiplies the transpose of matrix X by vector v1 and places the result in this vector.

Parameters:

X - matrix

v1 - vector

setRandom

public void setRandom()

Sets the elements of this vector to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).

setRandom

public void setRandom(double lower,
                      double upper)

Sets the elements of this vector to uniformly distributed random values in a specified range.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

setRandom

public void setRandom(double lower,
                      double upper,
                      java.util.Random generator)

Sets the elements of this vector to uniformly distributed random values in a specified range, using a supplied random number generator.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

generator - random number generator