maspack.spatialmotion
Class SpatialVector

java.lang.Object
  maspack.matrix.VectorObject
      maspack.spatialmotion.SpatialVector

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

Twist, Wrench

public abstract class SpatialVector

extends VectorObject

implements java.io.Serializable

A spatial vector, which is a 6-vector composed of two 3-vectors: a free vector and a line vector. Spatial vectors are described in Featherstone, Robot Dynamics Algorithms, and are used to represent quantities such as spatial velocities (or twists), spatial forces (or wrenchs).

Spatial vectors are either contarvariant (those associated with motion), or covariant (those associated with forces). For a contravariant spatial vector, elements 0-2 correspond to the free vector and elements 3-5 correspond to the line vector. For a covarient spatial vector, elements 0-2 correspond to the line vector and elements 3-5 correspond to the free vector (note that this transposing of element ordering is different from the treatment in Featherstone, which always asigns elements 0-2 to the line vector).

See Also:

Serialized Form

Method Summary

void	absolute() Sets the elements of this spatial vector to their absolute values.
double	dot(SpatialVector v1) Returns the dot product of this spatial vector and the spatial vector v1.
boolean	epsilonEquals(SpatialVector v1, double eps) Returns true if the elements of this spatial vector equal those of vector v1within a prescribed tolerance epsilon.
boolean	equals(SpatialVector v1) Returns true if the elements of this spatial vector exactly equal those of vector v1.
void	get(double[] values) Copies the elements of this spatial vector into an array of doubles.
double	get(int i) Gets a single element of this spatial vector.
double	infinityNorm() Returns the infinity norm of this spatial vector.
void	inverseTransform(RigidTransform3d X) Applies an inverse rigid spatial transformation to this vector, in place.
void	inverseTransform(RotationMatrix3d R) Applies an inverse rotational transformation to this spatial vector, in place.
boolean	isContravariant() Returns true if this spatial vector is contravariant.
double	maxElement() Returns the maximum element value of this spatial vector.
double	minElement() Returns the minimum element value of this spatial vector.
void	negate() Negates this spatial vector in place.
double	norm() Returns the 2 norm of this spatial vector.
void	normalize() Normalizes this spatial vector in place.
double	normSquared() Returns the square of the 2 norm of this spatial vector.
double	oneNorm() Returns the 1 norm of this spatial vector.
void	scale(double s) Scales the elements of this spatial vector by s.
void	set(double[] values) Sets the elements of this spatial vector from an array of doubles.
void	set(int i, double value) Sets a single element of this spatial vector.
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 spatial vector to zero.
int	size() Returns the size of this spatial vector (which is always 6)
java.lang.String	toString(NumberFormat fmt) Returns a String representation of this vector, in which each element is formated using a C printf style as decribed by the parameter NumberFormat. When called numerous times, this routine can be more efficient than toString(String), because the NumberFormat does not need to be recreated each time from a specification string.
void	transform(RigidTransform3d X) Applies a rigid spatial transformation to this spatial vector, in place.
void	transform(RotationMatrix3d R) Applies a rotational transformation to this spatial vector, in place.

Methods inherited from class maspack.matrix.VectorObject

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

Methods inherited from class java.lang.Object

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

Method Detail

size

public int size()

Returns the size of this spatial vector (which is always 6)

Specified by:

size in class VectorObject

Returns:

6

isContravariant

public boolean isContravariant()

Returns true if this spatial vector is contravariant.

Returns:

true for contravariant vectors.

get

public double get(int i)

Gets a single element of this spatial vector. The element ordering depends on whether the vector is contravariant or covariant.

Specified by:

get in class VectorObject

Parameters:

i - element index

Returns:

element value throws ArrayIndexOutOfBoundsException if i is not in the range 0 to 5.

get

public void get(double[] values)

Copies the elements of this spatial vector into an array of doubles. The element ordering depends on whether the vector is contravariant or covariant.

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 spatial vector. The element ordering depends on whether the vector is contravariant or covariant.

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 5.

set

public void set(double[] values)

Sets the elements of this spatial vector from an array of doubles. The element ordering depends on whether the vector is contravariant or covariant.

Overrides:

set in class VectorObject

Parameters:

values - array from which values are copied

negate

public void negate()

Negates this spatial vector in place.

scale

public void scale(double s)

Scales the elements of this spatial vector by s.

Parameters:

s - scaling factor

norm

public double norm()

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

Overrides:

normSquared in class VectorObject

Returns:

square of the 2 norm

maxElement

public double maxElement()

Returns the maximum element value of this spatial vector.

Overrides:

maxElement in class VectorObject

Returns:

maximal element

minElement

public double minElement()

Returns the minimum element value of this spatial vector.

Overrides:

minElement in class VectorObject

Returns:

minimal element

infinityNorm

public double infinityNorm()

Returns the infinity norm of this spatial 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 spatial 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(SpatialVector v1)

Returns the dot product of this spatial vector and the spatial vector v1.

Returns:

dot product

normalize

public void normalize()

Normalizes this spatial vector in place.

epsilonEquals

public boolean epsilonEquals(SpatialVector v1,
                             double eps)

Returns true if the elements of this spatial 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(SpatialVector v1)

Returns true if the elements of this spatial 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 spatial vector to zero.

absolute

public void absolute()

Sets the elements of this spatial vector to their absolute values.

transform

public void transform(RotationMatrix3d R)

Applies a rotational transformation to this spatial vector, in place.

Parameters:

R - rotational transformation matrix

inverseTransform

public void inverseTransform(RotationMatrix3d R)

Applies an inverse rotational transformation to this spatial vector, in place.

Parameters:

R - rotational transformation matrix

transform

public void transform(RigidTransform3d X)

Applies a rigid spatial transformation to this spatial vector, in place.

Parameters:

X - rigid spatial transformation

inverseTransform

public void inverseTransform(RigidTransform3d X)

Applies an inverse rigid spatial transformation to this vector, in place.

Parameters:

X - rigid spatial transformation

toString

public java.lang.String toString(NumberFormat fmt)

Returns a String representation of this vector, in which each element is formated using a C printf style as decribed by the parameter NumberFormat. When called numerous times, this routine can be more efficient than toString(String), because the NumberFormat does not need to be recreated each time from a specification string.

Overrides:

toString in class VectorObject

Parameters:

fmt - numeric format

Returns:

String representation of this 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