AxisAngle (Artisynth API documentation)

java.lang.Object
- maspack.matrix.AxisAngle

All Implemented Interfaces:

java.lang.Cloneable, Clonable
```
public class AxisAngle
extends java.lang.Object
implements Clonable
```
Axis-angle representation of a rigid-body rotation. Any spatial rotation can be represented as a rotation about a specific axis by a certain angular amount. An angle of 0 corresponds to the "identity" rotation (i.e., no rotation).
The axis value is normalized. However, the representation is still not unique: negating both axis and angle, or adding 2*PI to angle, results in the same rotation.

Field Summary

Fields
Modifier and Type	Field and Description
`double`	`angle` Angle of rotation about the axis, in radians.
`Vector3d`	`axis` Rotation axis.
`static AxisAngle`	`IDENTITY`
`static AxisAngle`	`ROT_X_90`
`static AxisAngle`	`ROT_Y_90`
`static AxisAngle`	`ROT_Z_90`
`static AxisAngle`	`ZERO`

Constructor Summary

Constructors
Constructor and Description
`AxisAngle()` Creates an AxisAngle and initializes it to the identity rotation.
`AxisAngle(AxisAngle axisAng)` Creates an AxisAngle and initializes it from an existing AxisAngle.
`AxisAngle(double[] values)` Creates an AxisAngle and initializes it to the prescribed values.
`AxisAngle(double x, double y, double z, double ang)` Creates an AxisAngle and initializes it to the prescribed values.
`AxisAngle(RotationMatrix3d R)` Creates an AxisAngle initialized to the specified rotation matrix.
`AxisAngle(Vector3d axis, double ang)` Creates an AxisAngle and sets it to the prescribed values.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`AxisAngle`	`clone()`
`boolean`	`epsilonEquals(AxisAngle axisAng, double eps)` Returns true if the elements of this AxisAngle equal those of another AxisAngle within a prescribed tolerance `epsilon`.
`boolean`	`equals(AxisAngle axisAng)` Returns true if the elements of this AxisAngle equal those of another AxisAngle exactly.
`boolean`	`equals(java.lang.Object obj)` Returns true if the supplied object is an AxisAngle and its elements equal those of this AxisAngle exactly.
`void`	`get(double[] vals)` Gets the values associated with this AxisAngle.
`void`	`get(double[] vals, double[] refs, int off, double angScale)` Copies the elements of this AxisAngle into an array of doubles.
`void`	`get(double[] vals, double[] refs, int off, RotationRep rotRep, double s)` Get a specified rotation representation from this AxisAngle.
`void`	`get(double[] vals, int off)` Gets the values associated with this AxisAngle.
`void`	`get(Quaternion q)` Gets the quaternion associated with this axis angle.
`void`	`inverseTransform(Vector3d vr, Vector3d v1)` Transforms a vector v1 by the rotation implied by the inverse of this axis-angle using Rodriguez's rotation formula
`void`	`negate()` Negates the axis and angle of this AxisAngle.
`double`	`numericDistance(Vector3d axis, double ang)` Returns the distance between this AxisAngle and a second specified by `axis` and `ang`.
`double`	`numericDistanceSquared(Vector3d axis, double ang)` Returns the square of the distance between this AxisAngle and a second specified by `axis` and `ang`, where distance is described in the docs for `numericDistance(maspack.matrix.Vector3d, double)`.
`void`	`set(AxisAngle axisAng)` Sets this AxisAngle to the values of another AxisAngle.
`void`	`set(double[] vals)` Sets this AxisAngle to the prescribed values.
`void`	`set(double[] vals, int off)` Sets this AxisAngle to the prescribed values.
`void`	`set(double[] vals, int off, RotationRep rotRep, double s)` Sets this AxisAngle from a set of doubles implementing a given rotation representation.
`void`	`set(double x, double y, double z, double ang)` Sets this AxisAngle to the prescribed values.
`void`	`set(Quaternion q)` Sets this AxisAngle to the values appropriate for the specified quaternion.
`void`	`set(RotationMatrix3d R)` Sets this AxisAngle to the values appropriate for the specified rotation matrix.
`void`	`set(Vector3d axis, double ang)` Sets this AxisAngle to the prescribed values.
`void`	`setRandom()` Sets this AxisAngle to a random one.
`java.lang.String`	`toString()` Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians).
`java.lang.String`	`toString(NumberFormat fmt)` Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians).
`java.lang.String`	`toString(java.lang.String fmtStr)` Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians).
`void`	`transform(Vector3d vr, Vector3d v1)` Transforms a vector v1 by the rotation implied by this axis-angle using Rodriguez's rotation formula

Methods inherited from class java.lang.Object
getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - IDENTITY
```
public static final AxisAngle IDENTITY
```
  - ZERO
```
public static final AxisAngle ZERO
```
  - ROT_X_90
```
public static final AxisAngle ROT_X_90
```
  - ROT_Y_90
```
public static final AxisAngle ROT_Y_90
```
  - ROT_Z_90
```
public static final AxisAngle ROT_Z_90
```
  - axis
```
public Vector3d axis
```
    Rotation axis.
  - angle
```
public double angle
```
    Angle of rotation about the axis, in radians.
- Constructor Detail
  - AxisAngle
```
public AxisAngle()
```
    Creates an AxisAngle and initializes it to the identity rotation.
  - AxisAngle
```
public AxisAngle(double[] values)
```
    Creates an AxisAngle and initializes it to the prescribed values. The axis values are normalized.
    
    Parameters:
    
    values - AxisAngle values given as an array. The x, y, and z directions of the rotation axis are given by elements 0 through 2, and the rotation angle (in radians) is given by element 3.
  - AxisAngle
```
public AxisAngle(double x,
                 double y,
                 double z,
                 double ang)
```
    Creates an AxisAngle and initializes it to the prescribed values. The axis values are normalized.
    
    Parameters:
    
    x - rotation axis x direction
    
    y - rotation axis y direction
    
    z - rotation axis z direction
    
    ang - rotation angle, in radians
  - AxisAngle
```
public AxisAngle(Vector3d axis,
                 double ang)
```
    Creates an AxisAngle and sets it to the prescribed values. The axis values are normalixed.
    
    Parameters:
    
    axis - rotation axis
    
    ang - rotation angle (in radians)
  - AxisAngle
```
public AxisAngle(AxisAngle axisAng)
```
    Creates an AxisAngle and initializes it from an existing AxisAngle.
    
    Parameters:
    
    axisAng - AxisAngle to supply initial values
  - AxisAngle
```
public AxisAngle(RotationMatrix3d R)
```
    Creates an AxisAngle initialized to the specified rotation matrix.
    
    Parameters:
    
    R - rotation matrix
- Method Detail
  - set
```
public void set(double x,
                double y,
                double z,
                double ang)
```
    Sets this AxisAngle to the prescribed values. The axis values are normalized.
    
    Parameters:
    
    x - rotation axis x direction
    
    y - rotation axis y direction
    
    z - rotation axis z direction
    
    ang - rotation angle, in radians
  - set
```
public void set(double[] vals,
                int off)
```
    Sets this AxisAngle to the prescribed values. The x, y, and z directions of the rotation axis are given by the first three values, and the rotation angle (in radians) is given by the fourth value. The axis values will be normalized.
    
    Parameters:
    
    vals - AxisAngle values given as an array
    
    off - offset within vals where the values begin
  - set
```
public void set(double[] vals)
```
    Sets this AxisAngle to the prescribed values. The x, y, and z directions of the rotation axis are given by the first three values, and the rotation angle (in radians) is given by the fourth value. The axis values will be normalized.
    
    Parameters:
    
    vals - AxisAngle values given as an array
  - set
```
public void set(Vector3d axis,
                double ang)
```
    Sets this AxisAngle to the prescribed values. The axis values are normalixed.
    
    Parameters:
    
    axis - rotation axis
    
    ang - rotation angle (in radians)
  - set
```
public void set(AxisAngle axisAng)
```
    Sets this AxisAngle to the values of another AxisAngle.
    
    Parameters:
    
    axisAng - AxisAngle supplying new values
  - set
```
public void set(RotationMatrix3d R)
```
    Sets this AxisAngle to the values appropriate for the specified rotation matrix.
    
    Parameters:
    
    R - rotation matrix
  - set
```
public void set(Quaternion q)
```
    Sets this AxisAngle to the values appropriate for the specified quaternion.
    
    Parameters:
    
    q - quaternion
  - get
```
public void get(Quaternion q)
```
    Gets the quaternion associated with this axis angle.
    
    Parameters:
    
    q - return the quaternion
  - get
```
public void get(double[] vals,
                int off)
```
    Gets the values associated with this AxisAngle. See set(double[]) for a description of the values.
    
    Parameters:
    
    vals - returns the AxisAngle values
    
    off - offset within vals where the values are stored
  - get
```
public void get(double[] vals,
                double[] refs,
                int off,
                double angScale)
```
    Copies the elements of this AxisAngle into an array of doubles. The array must have a length >= 4 + off. The method accepts an optional argument refs which specifies a reference AxisAngle. If the negative of this AxisAngle is closer distance-wise to the reference, then the negative values are copied instead.
    
    Parameters:
    
    vals - array into which values are copied
    
    refs - if non-null, specifies values of a reference AxisAngle
    
    off - offset within vals and refs where values are stored
    
    angScale - factor by which the output and reference angles are scaled
  - get
```
public void get(double[] vals)
```
    Gets the values associated with this AxisAngle. See set(double[]) for a description of the values.
    
    Parameters:
    
    vals - returns the AxisAngle values
  - transform
```
public void transform(Vector3d vr,
                      Vector3d v1)
```
    Transforms a vector v1 by the rotation implied by this axis-angle using Rodriguez's rotation formula
    
    Parameters:
    
    vr - result vector
    
    v1 - vector to be transformed
  - inverseTransform
```
public void inverseTransform(Vector3d vr,
                             Vector3d v1)
```
    Transforms a vector v1 by the rotation implied by the inverse of this axis-angle using Rodriguez's rotation formula
    
    Parameters:
    
    vr - result vector
    
    v1 - vector to be transformed
  - toString
```
public java.lang.String toString()
```
    Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians).
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    String representation
  - toString
```
public java.lang.String toString(java.lang.String fmtStr)
```
    Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians). Each element is formatted using a C printf style format string. For a description of the format string syntax, see NumberFormat.
    
    Parameters:
    
    fmtStr - numeric format specification
    
    Returns:
    
    String representation of this vector
  - toString
```
public java.lang.String toString(NumberFormat fmt)
```
    Returns a String representation of this AxisAngle, consisting of the x, y, and z components of the axis, followed by the angle (in radians). Each element is formatted 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.
    
    Parameters:
    
    fmt - numeric format
    
    Returns:
    
    String representation of this vector
  - epsilonEquals
```
public boolean epsilonEquals(AxisAngle axisAng,
                             double eps)
                      throws ImproperSizeException
```
    Returns true if the elements of this AxisAngle equal those of another AxisAngle within a prescribed tolerance epsilon.
    
    Parameters:
    
    axisAng - AxisAngle to compare with
    
    eps - comparison tolerance
    
    Returns:
    
    false if the AxisAngles are not equal within the specified tolerance
    
    Throws:
    
    ImproperSizeException
  - negate
```
public void negate()
```
    Negates the axis and angle of this AxisAngle.
  - equals
```
public boolean equals(AxisAngle axisAng)
```
    Returns true if the elements of this AxisAngle equal those of another AxisAngle exactly.
    
    Parameters:
    
    axisAng - AxisAngle to compare with
    
    Returns:
    
    false if the AxisAngles are not equal
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Returns true if the supplied object is an AxisAngle and its elements equal those of this AxisAngle exactly.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    obj - Object to compare with
    
    Returns:
    
    false if the Object does not equal this AxisAngle
  - clone
```
public AxisAngle clone()
```
    Specified by:
    
    clone in interface Clonable
    
    Overrides:
    
    clone in class java.lang.Object
  - set
```
public void set(double[] vals,
                int off,
                RotationRep rotRep,
                double s)
```
    Sets this AxisAngle from a set of doubles implementing a given rotation representation.
    
    Parameters:
    
    vals - values specifying the rotation
    
    off - offset within vals where rotation info starts
    
    rotRep - rotation representation
    
    s - factor by which values are scaled
  - get
```
public void get(double[] vals,
                double[] refs,
                int off,
                RotationRep rotRep,
                double s)
```
    Get a specified rotation representation from this AxisAngle.
    
    Parameters:
    
    vals - returns the values specifying the rotation
    
    refs - if non-null, specifies a reference set of values to be used to resolve non-unique solutions
    
    off - offset within vals where rotation info starts
    
    rotRep - rotation representation
    
    s - factor by which values are scaled
  - numericDistanceSquared
```
public double numericDistanceSquared(Vector3d axis,
                                     double ang)
```
    Returns the square of the distance between this AxisAngle and a second specified by axis and ang, where distance is described in the docs for numericDistance(maspack.matrix.Vector3d, double).
    
    Parameters:
    
    axis - axis of the AxisAngle to obtain distance squared to
    
    ang - angle of AxisAngle to obtain distance squared to
    
    Returns:
    
    distance squared to the specified AxisAngle
  - numericDistance
```
public double numericDistance(Vector3d axis,
                              double ang)
```
    Returns the distance between this AxisAngle and a second specified by axis and ang. Distance here refers not to angular distance between the two orientations, but distance between the representations themselves:
```
 d = sqrt( deltaAngle^2 + ||deltaAxis||^2 )
 
```
    where deltaAngle is the difference between the two angles (reduced to the range (-PI,PI], and deltaAxis is the difference between the two axes. In particular, an AxisAngle and its negative have maximal distance between each other, even though both describe the same orientation.
    Parameters:
    
    axis - axis of the AxisAngle to obtain distance to
    
    ang - angle of AxisAngle to obtain distance to
    
    Returns:
    
    distance to the specified AxisAngle
  - setRandom
```
public void setRandom()
```
    Sets this AxisAngle to a random one.

Class AxisAngle

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

IDENTITY

ZERO

ROT_X_90

ROT_Y_90

ROT_Z_90

axis

angle

Constructor Detail

AxisAngle

AxisAngle

AxisAngle

AxisAngle

AxisAngle

AxisAngle

Method Detail

set

set

set

set

set

set

set

get

get

get

get

transform

inverseTransform

toString

toString

toString

epsilonEquals

negate

equals

equals

clone

set

get

numericDistanceSquared

numericDistance

setRandom