RotationAxis (biojava 5.0.0 API)

java.lang.Object
- org.biojava.nbio.structure.align.util.RotationAxis

```
public final class RotationAxis
extends Object
```
Calculates the rotation axis for an alignment
A superposition of two structures is generally represented as a rotation matrix plus a translation vector. However, it can also be represented as an axis of rotation plus some translation.
This class calculates the rotation axis and stores it as four properties:
- A unit vector parallel to the rotation axis (getRotationAxis())
- The angle of rotation (getAngle())
- A point on the rotation axis (getRotationPos())
- Some translation parallel to the axis (getScrewTranslation())
The axis of rotation is poorly defined and numerically unstable for small angles. Therefore it's direction is left as null for angles less than MIN_ANGLE.
Author:

Spencer Bliven

Constructor Summary

Constructors
Constructor and Description
`RotationAxis(AFPChain afpChain)` Calculate the rotation axis for the first block of an AFPChain
`RotationAxis(Atom axis, Atom pos, double theta)` Create a rotation axis from a vector, a point, and an angle.
`RotationAxis(javax.vecmath.Matrix4d transform)` Create a rotation axis from a Matrix4d containing a rotational component and a translational component.
`RotationAxis(Matrix rotation, Atom translation)` Determine the location of the rotation axis based on a rotation matrix and a translation vector

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`getAngle()` The rotation angle
`static double`	`getAngle(AFPChain afpChain)` Calculate the rotation angle for a structure
`static double`	`getAngle(Matrix rotation)` Calculate the rotation angle for a given matrix
`javax.vecmath.AxisAngle4d`	`getAxisAngle4d()` Returns the rotation axis and angle in a single javax.vecmath.AxisAngle4d object
`Pair<Atom>`	`getAxisEnds(Atom[] atoms)` Find a segment of the axis that covers the specified set of atoms.
`Matrix`	`getFullMatrix()` Returns a matrix that describes both rotation and translation.
`String`	`getJmolScript(Atom[] atoms)` Returns a Jmol script which will display the axis of rotation.
`String`	`getJmolScript(Atom[] atoms, int axisID)` Returns a Jmol script which will display the axis of rotation.
`double`	`getProjectedDistance(Atom point)` Get the distance from a point to the axis of rotation
`Atom`	`getProjectedPoint(Atom point)` Projects a given point onto the axis of rotation
`Atom`	`getRotationAxis()` Get a unit vector along the rotation axis
`Matrix`	`getRotationMatrix()` Get the rotation matrix corresponding to this axis
`Matrix`	`getRotationMatrix(double theta)` Get the rotation matrix corresponding to a rotation about this axis
`Atom`	`getRotationPos()` Get a position on the rotation axis.
`Atom`	`getScrewTranslation()` Get the component of translation parallel to the axis of rotation
`double`	`getTranslation()`
`javax.vecmath.Vector3d`	`getVector3dScrewTranslation()`
`int`	`guessOrderFromAngle(double threshold, int maxOrder)` Returns the rotation order o that gives the lowest value of `\|2PI / o - theta`, given that the value is strictly lower than `threshold`, for orders {@code o=1,...
`boolean`	`isDefined()`
`void`	`rotate(Atom[] atoms, double theta)`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - RotationAxis
```
public RotationAxis(AFPChain afpChain)
             throws StructureException
```
    Calculate the rotation axis for the first block of an AFPChain
    
    Parameters:
    
    afpChain -
    
    Throws:
    
    StructureException
    
    NullPointerException - if afpChain does not contain a valid rotation matrix and shift vector
  - RotationAxis
```
public RotationAxis(Atom axis,
                    Atom pos,
                    double theta)
```
    Create a rotation axis from a vector, a point, and an angle. The result will be a pure rotation, with no screw component.
    
    Parameters:
    
    axis - A vector parallel to the axis of rotation
    
    pos - A point on the axis of rotation
    
    theta - The angle to rotate (radians)
  - RotationAxis
```
public RotationAxis(Matrix rotation,
                    Atom translation)
```
    Determine the location of the rotation axis based on a rotation matrix and a translation vector
    
    Parameters:
    
    rotation -
    
    translation -
  - RotationAxis
```
public RotationAxis(javax.vecmath.Matrix4d transform)
```
    Create a rotation axis from a Matrix4d containing a rotational component and a translational component.
    
    Parameters:
    
    transform -
- Method Detail
  - getAngle
```
public double getAngle()
```
    The rotation angle
    
    Returns:
    
    the angle, in radians
  - getRotationAxis
```
public Atom getRotationAxis()
```
    Get a unit vector along the rotation axis
    
    Returns:
    
    rotationAxis
  - getAxisAngle4d
```
public javax.vecmath.AxisAngle4d getAxisAngle4d()
```
    Returns the rotation axis and angle in a single javax.vecmath.AxisAngle4d object
    
    Returns:
  - getRotationPos
```
public Atom getRotationPos()
```
    Get a position on the rotation axis. Specifically, project the origin onto the rotation axis
    
    Returns:
    
    rotationPos
  - getScrewTranslation
```
public Atom getScrewTranslation()
```
    Get the component of translation parallel to the axis of rotation
    
    Returns:
  - getVector3dScrewTranslation
```
public javax.vecmath.Vector3d getVector3dScrewTranslation()
```
  - getTranslation
```
public double getTranslation()
```
  - getRotationMatrix
```
public Matrix getRotationMatrix()
```
    Get the rotation matrix corresponding to this axis
    
    Returns:
    
    A 3x3 rotation matrix
  - getRotationMatrix
```
public Matrix getRotationMatrix(double theta)
```
    Get the rotation matrix corresponding to a rotation about this axis
    
    Parameters:
    
    theta - The amount to rotate
    
    Returns:
    
    A 3x3 rotation matrix
  - guessOrderFromAngle
```
public int guessOrderFromAngle(double threshold,
                               int maxOrder)
```
    Returns the rotation order o that gives the lowest value of |2PI / o - theta, given that the value is strictly lower than threshold, for orders o=1,...,maxOrder.
  - getFullMatrix
```
public Matrix getFullMatrix()
```
    Returns a matrix that describes both rotation and translation.
  - getJmolScript
```
public String getJmolScript(Atom[] atoms)
```
    Returns a Jmol script which will display the axis of rotation. This consists of a cyan arrow along the axis, plus an arc showing the angle of rotation.
    As the rotation angle gets smaller, the axis of rotation becomes poorly defined and would need to get farther and farther away from the protein. This is not particularly useful, so we arbitrarily draw it parallel to the translation and omit the arc.
    
    Parameters:
    
    atoms - Some atoms from the protein, used for determining the bounds of the axis.
    
    Returns:
    
    The Jmol script, suitable for calls to jmol.evalString()
  - getAxisEnds
```
public Pair<Atom> getAxisEnds(Atom[] atoms)
```
    Find a segment of the axis that covers the specified set of atoms.
    Projects the input atoms onto the rotation axis and returns the bounding points.
    In the case of a pure translational axis, the axis location is undefined so the center of mass will be used instead.
    
    Parameters:
    
    atoms -
    
    Returns:
    
    two points defining the axis segment
  - getJmolScript
```
public String getJmolScript(Atom[] atoms,
                            int axisID)
```
    Returns a Jmol script which will display the axis of rotation. This consists of a cyan arrow along the axis, plus an arc showing the angle of rotation.
    As the rotation angle gets smaller, the axis of rotation becomes poorly defined and would need to get farther and farther away from the protein. This is not particularly useful, so we arbitrarily draw it parallel to the translation and omit the arc.
    
    Parameters:
    
    atoms - Some atoms from the protein, used for determining the bounds of the axis.
    
    axisID - in case of representing more than one axis in the same jmol panel, indicate the ID number.
    
    Returns:
    
    The Jmol script, suitable for calls to jmol.evalString()
  - getProjectedPoint
```
public Atom getProjectedPoint(Atom point)
```
    Projects a given point onto the axis of rotation
    
    Parameters:
    
    point -
    
    Returns:
    
    An atom which lies on the axis, or null if the RotationAxis is purely translational
  - getProjectedDistance
```
public double getProjectedDistance(Atom point)
```
    Get the distance from a point to the axis of rotation
    
    Parameters:
    
    point -
    
    Returns:
    
    The distance to the axis, or NaN if the RotationAxis is purely translational
  - rotate
```
public void rotate(Atom[] atoms,
                   double theta)
```
  - getAngle
```
public static double getAngle(AFPChain afpChain)
                       throws StructureException
```
    Calculate the rotation angle for a structure
    
    Parameters:
    
    afpChain -
    
    Returns:
    
    The rotation angle, in radians
    
    Throws:
    
    StructureException - If the alignment doesn't contain any blocks
    
    NullPointerException - If the alignment doesn't have a rotation matrix set
  - getAngle
```
public static double getAngle(Matrix rotation)
```
    Calculate the rotation angle for a given matrix
    
    Parameters:
    
    rotation - Rotation matrix
    
    Returns:
    
    The angle, in radians
  - isDefined
```
public boolean isDefined()
```
    Returns:
    
    If the rotation axis is well defined, rather than purely translational

Class RotationAxis

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

RotationAxis

RotationAxis

RotationAxis

RotationAxis

Method Detail

getAngle

getRotationAxis

getAxisAngle4d

getRotationPos

getScrewTranslation

getVector3dScrewTranslation

getTranslation

getRotationMatrix

getRotationMatrix

guessOrderFromAngle

getFullMatrix

getJmolScript

getAxisEnds

getJmolScript

getProjectedPoint

getProjectedDistance

rotate

getAngle

getAngle

isDefined