Package org.biojava.nbio.structure.align.util

Class 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:

    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 Detail

      • 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:

      • 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​(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

      • getAngle

        public static double getAngle​(javax.vecmath.Matrix4d transform)
        Quickly compute the rotation angle from a rotation matrix.
        Parameters:
        transform - 4D transformation matrix. Translation components are ignored.
        Returns:
        Angle, from 0 to PI

      • getAngle

        public static double getAngle​(javax.vecmath.Matrix3d transform)
        Quickly compute the rotation angle from a rotation matrix.
        Parameters:
        transform - 3D rotation matrix
        Returns:
        Angle, from 0 to PI