class Rotation3D

(Return to index)

Rotation in 3-dimensional space.

There are two possible external representations:

Matrix3D R

The matrix R is an element of SO(3). Its column vectors define the unit vectors of the rotated coordinate system, expressed in the original system. This representation is used internally and can only be read from a Rotation3D object. To build such an object, use the other representation.

Vector3D V

The direction of V defines the axis of rotation, and its length the sine of half the rotation angle. A zero vector represents the identity.

Type:	Instantiable
Include file:	./BeamlineGeometry/Rotation3D.hh

Synopsis (including inherited members):

• Public members:
  • Rotation3D () ;
  • Rotation3D (double,double,double) ;
  • bool operator== (const Rotation3D&)const ;
  • bool operator!= (const Rotation3D&)const ;
  • Rotation3D& operator*= (const Rotation3D&) ;
  • Rotation3D operator* (const Rotation3D&)const ;
  • Vector3D operator* (const Vector3D&)const ;
  • double operator() (int,int)const ;
  • Vector3D getAxis ()const ;
  • void getAxis (double&,double&,double&)const ;
  • Rotation3D inverse ()const ;
  • bool isIdentity ()const ;
  • bool isPureXRotation ()const ;
  • bool isPureYRotation ()const ;
  • bool isPureZRotation ()const ;
  • static Rotation3D Identity () ;
  • static Rotation3D XRotation (double) ;
  • static Rotation3D YRotation (double) ;
  • static Rotation3D ZRotation (double) ;

Documentation:

• Public members:

  static Rotation3D Identity () ;

  Make identity.

  Rotation3D () ;

  Default constructor.
  Constructs identity.

  Rotation3D (double,double,double) ;

  Constructor.
  Use axis vector (vx,vy,vz).

  static Rotation3D XRotation (double) ;

  Make rotation.
  Construct pure rotation around x-axis.

  static Rotation3D YRotation (double) ;

  Make rotation.
  Construct pure rotation around y-axis.

  static Rotation3D ZRotation (double) ;

  Make rotation.
  Construct pure rotation around z-axis.

  Vector3D getAxis ()const ;

  Get axis vector.
  Return the axis vector.

  void getAxis (double&,double&,double&)const ;

  Get axis vector.
  Return the axis vector in (vx,vy,vz).

  Rotation3D inverse ()const ;

  Inversion.

  bool isIdentity ()const ;

  Test for identity.

  bool isPureXRotation ()const ;

  Test for rotation.
  Return true, if this is a pure x-rotation.

  bool isPureYRotation ()const ;

  Test for rotation.
  Return true, if this is a pure y-rotation.

  bool isPureZRotation ()const ;

  Test for rotation.
  Return true, if this is a pure z-rotation.

  double operator() (int,int)const ;

  Get component.
  Return element (i,k) of the orthogonal matrix.

  Rotation3D operator* (const Rotation3D&)const ;

  Multiply.

  Vector3D operator* (const Vector3D&)const ;

  Rotate.
  Return vector rhs rotated by the rotation this.

  Rotation3D& operator*= (const Rotation3D&) ;

  Multiply and assign.