Rotations are currently represented using quaternions and a cached copy of the rotation matrix. The quaternion allows for fast and stable composition and the cached rotation matrix means that rotations are performed quickly. See http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation for a comparison of different implementations of rotations.
Currently the rotation can be initialized from either:
Public Member Functions | |
| const VectorD< 3 > | get_derivative (const VectorD< 3 > &o, unsigned int i) const |
| Return the derivative of the position x with respect to internal variable i. | |
| Rotation3D | get_inverse () const |
| Return the rotation which undoes this rotation. | |
| const VectorD< 4 > | get_quaternion (const VectorD< 4 > &q) const |
| return the quaterion so that it can be stored | |
| const VectorD< 4 > & | get_quaternion () const |
| return the quaterion so that it can be stored | |
| VectorD< 3 > | get_rotated (const VectorD< 3 > &o) const |
| Rotate a vector around the origin. | |
| double | get_rotated_one_coordinate (const VectorD< 3 > &o, unsigned int coord) const |
| Gets only the requested rotation coordinate of the vector. | |
| Rotation3D | operator* (const Rotation3D &q) const |
| multiply two rotations | |
| VectorD< 3 > | operator* (const VectorD< 3 > &v) const |
| Rotate a vector around the origin. | |
| Rotation3D | operator/ (const Rotation3D &r) const |
| Compute the rotation which when composed with r gives this. | |
| const Rotation3D & | operator/= (const Rotation3D &r) |
| Rotation3D (double a, double b, double c, double d) | |
| Create a rotation from a quaternion. | |
| Rotation3D () | |
| Create an invalid rotation. | |
| Rotation3D (const VectorD< 4 > &v) | |
| Create a rotation from an unnormalized vector 4. | |
Friends | |
| Rotation3D | compose (const Rotation3D &a, const Rotation3D &b) |
Related Functions | |
| (Note that these are not member functions.) | |
| std::pair< VectorD< 3 >, double > | get_axis_and_angle (const Rotation3D &rot) |
| Decompose a Rotation3D object into a rotation around an axis. | |
| double | get_distance (const Rotation3D &r0, const Rotation3D &r1) |
| Return a distance between the two rotations. | |
| Rotation3D | get_identity_rotation_3d () |
| Return a rotation that does not do anything. | |
| Rotation3D | get_random_rotation_3d (const Rotation3D ¢er, double distance) |
| Pick a rotation at random near the provided one. | |
| Rotation3D | get_random_rotation_3d () |
| Pick a rotation at random from all possible rotations. | |
| Rotation3D | get_rotation_from_matrix (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22) |
| Generate a Rotation3D object from a rotation matrix. | |
| Rotation3D | get_rotation_from_vector4d (const VectorD< 4 > &v) |
| Compute a rotatation from an unnormalized quaternion. | |
| Rotation3D | get_rotation_in_radians_about_axis (const VectorD< 3 > &axis, double angle) |
| Generate a Rotation3D object from a rotation around an axis. | |
| Rotation3D | get_rotation_taking_first_to_second (const VectorD< 3 > &v1, const VectorD< 3 > &v2) |
| Create a rotation from the first vector to the second one. | |
| Rotation3D | interpolate (const Rotation3D &a, const Rotation3D &b, double f) |
| Interpolate between two rotations. | |
Euler Angles | |
There are many conventions for how to define Euler angles, based on choices of which of the x,y,z axis to use in what order and whether the rotation axis is in the body frame (and hence affected by previous rotations) or in in a fixed frame. See http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles for a general description.
| |
| Rotation3D | get_rotation_from_fixed_zxz (double phi, double theta, double psi) |
| Initialize a rotation from euler angles. | |
| IMP::algebra::Rotation3D::Rotation3D | ( | double | a, | |
| double | b, | |||
| double | c, | |||
| double | d | |||
| ) |
Create a rotation from a quaternion.
| ValueException | if the rotation is not a unit vector. |
return the quaterion so that it can be stored
This quaternion has it sign chosen so as to be interoperable with q (that is, they are in the same hemisphere). Use this when writing code to average or clustering rotations.
| std::pair< VectorD< 3 >, double > get_axis_and_angle | ( | const Rotation3D & | rot | ) | [related] |
Decompose a Rotation3D object into a rotation around an axis.
www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm
| double get_distance | ( | const Rotation3D & | r0, | |
| const Rotation3D & | r1 | |||
| ) | [related] |
Return a distance between the two rotations.
The distance runs between 0 and 1. More precisely, the distance returned is the angle from the origin of the two quaternion vectors (with signs chosen appropriately), divided by pi/2.
| Rotation3D get_identity_rotation_3d | ( | ) | [related] |
Return a rotation that does not do anything.
| Rotation3D get_random_rotation_3d | ( | const Rotation3D & | center, | |
| double | distance | |||
| ) | [related] |
Pick a rotation at random near the provided one.
This method generates a rotation that is within the provided distance of center.
| [in] | center | The center of the rotational volume |
| [in] | distance | See get_distance(const Rotation3D&,const Rotation3D&) for a full definition. |
| Rotation3D get_random_rotation_3d | ( | ) | [related] |
Pick a rotation at random from all possible rotations.
| Rotation3D get_rotation_from_fixed_zxz | ( | double | phi, | |
| double | theta, | |||
| double | psi | |||
| ) | [related] |
Initialize a rotation from euler angles.
| [in] | phi | Rotation around the Z axis in radians |
| [in] | theta | Rotation around the X axis in radians |
| [in] | psi | Rotation around the Z axis in radians |
| Rotation3D get_rotation_from_vector4d | ( | const VectorD< 4 > & | v | ) | [related] |
Compute a rotatation from an unnormalized quaternion.
| Rotation3D get_rotation_in_radians_about_axis | ( | const VectorD< 3 > & | axis, | |
| double | angle | |||
| ) | [related] |
Generate a Rotation3D object from a rotation around an axis.
| [in] | axis | the rotation axis passes through (0,0,0) |
| [in] | angle | the rotation angle in radians |
www.euclideanspace.com/maths/geometry/rotations/conversions/ angleToQuaternion/index.htm
| Rotation3D interpolate | ( | const Rotation3D & | a, | |
| const Rotation3D & | b, | |||
| double | f | |||
| ) | [related] |
Interpolate between two rotations.
It f ==0, return b, if f==1 return a.
