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IMP Reference Guide
develop.d97d4ead1f,2024/11/21
The Integrative Modeling Platform
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3D rotation class. More...
#include <IMP/algebra/Rotation3D.h>
Inheritance diagram for IMP::algebra::Rotation3D:3D rotation class.
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 https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation for a comparison of different implementations of rotations.
Currently the rotation can be initialized from either:
See geometric primitives for more information.
Definition at line 52 of file Rotation3D.h.
Public Member Functions | |
| Rotation3D (const Rotation3D &rot) | |
| Rotation3D copy constructor. More... | |
| Rotation3D (const VectorD< 4 > &v, bool assume_normalized=false) | |
| Rotation3D () | |
| Create an invalid rotation. More... | |
| Rotation3D (double a, double b, double c, double d) | |
| Create a rotation from a quaternion. More... | |
| Vector3D | get_gradient_of_rotated (const Vector3D &v, unsigned int i, bool wrt_unnorm=false) const |
| Return the gradient of rotated vector wrt the ith quaternion element. More... | |
| Rotation3D | get_inverse () const |
| Return the rotation which undoes this rotation. More... | |
| bool | get_is_valid () const |
| Eigen::MatrixXd | get_jacobian_of_rotated (const Eigen::Vector3d &v, bool wrt_unnorm=false) const |
| Return the Jacobian of rotated vector wrt the quaternion. More... | |
| const Vector4D & | get_quaternion () const |
| Return the quaternion so that it can be stored. More... | |
| Vector3D | get_rotated (const Vector3D &o) const |
| Rotate a vector around the origin. More... | |
| void | get_rotated_adjoint (const Vector3D &v, const Vector3D &Dw, Vector3D *Dv, Rotation3DAdjoint *Dr) const |
Get adjoint of inputs to get_rotated from adjoint of output. More... | |
| RotatedVector3DAdjoint | get_rotated_adjoint (const Vector3D &v, const Vector3D &Dw) const |
Get adjoint of inputs to get_rotated from adjoint of output. More... | |
| double | get_rotated_one_coordinate (const Vector3D &o, unsigned int coord) const |
| Get only the requested rotation coordinate of the vector. More... | |
| Vector3D | get_rotation_matrix_row (int i) const |
| Vector3D | operator* (const Vector3D &v) const |
| Rotate a vector around the origin. More... | |
| Rotation3D | operator* (const Rotation3D &q) const |
| Multiply two rotations. More... | |
| Rotation3D | operator/ (const Rotation3D &r) const |
| Compute the rotation which when composed with r gives this. More... | |
| const Rotation3D & | operator/= (const Rotation3D &r) |
| Rotation3D & | operator= (const Rotation3D &rot) |
| void | show (std::ostream &out=std::cout) const |
Friends | |
| Rotation3D | compose (const Rotation3D &a, const Rotation3D &b) |
| IMP::algebra::Rotation3D::Rotation3D | ( | const Rotation3D & | rot | ) |
Rotation3D copy constructor.
Definition at line 106 of file Rotation3D.h.
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explicit |
Create a rotation from a vector of 4 quaternion coefficients.
Definition at line 119 of file Rotation3D.h.
| IMP::algebra::Rotation3D::Rotation3D | ( | ) |
Create an invalid rotation.
Definition at line 125 of file Rotation3D.h.
| 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. |
Definition at line 129 of file Rotation3D.h.
| Vector3D IMP::algebra::Rotation3D::get_gradient_of_rotated | ( | const Vector3D & | v, |
| unsigned int | i, | ||
| bool | wrt_unnorm = false |
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| ) | const |
Return the gradient of rotated vector wrt the ith quaternion element.
Given the rotation \(x = R(q) v\), where \(v\) is a vector, \(q=(q_0,q_1,q_2,q_3)\) is the quaternion of the rotation with elements \(q_i\), and \(R(q)\) is the corresponding rotation matrix, the function returns the gradient \(\nabla_{q_i} x\).
This function just returns a single column from get_jacobian(), so it is more efficient to call that function if all columns are needed.
| [in] | v | vector to be rotated by rotation \(R(q)\) |
| [in] | i | the quaternion element |
| [in] | wrt_unnorm | Gradient is computed wrt unnormalized quaternion. Rotation includes a normalization operation, and the gradient is projected to the tangent space at \(q\). |
| Rotation3D IMP::algebra::Rotation3D::get_inverse | ( | ) | const |
Return the rotation which undoes this rotation.
Definition at line 234 of file Rotation3D.h.
| bool IMP::algebra::Rotation3D::get_is_valid | ( | ) | const |
Return true is the rotation is valid, false if invalid or not initialized (e.g., only initialized by the empty constructor)
Definition at line 308 of file Rotation3D.h.
| Eigen::MatrixXd IMP::algebra::Rotation3D::get_jacobian_of_rotated | ( | const Eigen::Vector3d & | v, |
| bool | wrt_unnorm = false |
||
| ) | const |
Return the Jacobian of rotated vector wrt the quaternion.
Given the rotation \(x = R(q) v\), where \(v\) is a vector, \(q\) is the quaternion of the rotation, and \(R(q)\) is the corresponding rotation matrix, the function returns the 3x4 matrix \(J\) with elements \(J_{ij}=\frac{\partial x_i}{\partial q_j}\).
| [in] | v | vector to be rotated by rotation \(R(q)\) |
| [in] | wrt_unnorm | Jacobian is computed wrt unnormalized quaternion. Rotation includes a normalization operation, and the columns are projected to the tangent space at \(q\). |
| const Vector4D& IMP::algebra::Rotation3D::get_quaternion | ( | ) | const |
Return the quaternion so that it can be stored.
Note that there is no guarantee on which of the two equivalent quaternions is returned.
Definition at line 245 of file Rotation3D.h.
Rotate a vector around the origin.
Definition at line 193 of file Rotation3D.h.
| void IMP::algebra::Rotation3D::get_rotated_adjoint | ( | const Vector3D & | v, |
| const Vector3D & | Dw, | ||
| Vector3D * | Dv, | ||
| Rotation3DAdjoint * | Dr | ||
| ) | const |
Get adjoint of inputs to get_rotated from adjoint of output.
Compute the adjoint (reverse-mode sensitivity) of input vector to get_rotated and this rotation from the adjoint of the output vector.
| RotatedVector3DAdjoint IMP::algebra::Rotation3D::get_rotated_adjoint | ( | const Vector3D & | v, |
| const Vector3D & | Dw | ||
| ) | const |
Get adjoint of inputs to get_rotated from adjoint of output.
Compute the adjoint (reverse-mode sensitivity) of input vector to get_rotated and this rotation from the adjoint of the output vector.
| double IMP::algebra::Rotation3D::get_rotated_one_coordinate | ( | const Vector3D & | o, |
| unsigned int | coord | ||
| ) | const |
Get only the requested rotation coordinate of the vector.
Definition at line 217 of file Rotation3D.h.
Rotate a vector around the origin.
Definition at line 224 of file Rotation3D.h.
| Rotation3D IMP::algebra::Rotation3D::operator* | ( | const Rotation3D & | q | ) | const |
Multiply two rotations.
Definition at line 252 of file Rotation3D.h.
Here is the call graph for this function:| Rotation3D IMP::algebra::Rotation3D::operator/ | ( | const Rotation3D & | r | ) | const |
Compute the rotation which when composed with r gives this.
Definition at line 259 of file Rotation3D.h.
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friend |
Definition at line 491 of file Rotation3D.h.