rotation.h File Reference

Header file for rotation classes and functions. More...

#include "mpi.h"
#include <hpp/config.h>
#include <hpp/tensor.h>
#include <hpp/mpiUtils.h>
#include <hpp/external/ISOI/grid_generation.h>

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Classes
class	hpp::EulerAngles< T >
class	hpp::SO3Discrete< T >

Namespaces
	hpp

Enumerations
enum	hpp::SymmetryType { hpp::SYMMETRY_TYPE_NONE, hpp::SYMMETRY_TYPE_C4 }

Functions
template<typename T >
MPI_Datatype	hpp::getEulerAnglesTypeMPI ()
template<typename T >
EulerAngles< T >	hpp::polarToEuler (T theta, T phi)
	Convert polar angles to Euler angles. More...
template<typename T >
std::ostream &	hpp::operator<< (std::ostream &out, const EulerAngles< T > &angles)
template<typename T >
bool	hpp::operator== (const EulerAngles< T > &l, const EulerAngles< T > &r)
template<typename T >
bool	hpp::operator!= (const EulerAngles< T > &l, const EulerAngles< T > &r)
template<typename T >
Tensor2< T >	hpp::EulerZXZRotationMatrix (T alpha, T beta, T gamma)
template<typename T >
Tensor2< T >	hpp::EulerZXZRotationMatrix (EulerAngles< T > angle)
template<typename T >
EulerAngles< T >	hpp::getEulerZXZAngles (Tensor2< T > R)
	Get Euler angles from rotation matrix. More...
std::mt19937	hpp::makeMt19937 (bool defaultSeed)
template<typename T >
void	hpp::rotationTensorFrom3UniformRandomsArvo1992 (Tensor2< T > &A, T x1, T x2, T x3)
template<typename T >
void	hpp::randomRotationTensorArvo1992 (std::mt19937 &gen, Tensor2< T > &A)
template<typename T >
void	hpp::randomRotationTensorArvo1992 (Tensor2< T > &A, bool defaultSeed=false)
template<typename T >
void	hpp::rotationTensorFrom3UniformRandoms (Tensor2< T > &A, T x1, T x2, T x3)
template<typename T >
Tensor2< T >	hpp::randomRotationTensorStewart1980 (unsigned int dim, bool defaultSeed=false)
	Generate a random rotation tensor. More...
template<typename T >
void	hpp::randomRotationTensorInPlace (unsigned int dim, Tensor2< T > &A, bool defaultSeed=false)
	Generate a random rotation tensor. More...
template<typename T >
Tensor2< T >	hpp::randomRotationTensor (unsigned int dim, bool defaultSeed=false)
template<typename T >
EulerAngles< T >	hpp::quaternionToEulerAngles (isoi::Quaternion &q)

Detailed Description

Header file for rotation classes and functions.

A discrete and uniform sampling of SO(3) Using the methods and implementations from the following work: Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration. Anna Yershova, Swati Jain, Steven M. LaValle, and Julie C. Mitchell, International Journal of Robotics Research, IJRR 2009.

Euler Angles.

Author

Michael Malahe

Defined according to the following conventions:

• Right-handed
• Counter-clockwise
• Active
• Extrinsic
• Z-X-Z sequence
• \(\alpha\): The second applied Z rotation angle, \([0,2\pi) \)
• \(\beta\): The X rotation angle, \([0,\pi) \)
• \(\gamma\): The first applied Z rotation angle, \([0,2\pi) \)
• The resulting rotation matrix is the product \( R = Z(\alpha) X(\beta) Z(\gamma) \), Where Z is the elemental rotation matrix about z, and X is the elemental rotation matrix about X.