Namespace ennui::math

Namespace List > ennui > math

namespace for general mathematical operations

Classes

Type	Name
class	Units Fixed mathematical constants and conversion factors.

Public Functions

Type	Name
Matrix3x3	R3_to_SO3 (ConstRefVector3 & x) Euler's finite rotation, stable.
Matrix3x3	R3_to_so3 (const Vector3 & x) Vector to skew-symmetric matrix.
Matrix3x3	R4_to_SO3 (const Vector4 & q) Quaternion to rotation matrix.
Matrix3x3	euler_finite_rotation (const Eigen::Ref< const Matrix3x3 > & OmegaNormed, double xnorm) Euler's finite rotation, standard form.
Matrix3x3	euler_finite_rotation_approx (const Eigen::Ref< const Matrix3x3 > & Omega, double xnorm) Euler's finite rotation, small angle approximation.
Matrix3x3	mean_attitude_update (const Eigen::Ref< const Matrix3x3 > & alpha_cross, double alpha_norm) Mean attitude update from delta-theta ("exact")
Matrix3x3	mean_attitude_update_approx (const Eigen::Ref< const Matrix3x3 > & alpha_cross, double alpha_norm) Approximate mean attitude update from delta-theta.
Matrix3x3	normalize_SO3 (const Matrix3x3 R) Matrix normalization by SVD.
Matrix3x3	normalize_SO3_Groves (const Matrix3x3 R) Matrix normalization using Grove's approximation.

Public Functions Documentation

function R3_to_SO3

Euler's finite rotation, stable.

inline Matrix3x3 ennui::math::R3_to_SO3 (
    ConstRefVector3 & x
)

Parameters:

x rotation vector

Returns:

rotation matrix

Stable version of the rotation expansion. Switches between small-angle approximation and exact based on the vector magnitude to avoid numerical instability.

function R3_to_so3

Vector to skew-symmetric matrix.

inline Matrix3x3 ennui::math::R3_to_so3 (
    const Vector3 & x
)

function R4_to_SO3

Quaternion to rotation matrix.

inline Matrix3x3 ennui::math::R4_to_SO3 (
    const Vector4 & q
)

function euler_finite_rotation

Euler's finite rotation, standard form.

inline Matrix3x3 ennui::math::euler_finite_rotation (
    const Eigen::Ref< const Matrix3x3 > & OmegaNormed,
    double xnorm
)

Parameters:

OmegaNormed skew-symmetric matrix of normalized 3-vector
xnorm magnitude of the rotation vector

Returns:

rotation matrix

Supplying Omega normed and its magnitude as separate variables avoids computing the sinc function (well-defined at 0 but problematic numerically). See eq. (5.73) groves_principles_2013

function euler_finite_rotation_approx

Euler's finite rotation, small angle approximation.

inline Matrix3x3 ennui::math::euler_finite_rotation_approx (
    const Eigen::Ref< const Matrix3x3 > & Omega,
    double xnorm
)

Parameters:

Omega skew-symmetric matrix (NOT normalized)
xnorm magnitude of the rotation vector

Returns:

rotation matrix

Employing the small angle approximation avoids both evaluating trigonometric functions and variable division. See eq. (5.72) groves_principles_2013

function mean_attitude_update

Mean attitude update from delta-theta ("exact")

inline Matrix3x3 ennui::math::mean_attitude_update (
    const Eigen::Ref< const Matrix3x3 > & alpha_cross,
    double alpha_norm
)

Parameters:

alpha_cross skew-symmetric matrix (NOT normalized)
alpha_norm magnitude of the rotation vector

Returns:

general matrix (3x3)

See eq. (5.84) groves_principles_2013

function mean_attitude_update_approx

Approximate mean attitude update from delta-theta.

inline Matrix3x3 ennui::math::mean_attitude_update_approx (
    const Eigen::Ref< const Matrix3x3 > & alpha_cross,
    double alpha_norm
)

Parameters:

alpha_cross skew-symmetric matrix (NOT normalized)
alpha_norm magnitude of the rotation vector

Returns:

general matrix (3x3)

See eq. (5.84) groves_principles_2013

function normalize_SO3

Matrix normalization by SVD.

inline Matrix3x3 ennui::math::normalize_SO3 (
    const Matrix3x3 R
)

function normalize_SO3_Groves

Matrix normalization using Grove's approximation.

inline Matrix3x3 ennui::math::normalize_SO3_Groves (
    const Matrix3x3 R
)

The documentation for this class was generated from the following file Ennui/math/rotation.hpp