EulerRotations Class Reference

Class EulerRotations. More...

#include <euler_rotations.h>

Classes
struct	Euler
	Custom Euler angles struct. More...
struct	Quaternions
	Custom quaternions struct: . More...

Static Public Member Functions
static Quaternions	euler_to_quaternions (double phi, double theta, double psi)
	Convert Euler angles to quaternions. More...
static Euler	quaternions_to_euler (double w, double x, double y, double z)
	Convert quaternions to Euler angles. More...
static Eigen::Matrix3d	basic_rotation_x (double x)
	Basic rotation matrix wrt x axis. More...
static Eigen::Matrix3d	basic_rotation_y (double x)
	Basic rotation matrix wrt y axis. More...
static Eigen::Matrix3d	basic_rotation_z (double x)
	Basic rotation matrix wrt z axis. More...
static Eigen::Matrix3d	rotation (double phi, double theta, double psi)
	Euler rotation matrix z-y'-x''. More...
static Eigen::Matrix3d	rotation (Eigen::Vector3d euler_angles)
static Eigen::Matrix3d	rotation (std::vector< double > euler_angles)
static Eigen::Matrix3d	rotation (Euler euler_angles)

Detailed Description

Class EulerRotations.

This class contains definitions of rotation matrices and useful functionality for rotation releated operations.

Definition at line 12 of file euler_rotations.h.

Member Function Documentation

basic_rotation_x()

Eigen::Matrix3d EulerRotations::basic_rotation_x ( double  x )

static

Basic rotation matrix wrt x axis.

Return the basic rotation matrix around x axis by a given angle x.

Parameters

x	The rotation angle.

Returns

Eigen::Matrix3d The basic rotation matrix around x axis.

Definition at line 9 of file euler_rotations.cpp.

{
    // Matrix initialization
    Eigen::Matrix3d m;
 
    m << 1.0f, 0.0f, 0.0f, 
        0.0f, cos(x), -sin(x), 
        0.0f, sin(x), cos(x);
    return m;
}

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basic_rotation_y()

Eigen::Matrix3d EulerRotations::basic_rotation_y ( double  x )

static

Basic rotation matrix wrt y axis.

Return the basic rotation matrix around y axis by a given angle x.

Parameters

x	The rotation angle.

Returns

Eigen::Matrix3d The basic rotation matrix around y axis.

Definition at line 26 of file euler_rotations.cpp.

{
    // Matrix initialization
    Eigen::Matrix3d m;
 
    m << cos(x), 0.0f, sin(x), 
        0.0f, 1.0f, 0.0f, 
        -sin(x), 0.0f, cos(x);
    return m;
}

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basic_rotation_z()

Eigen::Matrix3d EulerRotations::basic_rotation_z ( double  x )

static

Basic rotation matrix wrt z axis.

Return the basic rotation matrix around z axis by a given angle x.

Parameters

x	The rotation angle.

Returns

Eigen::Matrix3d The basic rotation matrix around z axis.

Definition at line 43 of file euler_rotations.cpp.

{
    // Matrix initialization
    Eigen::Matrix3d m;
 
    m << cos(x), -sin(x), 0.0f, 
        sin(x), cos(x), 0.0f, 
        0.0f, 0.0f, 1.0f;
    return m;
}

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euler_to_quaternions()

EulerRotations::Quaternions EulerRotations::euler_to_quaternions ( double  phi, double  theta, double  psi  )

static

Convert Euler angles to quaternions.

This method will return a custom Quaternions struct from a set of Euler angles. Euler angles follow the post multiply sequence zyx. Rotate "psi" around Z (yaw), "theta" around y (pitch) and "phi" around x (roll).

Parameters

phi	Roll angle around x axis. (rad)
theta	Pitch angle around y axis. (rad)
psi	Yaw angle around z axis. (rad)

Returns

EulerRotations::Quaternions Quaterinos struct.

Definition at line 117 of file euler_rotations.cpp.

{
    EulerRotations::Quaternions quatern;
 
    double cy = cos(psi * 0.5); double sy = sin(psi * 0.5);
    double cp = cos(theta * 0.5); double sp = sin(theta * 0.5);
    double cr = cos(phi * 0.5); double sr = sin(phi * 0.5);
 
    quatern.w = cr * cp * cy + sr * sp * sy;
    quatern.x = sr * cp * cy - cr * sp * sy;
    quatern.y = cr * sp * cy + sr * cp * sy;
    quatern.z = cr * cp * sy - sr * sp * cy;
 
    // Return Quaternions
    return quatern;
}

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quaternions_to_euler()

EulerRotations::Euler EulerRotations::quaternions_to_euler ( double  w, double  x, double  y, double  z  )

static

Convert quaternions to Euler angles.

This method will return a custom Euler struct from a set of Quaternions. Euler angles follow the post multiply sequence zyx. Rotate "psi" around Z (yaw), "theta" around y (pitch) and "phi" around x (roll).

Parameters

w	Quaternion parameter w.
x	Quaternion parameter x.
y	Quaternion parameter y.
z	Quaternion parameter z.

Returns

EulerRotations::Euler Euler angles given in radians.

Definition at line 148 of file euler_rotations.cpp.

{
    EulerRotations::Euler euler_angles;
 
    // Roll (x-axis rotation)
    double sinr_cosp = 2.0 * (w * x + y * z);
    double cosr_cosp = 1.0 - 2.0 * (x * x + y * y);
    euler_angles.phi = std::atan2(sinr_cosp, cosr_cosp);
 
    // Pitch (y-axis rotation)
    double sinp = 2.0 * (w * y - z * x);
    if (std::abs(sinp) >= 1.0)
    {
        euler_angles.theta = std::copysign(M_PI / 2.0, sinp); // use 90 degrees if out of range
    }
    else
    {
        euler_angles.theta = std::asin(sinp);
    }
 
    // Yaw (z-axis rotation)
    double siny_cosp = 2.0 * (w * z + x * y);
    double cosy_cosp = 1.0 - 2.0 * (y * y + z * z);
    euler_angles.psi = std::atan2(siny_cosp, cosy_cosp);
 
    // Return Euler angles
    return euler_angles;
}

rotation() [1/4]

Eigen::Matrix3d EulerRotations::rotation ( double  phi, double  theta, double  psi  )

static

Euler rotation matrix z-y'-x''.

Compound rotation matrix given three Euler angles The Euler angles follow the post multiply * sequence zyx. Rotate "psi" around Z (yaw), "theta" around y (pitch) and "phi" around x (roll). Return the basic rotation matrix around z axis by a given angle x.

Parameters

phi	Roll angle around x axis. (rad)
theta	Pitch angle around y axis. (rad)
psi	Yaw angle around z axis. (rad)

Returns

Eigen::Matrix3d The compound rotation matrix.

Definition at line 66 of file euler_rotations.cpp.

{
    // Matrix initialization
    Eigen::Matrix3d m;
 
    // Basic rotations
    Eigen::Matrix3d rotx = basic_rotation_x(phi);
    Eigen::Matrix3d roty = basic_rotation_y(theta);
    Eigen::Matrix3d rotz = basic_rotation_z(psi);
 
    // Total rotation matrix
    m = rotz * roty * rotx;
 
    return m;
}

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rotation() [2/4]

Eigen::Matrix3d EulerRotations::rotation ( Eigen::Vector3d  euler_angles )

static

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 85 of file euler_rotations.cpp.

{
    return rotation(euler_angles(0), euler_angles(1), euler_angles(2));
}

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rotation() [3/4]

Eigen::Matrix3d EulerRotations::rotation ( Euler  euler_angles )

static

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 101 of file euler_rotations.cpp.

{
    return rotation(euler_angles.phi, euler_angles.theta, euler_angles.psi);
}

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rotation() [4/4]

Eigen::Matrix3d EulerRotations::rotation ( std::vector< double >  euler_angles )

static

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 93 of file euler_rotations.cpp.

{
    return rotation(euler_angles[0], euler_angles[1], euler_angles[2]);
}

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The documentation for this class was generated from the following files:

• include/euler_rotations.h
• src/euler_rotations.cpp