m5::math::Quaternion Struct Reference

Plain Hamilton quaternion (float) used to represent attitude. More...

#include <quaternion.hpp>

Public Member Functions
	Quaternion ()=default
	Default-construct as identity (no rotation)
constexpr	Quaternion (const float w_, const float x_, const float y_, const float z_)
	Construct from components.
Quaternion	operator* (const Quaternion &rhs) const
	Hamilton product (this rotation applied after rhs)
Quaternion	conjugated () const
	Conjugate (equals the inverse for a unit quaternion)
float	normSq () const
	Squared norm.
float	norm () const
	Norm (magnitude)
bool	normalize ()
	Normalize this quaternion in place.
Quaternion	normalized () const
	Return a normalized copy.
Vector3	rotate (const Vector3 &v) const
	Rotate a vector by this quaternion (active rotation, right-handed)
void	toEuler (float &roll_deg, float &pitch_deg, float &yaw_deg) const
	Decompose this quaternion into aerospace ZYX Euler angles.
void	integrate (const Vector3 &gyro_rad_s, const float dt)
	Integrate body-frame angular velocity over dt (gyro kinematics)

Static Public Member Functions
static Quaternion	identity ()
	Identity quaternion (no rotation)
static Quaternion	fromAxisAngle (const Vector3 &axis, const float angle_rad)
	Build a rotation quaternion from an axis and angle.
static Quaternion	fromEuler (const float roll_deg, const float pitch_deg, const float yaw_deg)
	Build a rotation quaternion from aerospace ZYX Euler angles.

Public Attributes
float	w {1.0f}
	Scalar part.
float	x {}
	Vector part X.
float	y {}
	Vector part Y.
float	z {}
	Vector part Z.

Detailed Description

Plain Hamilton quaternion (float) used to represent attitude.

Euler angle conversions use the aerospace ZYX (yaw-pitch-roll) convention, in degrees. Rotations are right-handed and active (rotate a vector, not the frame).

Member Function Documentation

fromAxisAngle()

static Quaternion m5::math::Quaternion::fromAxisAngle ( const Vector3 & axis, const float angle_rad )

inlinestatic

Build a rotation quaternion from an axis and angle.

Parameters

axis	Rotation axis (need not be normalized; zero axis yields identity)
angle_rad	Rotation angle in radians

Returns

Rotation quaternion

fromEuler()

static Quaternion m5::math::Quaternion::fromEuler ( const float roll_deg, const float pitch_deg, const float yaw_deg )

inlinestatic

Build a rotation quaternion from aerospace ZYX Euler angles.

Parameters

roll_deg	Roll (X axis) in degrees
pitch_deg	Pitch (Y axis) in degrees
yaw_deg	Yaw (Z axis) in degrees

Returns

Rotation quaternion

integrate()

void m5::math::Quaternion::integrate ( const Vector3 & gyro_rad_s, const float dt )

inline

Integrate body-frame angular velocity over dt (gyro kinematics)

Parameters

gyro_rad_s	Angular velocity in rad/s (body frame)
dt	Time step in seconds

Advances this quaternion by dq = 0.5 * q (X) (0, gyro_rad_s) * dt and renormalizes to counteract integration drift.

normalize()

bool m5::math::Quaternion::normalize ( )

inline

Normalize this quaternion in place.

Returns

false and leaves the quaternion unchanged if it is (near) zero

rotate()

Vector3 m5::math::Quaternion::rotate ( const Vector3 & v ) const

inline

Rotate a vector by this quaternion (active rotation, right-handed)

Parameters

v	Vector to rotate

Returns

Rotated vector

toEuler()

void m5::math::Quaternion::toEuler ( float & roll_deg, float & pitch_deg, float & yaw_deg ) const

inline

Decompose this quaternion into aerospace ZYX Euler angles.

Parameters

[out]	roll_deg	Roll (X axis) in degrees
[out]	pitch_deg	Pitch (Y axis) in degrees
[out]	yaw_deg	Yaw (Z axis) in degrees

The pitch asin argument is clamped to [-1, 1] so that values near the gimbal lock (pitch = +-90 deg) never produce NaN.