Quarternion Class Reference

#include <Quarternion.h>

Public Member Functions
	Quarternion ()
	Constructs a basic Quarternion. More...
	Quarternion (const Quarternion &other)
	Copy constructor. More...
	Quarternion (double x, double y, double z, double w)
	Constructs a a Quarternion using its four components. More...
	Quarternion (Vec3D axis, double angle)
	Constructs a Quarternion using a rotation around an axis. More...
void	getAxisAndAngle (Vec3D &axis, double &angle) const
	Returns the orientation as represented by a rotation around an axis. More...
Matrix3D	getRotationMatrix () const
void	reset ()
	Resets a the Quarternion. More...
void	normalise ()
	Normalises the Quarternion. More...
Quarternion	operator* (const Quarternion &other) const
	Multiplication operator. More...
void	integrate (const Vec3D &omega, double timeStep)
	Integration of the Quarternion using rotational velocity and timestep. More...
	Quarternion (const Vec3D &a)
	Constructs a Quaternion using the lab x-y-z sequence, where the object is. More...
Vec3D	get3DAngles () const
	Constructs a representation of the quarternion using 3 rotations in the lab x-y-z sequence, where the object is first rotated along lab X-axis then rotated along lab Y-axis then rotated along lab Z-axis. More...

Private Attributes
Mdouble	w_
Mdouble	x_
Mdouble	y_
Mdouble	z_

Friends
std::ostream &	operator<< (std::ostream &os, const Quarternion &q)
std::istream &	operator>> (std::istream &is, Quarternion &q)

Detailed Description

Definition at line 36 of file Quarternion.h.

Constructor & Destructor Documentation

Quarternion::Quarternion

(

)

Constructs a basic Quarternion.

Definition at line 32 of file Quarternion.cc.

References reset().

{
    reset();
}

Quarternion::Quarternion

(

const Quarternion &

other

)

Copy constructor.

Definition at line 37 of file Quarternion.cc.

References w_, x_, y_, and z_.

{
    x_ = other.x_;
    y_ = other.y_;
    z_ = other.z_;
    w_ = other.w_;
}

Quarternion::Quarternion	(	double	x,
		double	y,
		double	z,
		double	w
	)

Constructs a a Quarternion using its four components.

Definition at line 45 of file Quarternion.cc.

References w_, x_, y_, and z_.

{
    x_ = x;
    y_ = y;
    z_ = z;
    w_ = w;
}

Quarternion::Quarternion	(	Vec3D	axis,
		double	angle
	)

Constructs a Quarternion using a rotation around an axis.

Definition at line 53 of file Quarternion.cc.

References Vec3D::normalize(), w_, Vec3D::X, x_, Vec3D::Y, y_, Vec3D::Z, and z_.

{
    std::cout << "Axis=" << axis << " Angle=" << angle << std::endl;
    axis.normalize();
    x_ = std::sin(0.5 * angle) * axis.X;
    y_ = std::sin(0.5 * angle) * axis.Y;
    z_ = std::sin(0.5 * angle) * axis.Z;
    w_ = std::cos(0.5 * angle);
}

Quarternion::Quarternion

(

const Vec3D &

a

)

Constructs a Quaternion using the lab x-y-z sequence, where the object is.

first rotated along lab X-axis then rotated along lab Y-axis then rotated along lab Z-axis

Definition at line 63 of file Quarternion.cc.

References w_, Vec3D::X, x_, Vec3D::Y, y_, Vec3D::Z, and z_.

{
    x_ = sin(0.5 * a.X) * cos(0.5 * a.Y) * cos(0.5 * a.Z) - cos(0.5 * a.X) * sin(0.5 * a.Y) * sin(0.5 * a.Z);
    y_ = cos(0.5 * a.X) * sin(0.5 * a.Y) * cos(0.5 * a.Z) + sin(0.5 * a.X) * cos(0.5 * a.Y) * sin(0.5 * a.Z);
    z_ = cos(0.5 * a.X) * cos(0.5 * a.Y) * sin(0.5 * a.Z) - sin(0.5 * a.X) * sin(0.5 * a.Y) * cos(0.5 * a.Z);
    w_ = cos(0.5 * a.X) * cos(0.5 * a.Y) * cos(0.5 * a.Z) + sin(0.5 * a.X) * sin(0.5 * a.Y) * sin(0.5 * a.Z);
}

Member Function Documentation

Vec3D Quarternion::get3DAngles

(

)

const

Constructs a representation of the quarternion using 3 rotations in the lab x-y-z sequence, where the object is first rotated along lab X-axis then rotated along lab Y-axis then rotated along lab Z-axis.

Definition at line 143 of file Quarternion.cc.

References constants::pi, w_, x_, y_, and z_.

{
    double rotY, rotZ, rotX;
    double sqrtX = x_ * x_;
    double sqrtY = y_ * y_;
    double sqrtZ = z_ * z_;
    double sqrtW = w_ * w_;
    double unit = sqrtX + sqrtY + sqrtZ + sqrtW;
    double test = x_ * y_ + z_ * w_;
    if (test > 0.499999 * unit) // singularity at north pole
    {
        rotY = 2.0 * std::atan2(x_, w_);
        rotZ = constants::pi / 2;
        rotX = 0;
    }
    else if (test < -0.499999 * unit) // singularity at south pole
    {
        rotY = -2.0 * atan2(x_, w_);
        rotZ = -constants::pi / 2;
        rotX = 0;
    }
    else
    {
        rotY = atan2(2.0 * y_ * w_ - 2.0 * x_ * z_, sqrtX - sqrtY - sqrtZ + sqrtW);
        rotZ = asin(2.0 * test / unit);
        rotX = atan2(2.0 * x_ * w_ - 2.0 * y_ * z_, -sqrtX + sqrtY - sqrtZ + sqrtW);
    }
    return Vec3D(rotX, rotY, rotZ);
}

void Quarternion::getAxisAndAngle	(	Vec3D &	axis,
		double &	angle
	)		const

Returns the orientation as represented by a rotation around an axis.

Definition at line 71 of file Quarternion.cc.

References w_, x_, y_, and z_.

        {
    angle = 2.0 * std::acos(w_);
    axis = Vec3D(x_ / std::sin(0.5 * angle), y_ / std::sin(0.5 * angle), z_ / std::sin(0.5 * angle));
}

Matrix3D Quarternion::getRotationMatrix

(

)

const

Definition at line 77 of file Quarternion.cc.

References w_, x_, y_, and z_.

{
    double xx = w_ * w_ + x_ * x_ - y_ * y_ - z_ * z_;
    double xy = 2.0 * (x_ * y_ - w_ * z_);
    double xz = 2.0 * (w_ * y_ + x_ * z_);
    double yx = 2.0 * (x_ * y_ + w_ * z_);
    double yy = w_ * w_ - x_ * x_ + y_ * y_ - z_ * z_;
    double yz = 2.0 * (y_ * z_ - w_ * x_);
    double zx = 2.0 * (x_ * z_ - w_ * y_);
    double zy = 2.0 * (w_ * x_ + y_ * z_);
    double zz = w_ * w_ - x_ * x_ - y_ * y_ + z_ * z_;
    return Matrix3D(xx, xy, xz, yx, yy, yz, zx, zy, zz);
}

void Quarternion::integrate	(	const Vec3D &	omega,
		double	timeStep
	)

Integration of the Quarternion using rotational velocity and timestep.

Todo:

Are we sure this works? *this = deltaQ * *this

Author

weinhartt

Definition at line 118 of file Quarternion.cc.

References Vec3D::getLengthSquared(), w_, Vec3D::X, x_, Vec3D::Y, y_, Vec3D::Z, and z_.

{
    Quarternion deltaQ;
    Vec3D theta = 0.5 * omega * timeStep;
    double thetaMagSq = theta.getLengthSquared();
    double s;
    if (thetaMagSq * thetaMagSq / 24.0 < 1e-10)
    {
        std::cout << "Warning small rotation, needs additional checking" << std::endl;
        deltaQ.w_ = 1.0 - 0.5 * thetaMagSq;
        s = 1.0 - thetaMagSq / 6.0;
    }
    else
    {
        double thetaMag = std::sqrt(thetaMagSq);
        deltaQ.w_ = std::cos(thetaMag);
        s = std::sin(thetaMag) / thetaMag;
    }
    deltaQ.x_ = theta.X * s;
    deltaQ.y_ = theta.Y * s;
    deltaQ.z_ = theta.Z * s;
    *this = deltaQ * *this;
}

void Quarternion::normalise

(

)

Normalises the Quarternion.

Definition at line 99 of file Quarternion.cc.

References w_, x_, y_, and z_.

{
    double n = std::sqrt(x_ * x_ + y_ * y_ + z_ * z_ + w_ * w_);
    x_ /= n;
    y_ /= n;
    z_ /= n;
    w_ /= n;
}

Quarternion Quarternion::operator*

(

const Quarternion &

other

)

const

Multiplication operator.

Definition at line 108 of file Quarternion.cc.

References w_, x_, y_, and z_.

        {
    Quarternion result;
    result.w_ = w_ * other.w_ - x_ * other.x_ - y_ * other.y_ - z_ * other.z_;
    result.x_ = w_ * other.x_ + x_ * other.w_ + y_ * other.z_ - z_ * other.y_;
    result.y_ = w_ * other.y_ + y_ * other.w_ - x_ * other.z_ + z_ * other.x_;
    result.z_ = w_ * other.z_ + z_ * other.w_ + x_ * other.y_ - y_ * other.x_;
    return result;
}

void Quarternion::reset

(

)

Resets a the Quarternion.

Definition at line 91 of file Quarternion.cc.

References w_, x_, y_, and z_.

Referenced by Quarternion().

{
    x_ = 0.0;
    y_ = 0.0;
    z_ = 0.0;
    w_ = 1.0;
}

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  os, const Quarternion &  q  )

friend

Definition at line 173 of file Quarternion.cc.

{
    os << q.x_ << " " << q.y_ << " " << q.z_ << " " << q.w_;
    return os;
}

std::istream& operator>> ( std::istream &  is, Quarternion &  q  )

friend

Definition at line 179 of file Quarternion.cc.

{
    is >> q.x_ >> q.y_ >> q.z_ >> q.w_;
    return is;
}

Member Data Documentation

Mdouble Quarternion::w_

private

Definition at line 114 of file Quarternion.h.

Referenced by get3DAngles(), getAxisAndAngle(), getRotationMatrix(), integrate(), normalise(), operator*(), operator<<(), operator>>(), Quarternion(), and reset().

Mdouble Quarternion::x_

private

Definition at line 114 of file Quarternion.h.

Referenced by get3DAngles(), getAxisAndAngle(), getRotationMatrix(), integrate(), normalise(), operator*(), operator<<(), operator>>(), Quarternion(), and reset().

Mdouble Quarternion::y_

private

Definition at line 114 of file Quarternion.h.

Referenced by get3DAngles(), getAxisAndAngle(), getRotationMatrix(), integrate(), normalise(), operator*(), operator<<(), operator>>(), Quarternion(), and reset().

Mdouble Quarternion::z_

private

Definition at line 114 of file Quarternion.h.

Referenced by get3DAngles(), getAxisAndAngle(), getRotationMatrix(), integrate(), normalise(), operator*(), operator<<(), operator>>(), Quarternion(), and reset().

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

• Math/Quarternion.h
• Math/Quarternion.cc