Data structure for quaternion in three dimensions. More...

#include <JQuaternion3D.hh>

Inheritance diagram for JGEOMETRY3D::JQuaternion3D:

Public Member Functions
	JQuaternion3D ()
	Default constructor. More...

	JQuaternion3D (const double a, const double b, const double c, const double d)
	Constructor. More...

	JQuaternion3D (const double theta, const JVersor3D &dir)
	Constructor. More...

	JQuaternion3D (const JQuaternion3X &qx, const JQuaternion3Y &qy, const JQuaternion3Z &qz)
	Constructor. More...

const JQuaternion3D &	getQuaternion () const
	Get quaternion. More...

JQuaternion3D &	getQuaternion ()
	Get quaternion. More...

void	setQuaternion (const JQuaternion3D &quaternion)
	Set quaternion. More...

	operator JVector3D () const
	Type conversion operator. More...

	operator JVersor3D () const
	Type conversion operator. More...

double	getA () const
	Get a value. More...

double	getB () const
	Get b value. More...

double	getC () const
	Get c value. More...

double	getD () const
	Get d value. More...

JQuaternion3D &	setIdentity ()
	Set to identity matrix. More...

JQuaternion3D &	conjugate ()
	Conjugate quaternion. More...

JQuaternion3D &	negate ()
	Negate quaternion. More...

JQuaternion3D &	add (const JQuaternion3D &quaternion)
	Add quaternion. More...

JQuaternion3D &	sub (const JQuaternion3D &quaternion)
	Subtract quaternion. More...

JQuaternion3D &	mul (const double factor)
	Scale quaternion. More...

JQuaternion3D &	div (const double factor)
	Scale quaternion. More...

JQuaternion3D &	mul (const JQuaternion3D &first, const JQuaternion3X &second)
	Quaternion multiplicaion. More...

JQuaternion3D &	mul (const JQuaternion3D &first, const JQuaternion3Y &second)
	Quaternion multiplicaion. More...

JQuaternion3D &	mul (const JQuaternion3D &first, const JQuaternion3Z &second)
	Quaternion multiplicaion. More...

JQuaternion3D &	mul (const JQuaternion3D &first, const JQuaternion3D &second)
	Quaternion multiplicaion. More...

JQuaternion3D &	mul (const JQuaternion3X &qx, const JQuaternion3Y &qy, const JQuaternion3Z &qz)
	Quaternion multiplicaion. More...

void	rotate (double &__x, double &__y, double &__z) const
	Rotate. More...

void	rotate_back (double &__x, double &__y, double &__z) const
	Rotate back. More...

bool	equals (const JQuaternion3D &quaternion, const double precision=std::numeric_limits< double >::min()) const
	Check equality. More...

double	getLengthSquared () const
	Get length squared. More...

double	getLength () const
	Get length. More...

double	getDistanceSquared (const JQuaternion3D &quaternion) const
	Get squared of distance to quaternion. More...

double	getDistance (const JQuaternion3D &quaternion) const
	Get distance to quaternion. More...

double	getDot (const JQuaternion3D &quaternion) const
	Get dot product. More...

JQuaternion3D &	normalise ()
	Normalise quaternion. More...

JFirst_t &	mul (const JSecond_t &object)
	Multiply with object. More...

Protected Attributes
double	__a

double	__b

double	__c

double	__d

Friends
std::istream &	operator>> (std::istream &in, JQuaternion3D &quaternion)
	Write quaternion from input. More...

std::ostream &	operator<< (std::ostream &out, const JQuaternion3D &quaternion)
	Write quaternion to output. More...

JReader &	operator>> (JReader &in, JQuaternion3D &quaternion)
	Read quaternion from input. More...

JWriter &	operator<< (JWriter &out, const JQuaternion3D &quaternion)
	Write quaternion to output. More...

Detailed Description

Data structure for quaternion in three dimensions.

This class implements the JMATH::JMath and JLANG::JEquals interfaces.

Definition at line 240 of file JQuaternion3D.hh.

Constructor & Destructor Documentation

JGEOMETRY3D::JQuaternion3D::JQuaternion3D ( )

inline

Default constructor.

Definition at line 258 of file JQuaternion3D.hh.

                     :
       __a(0.0),
       __b(0.0),
       __c(0.0),
       __d(0.0)
     {}

JGEOMETRY3D::JQuaternion3D::JQuaternion3D	(	const double	a,
		const double	b,
		const double	c,
		const double	d
	)

inline

Constructor.

Parameters

a	a value
b	b value
c	c value
d	d value

Definition at line 274 of file JQuaternion3D.hh.

                                   :
       __a(a),
       __b(b),
       __c(c),
       __d(d)
     {}

JGEOMETRY3D::JQuaternion3D::JQuaternion3D	(	const double	theta,
		const JVersor3D &	dir
	)

inline

Constructor.

This constructor represents a rotation around the given axis by the given angle.

Parameters

theta	rotation angle [rad]
dir	rotation axis

Definition at line 293 of file JQuaternion3D.hh.

     {
       const double ct = cos(0.5*theta);
       const double st = sin(0.5*theta);
 
       __a = ct;
       __b = st * dir.getDX();
       __c = st * dir.getDY();
       __d = st * dir.getDZ();
     }

JGEOMETRY3D::JQuaternion3D::JQuaternion3D	(	const JQuaternion3X &	qx,
		const JQuaternion3Y &	qy,
		const JQuaternion3Z &	qz
	)

inline

Constructor.

Parameters

qx	rotation around x-axis
qy	rotation around y-axis
qz	rotation around x-axis

Definition at line 313 of file JQuaternion3D.hh.

                                            :
       __a(1.0),
       __b(0.0),
       __c(0.0),
       __d(0.0)
     {
       mul(qz).mul(qy).mul(qx);
     }

Member Function Documentation

const JQuaternion3D& JGEOMETRY3D::JQuaternion3D::getQuaternion ( ) const

inline

Get quaternion.

Returns: quaternion

Definition at line 330 of file JQuaternion3D.hh.

     {
       return static_cast<const JQuaternion3D&>(*this);
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::getQuaternion ( )

inline

Get quaternion.

Returns: quaternion

Definition at line 341 of file JQuaternion3D.hh.

     {
       return static_cast<JQuaternion3D&>(*this);
     }

void JGEOMETRY3D::JQuaternion3D::setQuaternion ( const JQuaternion3D & quaternion )

inline

Set quaternion.

Parameters

quaternion quaternion

Definition at line 352 of file JQuaternion3D.hh.

     {
       static_cast<JQuaternion3D&>(*this) = quaternion;
     }

JGEOMETRY3D::JQuaternion3D::operator JVector3D ( ) const

inline

Type conversion operator.

Returns: position

Definition at line 363 of file JQuaternion3D.hh.

     {
       return JVector3D(this->getB(), this->getC(), this->getD());
     }

JGEOMETRY3D::JQuaternion3D::operator JVersor3D ( ) const

inline

Type conversion operator.

Returns: direction

Definition at line 374 of file JQuaternion3D.hh.

     {
       return JVersor3D(this->getB(), this->getC(), this->getD());
     }

double JGEOMETRY3D::JQuaternion3D::getA ( ) const

inline

Get a value.

Returns: a value

Definition at line 385 of file JQuaternion3D.hh.

     { 
       return __a;
     }

double JGEOMETRY3D::JQuaternion3D::getB ( ) const

inline

Get b value.

Returns: b value

Definition at line 396 of file JQuaternion3D.hh.

     { 
       return __b;
     }

double JGEOMETRY3D::JQuaternion3D::getC ( ) const

inline

Get c value.

Returns: c value

Definition at line 407 of file JQuaternion3D.hh.

     { 
       return __c;
     }

double JGEOMETRY3D::JQuaternion3D::getD ( ) const

inline

Get d value.

Returns: d value

Definition at line 418 of file JQuaternion3D.hh.

     { 
       return __d;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::setIdentity ( )

inline

Set to identity matrix.

Returns: this quaternion

Definition at line 429 of file JQuaternion3D.hh.

     {
       __a = 1.0;
       __b = 0.0;
       __c = 0.0;
       __d = 0.0;
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::conjugate ( )

inline

Conjugate quaternion.

Returns: this quaternion

Definition at line 445 of file JQuaternion3D.hh.

     {
       __b = -__b;
       __c = -__c;
       __d = -__d;
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::negate ( )

inline

Negate quaternion.

Returns: this quaternion

Definition at line 460 of file JQuaternion3D.hh.

     {
       __a = -__a;
       __b = -__b;
       __c = -__c;
       __d = -__d;
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::add ( const JQuaternion3D & quaternion )

inline

Add quaternion.

Parameters

quaternion quaternion

Returns: this quaternion

Definition at line 477 of file JQuaternion3D.hh.

     {
       __a += quaternion.getA();
       __b += quaternion.getB();
       __c += quaternion.getC();
       __d += quaternion.getD();
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::sub ( const JQuaternion3D & quaternion )

inline

Subtract quaternion.

Parameters

quaternion quaternion

Returns: this quaternion

Definition at line 494 of file JQuaternion3D.hh.

     {
       __a -= quaternion.getA();
       __b -= quaternion.getB();
       __c -= quaternion.getC();
       __d -= quaternion.getD();
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul ( const double factor )

inline

Scale quaternion.

Parameters

factor multiplication factor

Returns: this quaternion

Definition at line 511 of file JQuaternion3D.hh.

     {
       __a *= factor;
       __b *= factor;
       __c *= factor;
       __d *= factor;
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::div ( const double factor )

inline

Scale quaternion.

Parameters

factor division factor

Returns: this quaternion

Definition at line 528 of file JQuaternion3D.hh.

     {
       __a /= factor;
       __b /= factor;
       __c /= factor;
       __d /= factor;
 
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul	(	const JQuaternion3D &	first,
		const JQuaternion3X &	second
	)

inline

Quaternion multiplicaion.

This method evaluates the Hamilton product (also called cross product).

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 548 of file JQuaternion3D.hh.

     {
       __a =  first.getA() * second.getA() - first.getB() * second.getB();
       __b =  first.getA() * second.getB() + first.getB() * second.getA();
       __c =  first.getC() * second.getA() + first.getD() * second.getB();
       __d = -first.getC() * second.getB() + first.getD() * second.getA();
       
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul	(	const JQuaternion3D &	first,
		const JQuaternion3Y &	second
	)

inline

Quaternion multiplicaion.

This method evaluates the Hamilton product (or cross product).

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 568 of file JQuaternion3D.hh.

     {
       __a =  first.getA() * second.getA() - first.getC() * second.getC();
       __b =  first.getB() * second.getA() - first.getD() * second.getC();
       __c =  first.getA() * second.getC() + first.getC() * second.getA();
       __d =  first.getB() * second.getC() + first.getD() * second.getA();
       
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul	(	const JQuaternion3D &	first,
		const JQuaternion3Z &	second
	)

inline

Quaternion multiplicaion.

This method evaluates the Hamilton product (or cross product).

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 589 of file JQuaternion3D.hh.

     {
       __a =  first.getA() * second.getA() - first.getD() * second.getD();
       __b =  first.getB() * second.getA() + first.getC() * second.getD();
       __c = -first.getB() * second.getD() + first.getC() * second.getA();
       __d =  first.getA() * second.getD() + first.getD() * second.getA();
       
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul	(	const JQuaternion3D &	first,
		const JQuaternion3D &	second
	)

inline

Quaternion multiplicaion.

This method evaluates the Hamilton product (or cross product).

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 610 of file JQuaternion3D.hh.

     {
       __a = first.getA() * second.getA() - first.getB() * second.getB() - first.getC() * second.getC() - first.getD() * second.getD();
       __b = first.getA() * second.getB() + first.getB() * second.getA() + first.getC() * second.getD() - first.getD() * second.getC();
       __c = first.getA() * second.getC() - first.getB() * second.getD() + first.getC() * second.getA() + first.getD() * second.getB();
       __d = first.getA() * second.getD() + first.getB() * second.getC() - first.getC() * second.getB() + first.getD() * second.getA();
       
       return *this;
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::mul	(	const JQuaternion3X &	qx,
		const JQuaternion3Y &	qy,
		const JQuaternion3Z &	qz
	)

inline

Quaternion multiplicaion.

Parameters

qx	rotation around x-axis
qy	rotation around y-axis
qz	rotation around x-axis

Returns: this quaternion

Definition at line 630 of file JQuaternion3D.hh.

     {
       return *this = JQuaternion3D().setIdentity().mul(qz).mul(qy).mul(qx);
     }

void JGEOMETRY3D::JQuaternion3D::rotate	(	double &	__x,
		double &	__y,
		double &	__z
	)		const

inline

Rotate.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 645 of file JQuaternion3D.hh.

     {
       const double qx = 2.0 * (__c*__z - __d*__y);
       const double qy = 2.0 * (__d*__x - __b*__z);
       const double qz = 2.0 * (__b*__y - __c*__x);
 
       const double x  = __x + __c*qz - __d*qy + __a*qx;
       const double y  = __y - __b*qz + __a*qy + __d*qx;
       const double z  = __z + __a*qz + __b*qy - __c*qx;
 
       __x = x;
       __y = y;
       __z = z;
     }

void JGEOMETRY3D::JQuaternion3D::rotate_back	(	double &	__x,
		double &	__y,
		double &	__z
	)		const

inline

Rotate back.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 668 of file JQuaternion3D.hh.

     {
       const double qx = 2.0 * (__d*__y - __c*__z);
       const double qy = 2.0 * (__b*__z - __d*__x);
       const double qz = 2.0 * (__c*__x - __b*__y);
 
       const double x  = __x - __c*qz + __d*qy + __a*qx;
       const double y  = __y + __b*qz + __a*qy - __d*qx;
       const double z  = __z + __a*qz - __b*qy + __c*qx;
 
       __x = x;
       __y = y;
       __z = z;
     }

bool JGEOMETRY3D::JQuaternion3D::equals	(	const JQuaternion3D &	quaternion,
		const double	precision = `std::numeric_limits<double>::min()`
	)		const

inline

Check equality.

Parameters

quaternion	quaternion
precision	numerical precision

Returns: true if quaternions are equal; else false

Definition at line 691 of file JQuaternion3D.hh.

     {
       return (fabs(getA() - quaternion.getA()) <= precision && 
               fabs(getB() - quaternion.getB()) <= precision &&
               fabs(getC() - quaternion.getC()) <= precision &&
               fabs(getD() - quaternion.getD()) <= precision);
     }

double JGEOMETRY3D::JQuaternion3D::getLengthSquared ( ) const

inline

Get length squared.

Returns: square of length

Definition at line 706 of file JQuaternion3D.hh.

     { 
       return getA()*getA() + getB()*getB() + getC()*getC() + getD()*getD();
     }

double JGEOMETRY3D::JQuaternion3D::getLength ( ) const

inline

Get length.

Returns: length

Definition at line 717 of file JQuaternion3D.hh.

     { 
       return sqrt(getLengthSquared());
     }

double JGEOMETRY3D::JQuaternion3D::getDistanceSquared ( const JQuaternion3D & quaternion ) const

inline

Get squared of distance to quaternion.

Parameters

quaternion quaternion

Returns: square of distance

Definition at line 729 of file JQuaternion3D.hh.

     {
       return JQuaternion3D(quaternion).sub(*this).getLengthSquared();
     }

double JGEOMETRY3D::JQuaternion3D::getDistance ( const JQuaternion3D & quaternion ) const

inline

Get distance to quaternion.

Parameters

quaternion quaternion

Returns: distance

Definition at line 741 of file JQuaternion3D.hh.

     {
       return sqrt(getDistanceSquared(quaternion));
     }

double JGEOMETRY3D::JQuaternion3D::getDot ( const JQuaternion3D & quaternion ) const

inline

Get dot product.

Parameters

quaternion quaternion

Returns: dot product

Definition at line 753 of file JQuaternion3D.hh.

     {
       return
         getA() * quaternion.getA() -
         getB() * quaternion.getB() -
         getC() * quaternion.getC() -
         getD() * quaternion.getD();
     }

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::normalise ( )

inline

Normalise quaternion.

Returns: this quaternion

Definition at line 840 of file JQuaternion3D.hh.

     {
       const double v = getLength();
 
       if (v != 0.0) {
         mul(1.0 / v);
       }
 
       return *this;
     }

template<class JFirst_t, class JSecond_t = JNullType>

JFirst_t& JMATH::JMath< JFirst_t, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 273 of file JMath.hh.

     {
       return static_cast<JFirst_t&>(*this) = JCalculator<JFirst_t>::calculator.mul(static_cast<const JFirst_t&>(*this), object);
     }

Friends And Related Function Documentation

std::istream& operator>>	(	std::istream &	in,
		JQuaternion3D &	quaternion
	)

friend

Write quaternion from input.

Parameters

in	input stream
quaternion	quaternion

Returns: input stream

Definition at line 770 of file JQuaternion3D.hh.

     {
       in >> quaternion.__a;
       in >> quaternion.__b;
       in >> quaternion.__c;
       in >> quaternion.__d;
 
       return in;
     }

std::ostream& operator<<	(	std::ostream &	out,
		const JQuaternion3D &	quaternion
	)

friend

Write quaternion to output.

Parameters

out	output stream
quaternion	quaternion

Returns: output stream

Definition at line 788 of file JQuaternion3D.hh.

     {
       out << quaternion.getA() << ' '
           << quaternion.getB() << ' '
           << quaternion.getC() << ' '
           << quaternion.getD();
 
       return out;
     }

JReader& operator>>	(	JReader &	in,
		JQuaternion3D &	quaternion
	)

friend

Read quaternion from input.

Parameters

in	reader
quaternion	quaternion

Returns: reader

Definition at line 806 of file JQuaternion3D.hh.

     {
       in >> quaternion.__a;
       in >> quaternion.__b;
       in >> quaternion.__c;
       in >> quaternion.__d;
 
       return in;
     }

JWriter& operator<<	(	JWriter &	out,
		const JQuaternion3D &	quaternion
	)

friend

Write quaternion to output.

Parameters

out	writer
quaternion	quaternion

Returns: writer

Definition at line 824 of file JQuaternion3D.hh.

     {
       out << quaternion.getA();
       out << quaternion.getB();
       out << quaternion.getC();
       out << quaternion.getD();
 
       return out;
     }

Member Data Documentation

double JGEOMETRY3D::JQuaternion3D::__a

protected

Definition at line 852 of file JQuaternion3D.hh.

double JGEOMETRY3D::JQuaternion3D::__b

protected

Definition at line 853 of file JQuaternion3D.hh.

double JGEOMETRY3D::JQuaternion3D::__c

protected

Definition at line 854 of file JQuaternion3D.hh.

double JGEOMETRY3D::JQuaternion3D::__d

protected

Definition at line 855 of file JQuaternion3D.hh.

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

JQuaternion3D.hh

Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation