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

#include <JQuaternion3D.hh>

Inheritance diagram for JGEOMETRY3D::JQuaternion3D:

Classes
struct	decomposition
	Auxiliary data structure for decomposition of quaternion in twist and swing quaternions. More...

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 double w, const JVector3D &dir)
	Constructor. More...

	JQuaternion3D (const JQuaternion3X &qx)
	Constructor. More...

	JQuaternion3D (const JQuaternion3Y &qy)
	Constructor. More...

	JQuaternion3D (const JQuaternion3Z &qz)
	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	getAngle () const
	Get rotation angle. 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 quaternion. 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 multiplication. More...

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

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

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

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

bool	isIdentity (const double precision=std::numeric_limits< double >::min()) const
	Test identity. 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	getConjugate () const
	Get conjugate of this quaternion. More...

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

JQuaternion3D &	pow (const double y)
	Raise quaternion to given power. More...

JQuaternion3D &	interpolate (const JQuaternion3D &object, const double alpha)
	Interpolation between quaternions. More...

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

Static Public Member Functions
static const JQuaternion3D &	getIdentity ()
	Get identity quaternion. 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 unit quaternion in three dimensions.

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

Definition at line 303 of file JQuaternion3D.hh.

Constructor & Destructor Documentation

◆ JQuaternion3D() [1/8]

JGEOMETRY3D::JQuaternion3D::JQuaternion3D ( )

inline

Default constructor.

Definition at line 324 of file JQuaternion3D.hh.

                     :
       __a(1.0),
       __b(0.0),
       __c(0.0),
       __d(0.0)
     {}

◆ JQuaternion3D() [2/8]

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 340 of file JQuaternion3D.hh.

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

◆ JQuaternion3D() [3/8]

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 361 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();
     }

◆ JQuaternion3D() [4/8]

JGEOMETRY3D::JQuaternion3D::JQuaternion3D	(	const double	w,
		const JVector3D &	dir
	)

inline

Constructor.

Parameters

w	weight
dir	rotation axis

Definition at line 380 of file JQuaternion3D.hh.

     {
       __a = w;
       __b = dir.getX();
       __c = dir.getY();
       __d = dir.getZ();
  
       normalise();
     }

◆ JQuaternion3D() [5/8]

JGEOMETRY3D::JQuaternion3D::JQuaternion3D ( const JQuaternion3X & qx )

inline

Constructor.

Parameters

qx	rotation around x-axis

Definition at line 397 of file JQuaternion3D.hh.

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

◆ JQuaternion3D() [6/8]

JGEOMETRY3D::JQuaternion3D::JQuaternion3D ( const JQuaternion3Y & qy )

inline

Constructor.

Parameters

qy	rotation around y-axis

Definition at line 412 of file JQuaternion3D.hh.

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

◆ JQuaternion3D() [7/8]

JGEOMETRY3D::JQuaternion3D::JQuaternion3D ( const JQuaternion3Z & qz )

inline

Constructor.

Parameters

qz	rotation around x-axis

Definition at line 427 of file JQuaternion3D.hh.

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

◆ JQuaternion3D() [8/8]

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 z-axis

Definition at line 444 of file JQuaternion3D.hh.

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

Member Function Documentation

◆ getIdentity()

static const JQuaternion3D& JGEOMETRY3D::JQuaternion3D::getIdentity ( )

inlinestatic

Get identity quaternion.

Returns: identity quaternion

Definition at line 463 of file JQuaternion3D.hh.

     {
       static const JQuaternion3D Q = JQuaternion3D().setIdentity();
  
       return Q;
     }

◆ getQuaternion() [1/2]

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

inline

Get quaternion.

Returns: quaternion

Definition at line 476 of file JQuaternion3D.hh.

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

◆ getQuaternion() [2/2]

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::getQuaternion ( )

inline

Get quaternion.

Returns: quaternion

Definition at line 487 of file JQuaternion3D.hh.

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

◆ setQuaternion()

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

inline

Set quaternion.

Parameters

quaternion quaternion

Definition at line 498 of file JQuaternion3D.hh.

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

◆ operator JVector3D()

JGEOMETRY3D::JQuaternion3D::operator JVector3D ( ) const

inline

Type conversion operator.

Returns: position

Definition at line 509 of file JQuaternion3D.hh.

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

◆ operator JVersor3D()

JGEOMETRY3D::JQuaternion3D::operator JVersor3D ( ) const

inline

Type conversion operator.

Returns: direction

Definition at line 520 of file JQuaternion3D.hh.

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

◆ getAngle()

double JGEOMETRY3D::JQuaternion3D::getAngle ( ) const

inline

Get rotation angle.

Returns: angle [rad]

Definition at line 531 of file JQuaternion3D.hh.

     {
       return atan2(sqrt(this->getB()*this->getB() +
                         this->getC()*this->getC() +
                         this->getD()*this->getD()),
                    this->getA()) * 2.0;
     }

◆ getA()

double JGEOMETRY3D::JQuaternion3D::getA ( ) const

inline

Get a value.

Returns: a value

Definition at line 545 of file JQuaternion3D.hh.

     { 
       return __a;
     }

◆ getB()

double JGEOMETRY3D::JQuaternion3D::getB ( ) const

inline

Get b value.

Returns: b value

Definition at line 556 of file JQuaternion3D.hh.

     { 
       return __b;
     }

◆ getC()

double JGEOMETRY3D::JQuaternion3D::getC ( ) const

inline

Get c value.

Returns: c value

Definition at line 567 of file JQuaternion3D.hh.

     { 
       return __c;
     }

◆ getD()

double JGEOMETRY3D::JQuaternion3D::getD ( ) const

inline

Get d value.

Returns: d value

Definition at line 578 of file JQuaternion3D.hh.

     { 
       return __d;
     }

◆ setIdentity()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::setIdentity ( )

inline

Set to identity quaternion.

Returns: this quaternion

Definition at line 589 of file JQuaternion3D.hh.

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

◆ conjugate()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::conjugate ( )

inline

Conjugate quaternion.

Returns: this quaternion

Definition at line 605 of file JQuaternion3D.hh.

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

◆ negate()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::negate ( )

inline

Negate quaternion.

Returns: this quaternion

Definition at line 620 of file JQuaternion3D.hh.

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

◆ add()

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

inline

Add quaternion.

Parameters

quaternion quaternion

Returns: this quaternion

Definition at line 637 of file JQuaternion3D.hh.

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

◆ sub()

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

inline

Subtract quaternion.

Parameters

quaternion quaternion

Returns: this quaternion

Definition at line 654 of file JQuaternion3D.hh.

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

◆ mul() [1/7]

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

inline

Scale quaternion.

Parameters

factor multiplication factor

Returns: this quaternion

Definition at line 671 of file JQuaternion3D.hh.

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

◆ div()

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

inline

Scale quaternion.

Parameters

factor division factor

Returns: this quaternion

Definition at line 688 of file JQuaternion3D.hh.

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

◆ mul() [2/7]

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

inline

Quaternion multiplication.

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

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 708 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;
     }

◆ mul() [3/7]

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

inline

Quaternion multiplication.

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

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 728 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;
     }

◆ mul() [4/7]

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

inline

Quaternion multiplication.

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

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 749 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;
     }

◆ mul() [5/7]

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

inline

Quaternion multiplication.

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

Parameters

first	first quaternion
second	second quaternion

Returns: this quaternion

Definition at line 770 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;
     }

◆ mul() [6/7]

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

inline

Quaternion multiplication.

Parameters

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

Returns: this quaternion

Definition at line 790 of file JQuaternion3D.hh.

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

◆ rotate()

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 805 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);
  
       __x = __x + __c*qz - __d*qy + __a*qx;
       __y = __y - __b*qz + __a*qy + __d*qx;
       __z = __z + __a*qz + __b*qy - __c*qx;
     }

◆ rotate_back()

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 824 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);
  
       __x = __x - __c*qz + __d*qy + __a*qx;
       __y = __y + __b*qz + __a*qy - __d*qx;
       __z = __z + __a*qz - __b*qy + __c*qx;
     }

◆ equals()

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 843 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);
     }

◆ isIdentity()

bool JGEOMETRY3D::JQuaternion3D::isIdentity ( const double precision = std::numeric_limits<double>::min() ) const

inline

Test identity.

Parameters

precision precision

Returns: true if identity quaternion; else false

Definition at line 859 of file JQuaternion3D.hh.

     {
       if (fabs(getA()) <= precision) {
  
         if (fabs(getB()) <= precision)
           return ((fabs(getC())       <= precision && fabs(fabs(getD()) - 1.0) <= precision)  ||
                   (fabs(fabs(getC()) - 1.0) <= precision && fabs(getD())       <= precision));
         else
           return (fabs(fabs(getB()) - 1.0) <= precision && 
                   fabs(getC())             <= precision &&
                   fabs(getD())             <= precision);
  
       } else {
  
         return (fabs(fabs(getA()) - 1.0) <= precision && 
                 fabs(getB())             <= precision &&
                 fabs(getC())             <= precision &&
                 fabs(getD())             <= precision);
       }
     }

◆ getLengthSquared()

double JGEOMETRY3D::JQuaternion3D::getLengthSquared ( ) const

inline

Get length squared.

Returns: square of length

Definition at line 886 of file JQuaternion3D.hh.

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

◆ getLength()

double JGEOMETRY3D::JQuaternion3D::getLength ( ) const

inline

Get length.

Returns: length

Definition at line 897 of file JQuaternion3D.hh.

     { 
       return sqrt(getLengthSquared());
     }

◆ getDistanceSquared()

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 909 of file JQuaternion3D.hh.

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

◆ getDistance()

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

inline

Get distance to quaternion.

Parameters

quaternion quaternion

Returns: distance

Definition at line 921 of file JQuaternion3D.hh.

     {
       return sqrt(getDistanceSquared(quaternion));
     }

◆ getDot()

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

inline

Get dot product.

Parameters

quaternion quaternion

Returns: dot product

Definition at line 933 of file JQuaternion3D.hh.

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

◆ getConjugate()

JQuaternion3D JGEOMETRY3D::JQuaternion3D::getConjugate ( ) const

inline

Get conjugate of this quaternion.

Returns: conjugate quaternion

Definition at line 948 of file JQuaternion3D.hh.

     {
       return JQuaternion3D(*this).conjugate();
     }

◆ normalise()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::normalise ( )

inline

Normalise quaternion.

Returns: this quaternion

Definition at line 959 of file JQuaternion3D.hh.

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

◆ pow()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::pow ( const double y )

inline

Raise quaternion to given power.

Parameters

y power

Returns: this object

Definition at line 977 of file JQuaternion3D.hh.

     {
       const double v = sqrt(getB() * getB()  +
                             getC() * getC()  +
                             getD() * getD());
  
       if (v != 0.0) {
  
         const JVersor3D u(getB(), getC(), getD());
  
         const double theta = atan2(v, getA());
  
         *this = JQuaternion3D(2.0 * theta * y, u);
       }
  
       return *this;
     }

◆ interpolate()

JQuaternion3D& JGEOMETRY3D::JQuaternion3D::interpolate	(	const JQuaternion3D &	object,
		const double	alpha
	)

inline

Interpolation between quaternions.

The result is equal to *this = (1 - alpha) * (*this) + (alpha) * (object).

Parameters

object	object
alpha	interpolation factor `[0, 1]`

Returns: this object

Definition at line 1004 of file JQuaternion3D.hh.

     {
       const double MAXIMAL_DOT_PRODUCT = 0.9995;
       
       JQuaternion3D v0(*this);
       JQuaternion3D v1(object);
  
       v0.normalise();
       v1.normalise();
  
       double dot = v0.getDot(v1);
  
       if (dot < 0.0) {
         v1  = -v1;
         dot = -dot;
       }
  
       double s1 = alpha;
       double s0 = 1.0 - alpha;
  
       if (dot <= MAXIMAL_DOT_PRODUCT) {
  
         const double theta_0 = acos(dot);
         const double theta_1 = theta_0 * alpha;
       
         s1 = sin(theta_1) / sin(theta_0);
         s0 = cos(theta_1) - dot * s1;
       }
  
       *this = (s0 * v0)  +  (s1 * v1);
  
       return normalise();
     }

◆ mul() [7/7]

template<class JFirst_t , class JSecond_t >

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 354 of file JMath.hh.

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

Friends And Related Function Documentation

◆ operator>> [1/2]

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 1047 of file JQuaternion3D.hh.

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

◆ operator<< [1/2]

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 1067 of file JQuaternion3D.hh.

     {
       const JFormat format(out, getFormat<JQuaternion3D>(JFormat_t(9, 6, std::ios::fixed | std::ios::showpos)));
  
       out << format << quaternion.getA() << ' '
           << format << quaternion.getB() << ' '
           << format << quaternion.getC() << ' '
           << format << quaternion.getD();
  
       return out;
     }

◆ operator>> [2/2]

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

friend

Read quaternion from input.

Parameters

in	reader
quaternion	quaternion

Returns: reader

Definition at line 1087 of file JQuaternion3D.hh.

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

◆ operator<< [2/2]

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

friend

Write quaternion to output.

Parameters

out	writer
quaternion	quaternion

Returns: writer

Definition at line 1105 of file JQuaternion3D.hh.

     {
       out << quaternion.__a;
       out << quaternion.__b;
       out << quaternion.__c;
       out << quaternion.__d;
  
       return out;
     }

Member Data Documentation

◆ __a

double JGEOMETRY3D::JQuaternion3D::__a

protected

Definition at line 1117 of file JQuaternion3D.hh.

◆ __b

double JGEOMETRY3D::JQuaternion3D::__b

protected

Definition at line 1118 of file JQuaternion3D.hh.

◆ __c

double JGEOMETRY3D::JQuaternion3D::__c

protected

Definition at line 1119 of file JQuaternion3D.hh.

◆ __d

double JGEOMETRY3D::JQuaternion3D::__d

protected

Definition at line 1120 of file JQuaternion3D.hh.

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

JQuaternion3D.hh

Classes

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ JQuaternion3D() [1/8]

◆ JQuaternion3D() [2/8]

◆ JQuaternion3D() [3/8]

◆ JQuaternion3D() [4/8]

◆ JQuaternion3D() [5/8]

◆ JQuaternion3D() [6/8]

◆ JQuaternion3D() [7/8]

◆ JQuaternion3D() [8/8]

Member Function Documentation

◆ getIdentity()

◆ getQuaternion() [1/2]

◆ getQuaternion() [2/2]

◆ setQuaternion()

◆ operator JVector3D()

◆ operator JVersor3D()

◆ getAngle()

◆ getA()

◆ getB()

◆ getC()

◆ getD()

◆ setIdentity()

◆ conjugate()

◆ negate()

◆ add()

◆ sub()

◆ mul() [1/7]

◆ div()

◆ mul() [2/7]

◆ mul() [3/7]

◆ mul() [4/7]

◆ mul() [5/7]

◆ mul() [6/7]

◆ rotate()

◆ rotate_back()

◆ equals()

◆ isIdentity()

◆ getLengthSquared()

◆ getLength()

◆ getDistanceSquared()

◆ getDistance()

◆ getDot()

◆ getConjugate()

◆ normalise()

◆ pow()

◆ interpolate()

◆ mul() [7/7]

Friends And Related Function Documentation

◆ operator>> [1/2]

◆ operator<< [1/2]

◆ operator>> [2/2]

◆ operator<< [2/2]

Member Data Documentation

◆ __a

◆ __b

◆ __c

◆ __d