Dtk_dir Class Reference

This is a mathematical direction class. More...

Inheritance diagram for Dtk_dir:

Public Member Functions
Dtk_dir	Affinitised (const Dtk_pnt &p, const Dtk_dir &xdir, const Dtk_dir &ydir, double f[3]) const
void	Affinity (const Dtk_pnt &, const Dtk_dir &xdir, const Dtk_dir &ydir, double[3])
void	Affinity (double f[3])
double	Angle (const Dtk_dir &vRef, const Dtk_dir &vAxe, double tolerance=0.00000001) const
double	AngleXY (double tolerance=0.00000001) const
Dtk_Double64	ComputeAngleByQuadrant (const Dtk_dir &V2, const Dtk_dir &ref_Z) const
void	Cross (const Dtk_dir &right)
void	CrossCross (const Dtk_dir &c1, const Dtk_dir &c2)
Dtk_dir	CrossCrossed (const Dtk_dir &c1, const Dtk_dir &c2) const
Dtk_dir	Crossed (const Dtk_dir &right) const
Dtk_dir	DerivativeOfCrossProduct (const Dtk_dir &other, const Dtk_dir &thisPrime, const Dtk_dir &otherPrime) const
double	DerivativeOfNorm (const Dtk_dir &thisPrime) const
double	Dot (const Dtk_dir &other) const
double	DotCross (const Dtk_dir &c1, const Dtk_dir &c2) const
	Dtk_dir ()
	Dtk_dir (const Dtk_dir &s)
	Dtk_dir (const Dtk_pnt &, const Dtk_pnt &)
	Dtk_dir (const Dtk_pnt &pnt)
	Dtk_dir (double a, double b, double c=0.0)
	Dtk_dir (Dtk_dir &&s) DTK_NOEXCEPT
Dtk_dir	GetNormal () const
void	GetXYZ (Dtk_Double64 &outX, Dtk_Double64 &outY, Dtk_Double64 &outZ) const
	Retrieves to the 3 coordinates of the class. More...
int	IsEqual (const Dtk_pnt &inPointToCompare, const double inTolerance) const
	test if 2 Dtk_pnt are equal - with a tolerance - More...
Dtk_dir	Multiplied (const CDtk_3dMat &matrix) const
Dtk_dir	MultipliedByTransposed (const CDtk_3dMat &matrix) const
Dtk_dir	MultipliedNormalize (const CDtk_3dMat &matrix) const
void	Multiply (const CDtk_3dMat &matrix)
void	MultiplyByTransposed (const CDtk_3dMat &matrix)
void	MultiplyNormalize (const CDtk_3dMat &matrix)
double	norm () const
int	normalize ()
double	Normalize ()
Dtk_dir	Normalized () const
double	operator& (const Dtk_dir &other) const
Dtk_dir	operator* (const CDtk_3dMat &matrix) const
Dtk_dir	operator* (double a) const
void	operator*= (const CDtk_3dMat &matrix)
Dtk_dir &	operator*= (double)
Dtk_dir	operator+ () const
Dtk_dir	operator+ (const Dtk_dir &v)
Dtk_dir &	operator+= (const Dtk_dir &)
Dtk_dir &	operator+= (const Dtk_pnt &)
Dtk_pnt	operator- ()
Dtk_dir	operator- () const
Dtk_dir	operator- (const Dtk_dir &v)
Dtk_dir &	operator-= (const Dtk_dir &)
Dtk_dir &	operator-= (const Dtk_pnt &)
Dtk_dir &	operator/= (double)
Dtk_dir &	operator= (const Dtk_dir &)
double &	operator[] (Dtk_Size_t i)
	access to a specified coordinate of the Dtk_pnt More...
const double &	operator[] (Dtk_Size_t i) const
	access to a specified coordinate of the Dtk_pnt. More...
void	operator^= (const Dtk_dir &right)
Dtk_dir	PostMultiplied (const CDtk_3dMat &matrix) const
void	PostMultiply (const CDtk_3dMat &matrix)
double	Project (const Dtk_dir &zdir, double d)
double	Project (const Dtk_dir &zdir, double d, const Dtk_dir &zPrj)
double	Project (const Dtk_pnt &org, const Dtk_dir &zdir)
double	Project (const Dtk_pnt &org, const Dtk_dir &zdir, const Dtk_dir &zPrj)
Dtk_pnt	Projected (const Dtk_dir &zdir, double d) const
Dtk_pnt	Projected (const Dtk_dir &zdir, double d, const Dtk_dir &zPrj) const
Dtk_pnt	Projected (const Dtk_pnt &org, const Dtk_dir &zdir) const
Dtk_pnt	Projected (const Dtk_pnt &org, const Dtk_dir &zdir, const Dtk_dir &zPrj) const
Dtk_pnt	ProjectedOnLine (const Dtk_pnt &org, const Dtk_dir &dir) const
void	ProjectOnLine (const Dtk_pnt &org, const Dtk_dir &dir)
void	reverse ()
Dtk_dir	reversed () const
void	Rotate (const Dtk_dir &dir, double angle, const Dtk_pnt &center)
int	rotate (const Dtk_dir &Z, double angle)
void	Rotate (const Dtk_pnt &p0, const CDtk_3dMat &matrix)
Dtk_dir	Rotated (const Dtk_dir &dir, double angle, const Dtk_pnt &center) const
Dtk_dir	Rotated (const Dtk_pnt &p0, const CDtk_3dMat &matrix) const
void	Scale (const Dtk_pnt &p0, double s)
Dtk_dir	Scaled (const Dtk_pnt &p0, double s) const
Dtk_dir	SecondDerivativeOfCrossProduct (const Dtk_dir &other, const Dtk_dir &thisPrime, const Dtk_dir &otherPrime, const Dtk_dir &thisSecond, const Dtk_dir &otherSecond) const
double	SecondDerivativeOfNorm (const Dtk_dir &thisPrime, const Dtk_dir &thisSecond) const
	SetAsDeprecated ("Undefined", "Use ComputeAngleByQuadrant") double angle_with_Dtk_dir(const Dtk_dir &V2
void	SetXYZ (const Dtk_Double64 &inX, const Dtk_Double64 &inY, const Dtk_Double64 &inZ)
	Sets the 3 coordinates of the class. More...
double	Solve (const CDtk_3dMat &matrix, const Dtk_dir &col3)
double	Solve (const Dtk_dir &col0, const Dtk_dir &col1, const Dtk_dir &col2, const Dtk_dir &col3)
double	SquareModulus ()
Dtk_dir	Symetrised (const Dtk_pnt &opl, const Dtk_dir &zpl) const
void	Symetry (const Dtk_dir &zpl)
void	Symetry (const Dtk_pnt &opl, const Dtk_dir &zpl)
void	Transform (const CDtk_3dMat &matrix)
Dtk_dir	Transformed (const CDtk_3dMat &matrix) const
void	Translate (const Dtk_dir &dir)
void	Translate (const Dtk_pnt &p0, const Dtk_pnt &p1)
Dtk_dir	Translated (const Dtk_dir &dir) const
Dtk_dir	Translated (const Dtk_pnt &p0, const Dtk_pnt &p1) const
Dtk_dir	UnitizedDerivative (const Dtk_dir &thisPrime) const
Dtk_dir	UnitizedSecondDerivative (const Dtk_dir &thisPrime, const Dtk_dir &thisSecond) const
double &	x ()
	access to x coordinate of the Dtk_pnt. More...
const double &	x () const
	access to x coordinate of the Dtk_pnt. More...
double &	y ()
	access to y coordinate of the Dtk_pnt. More...
const double &	y () const
	access to y coordinate of the Dtk_pnt. More...
double &	z ()
	access to z coordinate of the Dtk_pnt. More...
const double &	z () const
	access to z coordinate of the Dtk_pnt. More...
	~Dtk_dir ()

Static Public Member Functions
static Dtk_Double64	ProcessDistance (const Dtk_pnt &inPoint1, const Dtk_pnt &inPoint2)
static void	ProcessMiddlePoint (const Dtk_pnt &inPntA, const Dtk_pnt &inPntB, Dtk_pnt &outMiddlePnt)

Data Fields
const Dtk_dir &	ref_Z

Protected Attributes
double	_Coords [3]

Detailed Description

This is a mathematical direction class.

This class provides all method about direction

Constructor & Destructor Documentation

Dtk_dir() [1/6]

Dtk_dir::Dtk_dir

(

)

~Dtk_dir()

Dtk_dir::~Dtk_dir

(

)

{}

Dtk_dir() [2/6]

Dtk_dir::Dtk_dir

(

const Dtk_dir &

s

)

Dtk_dir() [3/6]

Dtk_dir::Dtk_dir

(

Dtk_dir &&

s

)

Dtk_dir() [4/6]

Dtk_dir::Dtk_dir

(

const Dtk_pnt &

pnt

)

Dtk_dir() [5/6]

Dtk_dir::Dtk_dir	(	double	a,
		double	b,
		double	c = 0.0
	)

Dtk_dir() [6/6]

Dtk_dir::Dtk_dir	(	const Dtk_pnt &	,
		const Dtk_pnt &
	)

Member Function Documentation

Affinitised()

Dtk_dir Dtk_dir::Affinitised	(	const Dtk_pnt &	p,
		const Dtk_dir &	xdir,
		const Dtk_dir &	ydir,
		double	f[3]
	)		const

Affinity() [1/2]

void Dtk_dir::Affinity	(	const Dtk_pnt &	,
		const Dtk_dir &	xdir,
		const Dtk_dir &	ydir,
		double	[3]
	)

Affinity() [2/2]

void Dtk_dir::Affinity

(

double

f[3]

)

{ _Coords[ 0 ] *= f[ 0 ]; _Coords[ 1 ] *= f[ 1 ];  _Coords[ 2 ] *= f[ 2 ]; }

Angle()

double Dtk_dir::Angle	(	const Dtk_dir &	vRef,
		const Dtk_dir &	vAxe,
		double	tolerance = 0.00000001
	)		const

AngleXY()

double Dtk_dir::AngleXY

(

double

tolerance = 0.00000001

)

const

ComputeAngleByQuadrant()

Dtk_Double64 Dtk_dir::ComputeAngleByQuadrant	(	const Dtk_dir &	V2,
		const Dtk_dir &	ref_Z
	)		const

Cross()

void Dtk_dir::Cross

(

const Dtk_dir &

right

)

CrossCross()

void Dtk_dir::CrossCross	(	const Dtk_dir &	c1,
		const Dtk_dir &	c2
	)

CrossCrossed()

Dtk_dir Dtk_dir::CrossCrossed	(	const Dtk_dir &	c1,
		const Dtk_dir &	c2
	)		const

Crossed()

Dtk_dir Dtk_dir::Crossed

(

const Dtk_dir &

right

)

const

DerivativeOfCrossProduct()

Dtk_dir Dtk_dir::DerivativeOfCrossProduct	(	const Dtk_dir &	other,
		const Dtk_dir &	thisPrime,
		const Dtk_dir &	otherPrime
	)		const

DerivativeOfNorm()

double Dtk_dir::DerivativeOfNorm

(

const Dtk_dir &

thisPrime

)

const

Dot()

double Dtk_dir::Dot

(

const Dtk_dir &

other

)

const

{ return ( *this * other ); }

DotCross()

double Dtk_dir::DotCross	(	const Dtk_dir &	c1,
		const Dtk_dir &	c2
	)		const

GetNormal()

Dtk_dir Dtk_dir::GetNormal

(

)

const

GetXYZ()

void Dtk_pnt::GetXYZ ( Dtk_Double64 &  outX, Dtk_Double64 &  outY, Dtk_Double64 &  outZ  ) const

inherited

Retrieves to the 3 coordinates of the class.

Warning

You can't modify the returned value.

     {
          outX = _Coords[ 0 ];
          outY = _Coords[ 1 ];
          outZ = _Coords[ 2 ];
     }

IsEqual()

int Dtk_pnt::IsEqual ( const Dtk_pnt &  inPointToCompare, const double  inTolerance  ) const

inherited

test if 2 Dtk_pnt are equal - with a tolerance -

Parameters

pnt2	the Dtk_pnt to compare
tol	the tolerance to compare

Returns

0 if not equals != 0 else

Sample:

Dtk_pnt a(0.0,0.0,0.0);
Dtk_pnt b(15.0,0.0,0.0);
...
if(a.is_equal(b, 0.1))
{...}

Multiplied()

Dtk_dir Dtk_dir::Multiplied

(

const CDtk_3dMat &

matrix

)

const

MultipliedByTransposed()

Dtk_dir Dtk_dir::MultipliedByTransposed

(

const CDtk_3dMat &

matrix

)

const

MultipliedNormalize()

Dtk_dir Dtk_dir::MultipliedNormalize

(

const CDtk_3dMat &

matrix

)

const

Multiply()

void Dtk_dir::Multiply

(

const CDtk_3dMat &

matrix

)

MultiplyByTransposed()

void Dtk_dir::MultiplyByTransposed

(

const CDtk_3dMat &

matrix

)

MultiplyNormalize()

void Dtk_dir::MultiplyNormalize

(

const CDtk_3dMat &

matrix

)

norm()

double Dtk_dir::norm

(

)

const

normalize()

int Dtk_dir::normalize

(

)

Normalize()

double Dtk_dir::Normalize

(

)

Normalized()

Dtk_dir Dtk_dir::Normalized

(

)

const

operator&()

double Dtk_dir::operator&

(

const Dtk_dir &

other

)

const

{ return ( *this * other ); }

operator*() [1/2]

Dtk_dir Dtk_dir::operator*

(

const CDtk_3dMat &

matrix

)

const

{ return Multiplied( matrix ); };

operator*() [2/2]

Dtk_dir Dtk_dir::operator*

(

double

a

)

const

{ return Dtk_dir( _Coords[ 0 ] * a, _Coords[ 1 ] * a, _Coords[ 2 ] * a ); }

operator*=() [1/2]

void Dtk_dir::operator*=

(

const CDtk_3dMat &

matrix

)

{ Multiply( matrix ); };

operator*=() [2/2]

Dtk_dir& Dtk_dir::operator*=

(

double

)

operator+() [1/2]

Dtk_dir Dtk_dir::operator+

(

)

const

operator+() [2/2]

Dtk_dir Dtk_dir::operator+

(

const Dtk_dir &

v

)

{ return Dtk_dir( _Coords[ 0 ] + v._Coords[ 0 ], _Coords[ 1 ] + v._Coords[ 1 ], _Coords[ 2 ] + v._Coords[ 2 ] ); }

operator+=() [1/2]

Dtk_dir& Dtk_dir::operator+=

(

const Dtk_dir &

)

operator+=() [2/2]

Dtk_dir& Dtk_dir::operator+=

(

const Dtk_pnt &

)

operator-() [1/3]

Dtk_pnt Dtk_pnt::operator- ( )

inherited

operator-() [2/3]

Dtk_dir Dtk_dir::operator-

(

)

const

operator-() [3/3]

Dtk_dir Dtk_dir::operator-

(

const Dtk_dir &

v

)

{ return Dtk_dir( _Coords[ 0 ] - v._Coords[ 0 ], _Coords[ 1 ] - v._Coords[ 1 ], _Coords[ 2 ] - v._Coords[ 2 ] ); }

operator-=() [1/2]

Dtk_dir& Dtk_dir::operator-=

(

const Dtk_dir &

)

operator-=() [2/2]

Dtk_dir& Dtk_dir::operator-=

(

const Dtk_pnt &

)

operator/=()

Dtk_dir& Dtk_dir::operator/=

(

double

)

operator=()

Dtk_dir& Dtk_dir::operator=

(

const Dtk_dir &

)

operator[]() [1/2]

double& Dtk_dir::operator[]

(

Dtk_Size_t

i

)

access to a specified coordinate of the Dtk_pnt

• i = 0 => X coordinate
• i = 1 => Y coordinate
• i = 2 => Z coordinate

     {
          Pdtk_Assert( i < 3 );
          return _Coords[ i ];
     }

operator[]() [2/2]

const double& Dtk_dir::operator[]

(

Dtk_Size_t

i

)

const

access to a specified coordinate of the Dtk_pnt.

Warning

You can't modify the returned value.

• i = 0 => X coordinate
• i = 1 => Y coordinate
• i = 2 => Z coordinate

     {
          Pdtk_Assert( i < 3 );
          return _Coords[ i ];
     }

operator^=()

void Dtk_dir::operator^=

(

const Dtk_dir &

right

)

{ Cross( right ); }

PostMultiplied()

Dtk_dir Dtk_dir::PostMultiplied

(

const CDtk_3dMat &

matrix

)

const

PostMultiply()

void Dtk_dir::PostMultiply

(

const CDtk_3dMat &

matrix

)

ProcessDistance()

static Dtk_Double64 Dtk_pnt::ProcessDistance ( const Dtk_pnt &  inPoint1, const Dtk_pnt &  inPoint2  )

staticinherited

     {
          Dtk_Double64 dist = 0.0;
          Dtk_Size_t i;
 
          for( i = 0; i < 3; i++ )
               dist += ( inPoint1[ i ] - inPoint2[ i ] ) * ( inPoint1[ i ] - inPoint2[ i ] );
 
          return static_cast< Dtk_Double64 >( sqrt( dist ) );
     }

ProcessMiddlePoint()

static void Dtk_pnt::ProcessMiddlePoint ( const Dtk_pnt &  inPntA, const Dtk_pnt &  inPntB, Dtk_pnt &  outMiddlePnt  )

staticinherited

     {
          for( Dtk_Size_t i = 0; i < 3; i++ )
               outMiddlePnt[ i ] = ( inPntA[ i ] + inPntB[ i ] ) / 2.0;
     }

Project() [1/4]

double Dtk_pnt::Project ( const Dtk_dir &  zdir, double  d  )

inherited

Project() [2/4]

double Dtk_pnt::Project ( const Dtk_dir &  zdir, double  d, const Dtk_dir &  zPrj  )

inherited

Project() [3/4]

double Dtk_pnt::Project ( const Dtk_pnt &  org, const Dtk_dir &  zdir  )

inherited

Project() [4/4]

double Dtk_pnt::Project ( const Dtk_pnt &  org, const Dtk_dir &  zdir, const Dtk_dir &  zPrj  )

inherited

Projected() [1/4]

Dtk_pnt Dtk_pnt::Projected ( const Dtk_dir &  zdir, double  d  ) const

inherited

{    Dtk_pnt tmp = *this; tmp.Project( zdir, d ); return tmp; };

Projected() [2/4]

Dtk_pnt Dtk_pnt::Projected ( const Dtk_dir &  zdir, double  d, const Dtk_dir &  zPrj  ) const

inherited

{    Dtk_pnt tmp = *this; tmp.Project( zdir, d, zPrj ); return tmp; };

Projected() [3/4]

Dtk_pnt Dtk_pnt::Projected ( const Dtk_pnt &  org, const Dtk_dir &  zdir  ) const

inherited

{    Dtk_pnt tmp = *this; tmp.Project( org, zdir ); return tmp; };

Projected() [4/4]

Dtk_pnt Dtk_pnt::Projected ( const Dtk_pnt &  org, const Dtk_dir &  zdir, const Dtk_dir &  zPrj  ) const

inherited

{    Dtk_pnt tmp = *this; tmp.Project( org, zdir, zPrj ); return tmp; };

ProjectedOnLine()

Dtk_pnt Dtk_pnt::ProjectedOnLine ( const Dtk_pnt &  org, const Dtk_dir &  dir  ) const

inherited

{    Dtk_pnt tmp = *this; tmp.ProjectOnLine( org, dir ); return tmp; };

ProjectOnLine()

void Dtk_pnt::ProjectOnLine ( const Dtk_pnt &  org, const Dtk_dir &  dir  )

inherited

reverse()

void Dtk_dir::reverse

(

)

reversed()

Dtk_dir Dtk_dir::reversed

(

)

const

Rotate() [1/2]

void Dtk_dir::Rotate	(	const Dtk_dir &	dir,
		double	angle,
		const Dtk_pnt &	center
	)

rotate()

int Dtk_dir::rotate	(	const Dtk_dir &	Z,
		double	angle
	)

Rotate() [2/2]

void Dtk_dir::Rotate	(	const Dtk_pnt &	p0,
		const CDtk_3dMat &	matrix
	)

Rotated() [1/2]

Dtk_dir Dtk_dir::Rotated	(	const Dtk_dir &	dir,
		double	angle,
		const Dtk_pnt &	center
	)		const

Rotated() [2/2]

Dtk_dir Dtk_dir::Rotated	(	const Dtk_pnt &	p0,
		const CDtk_3dMat &	matrix
	)		const

Scale()

void Dtk_dir::Scale	(	const Dtk_pnt &	p0,
		double	s
	)

Scaled()

Dtk_dir Dtk_dir::Scaled	(	const Dtk_pnt &	p0,
		double	s
	)		const

SecondDerivativeOfCrossProduct()

Dtk_dir Dtk_dir::SecondDerivativeOfCrossProduct	(	const Dtk_dir &	other,
		const Dtk_dir &	thisPrime,
		const Dtk_dir &	otherPrime,
		const Dtk_dir &	thisSecond,
		const Dtk_dir &	otherSecond
	)		const

SecondDerivativeOfNorm()

double Dtk_dir::SecondDerivativeOfNorm	(	const Dtk_dir &	thisPrime,
		const Dtk_dir &	thisSecond
	)		const

SetAsDeprecated()

Dtk_dir::SetAsDeprecated	(	"Undefined"	,
		"Use ComputeAngleByQuadrant"
	)		const &

Deprecated:

Use ComputeAngleByQuadrant.

SetXYZ()

void Dtk_pnt::SetXYZ ( const Dtk_Double64 &  inX, const Dtk_Double64 &  inY, const Dtk_Double64 &  inZ  )

inherited

Sets the 3 coordinates of the class.

     {
          _Coords[ 0 ] = inX;
          _Coords[ 1 ] = inY;
          _Coords[ 2 ] = inZ;
     }

Solve() [1/2]

double Dtk_pnt::Solve ( const CDtk_3dMat &  matrix, const Dtk_dir &  col3  )

inherited

Solve() [2/2]

double Dtk_pnt::Solve ( const Dtk_dir &  col0, const Dtk_dir &  col1, const Dtk_dir &  col2, const Dtk_dir &  col3  )

inherited

SquareModulus()

double Dtk_dir::SquareModulus

(

)

Symetrised()

Dtk_dir Dtk_dir::Symetrised	(	const Dtk_pnt &	opl,
		const Dtk_dir &	zpl
	)		const

Symetry() [1/2]

void Dtk_dir::Symetry

(

const Dtk_dir &

zpl

)

Symetry() [2/2]

void Dtk_dir::Symetry	(	const Dtk_pnt &	opl,
		const Dtk_dir &	zpl
	)

Transform()

void Dtk_dir::Transform

(

const CDtk_3dMat &

matrix

)

Transformed()

Dtk_dir Dtk_dir::Transformed

(

const CDtk_3dMat &

matrix

)

const

Translate() [1/2]

void Dtk_dir::Translate

(

const Dtk_dir &

dir

)

Translate() [2/2]

void Dtk_dir::Translate	(	const Dtk_pnt &	p0,
		const Dtk_pnt &	p1
	)

Translated() [1/2]

Dtk_dir Dtk_dir::Translated

(

const Dtk_dir &

dir

)

const

Translated() [2/2]

Dtk_dir Dtk_dir::Translated	(	const Dtk_pnt &	p0,
		const Dtk_pnt &	p1
	)		const

UnitizedDerivative()

Dtk_dir Dtk_dir::UnitizedDerivative

(

const Dtk_dir &

thisPrime

)

const

UnitizedSecondDerivative()

Dtk_dir Dtk_dir::UnitizedSecondDerivative	(	const Dtk_dir &	thisPrime,
		const Dtk_dir &	thisSecond
	)		const

x() [1/2]

double& Dtk_dir::x

(

)

access to x coordinate of the Dtk_pnt.

{ return _Coords[ 0 ]; }

x() [2/2]

const double& Dtk_dir::x

(

)

const

access to x coordinate of the Dtk_pnt.

Warning

You can't modify the returned value.

{ return _Coords[ 0 ]; }

y() [1/2]

double& Dtk_dir::y

(

)

access to y coordinate of the Dtk_pnt.

{ return _Coords[ 1 ]; }

y() [2/2]

const double& Dtk_dir::y

(

)

const

access to y coordinate of the Dtk_pnt.

Warning

You can't modify the returned value.

{ return _Coords[ 1 ]; }

z() [1/2]

double& Dtk_dir::z

(

)

access to z coordinate of the Dtk_pnt.

{ return _Coords[ 2 ]; }

z() [2/2]

const double& Dtk_dir::z

(

)

const

access to z coordinate of the Dtk_pnt.

Warning

You can't modify the returned value.

{ return _Coords[ 2 ]; }

Field Documentation

_Coords

double Dtk_pnt::_Coords[3]

protectedinherited

ref_Z

const Dtk_dir& Dtk_dir::ref_Z