Generates a "classical" representation of a Klein bottle. More...

#include <vtkParametricKlein.h>

Inheritance diagram for vtkParametricKlein:

Collaboration diagram for vtkParametricKlein:

Public Types
typedef vtkParametricFunction	Superclass

Public Types inherited from vtkParametricFunction
typedef vtkObject	Superclass

Public Member Functions
virtual int	IsA (const char *type)

vtkParametricKlein *	NewInstance () const

void	PrintSelf (ostream &os, vtkIndent indent)

virtual int	GetDimension ()
	Initialise the parameters for the Klein bottle. More...

virtual void	Evaluate (double uvw[3], double Pt[3], double Duvw[9])

virtual double	EvaluateScalar (double uvw[3], double Pt[3], double Duvw[9])

Public Member Functions inherited from vtkParametricFunction
vtkParametricFunction *	NewInstance () const

void	PrintSelf (ostream &os, vtkIndent indent)

virtual void	SetMinimumU (double)

virtual double	GetMinimumU ()

virtual void	SetMaximumU (double)

virtual double	GetMaximumU ()

virtual void	SetMinimumV (double)

virtual double	GetMinimumV ()

virtual void	SetMaximumV (double)

virtual double	GetMaximumV ()

virtual void	SetMinimumW (double)

virtual double	GetMinimumW ()

virtual void	SetMaximumW (double)

virtual double	GetMaximumW ()

virtual void	SetJoinU (int)

virtual int	GetJoinU ()

virtual void	JoinUOn ()

virtual void	JoinUOff ()

virtual void	SetJoinV (int)

virtual int	GetJoinV ()

virtual void	JoinVOn ()

virtual void	JoinVOff ()

virtual void	SetTwistU (int)

virtual int	GetTwistU ()

virtual void	TwistUOn ()

virtual void	TwistUOff ()

virtual void	SetTwistV (int)

virtual int	GetTwistV ()

virtual void	TwistVOn ()

virtual void	TwistVOff ()

virtual void	SetClockwiseOrdering (int)

virtual int	GetClockwiseOrdering ()

virtual void	ClockwiseOrderingOn ()

virtual void	ClockwiseOrderingOff ()

virtual void	SetDerivativesAvailable (int)

virtual int	GetDerivativesAvailable ()

virtual void	DerivativesAvailableOn ()

virtual void	DerivativesAvailableOff ()

Static Public Member Functions
static int	IsTypeOf (const char *type)

static vtkParametricKlein *	SafeDownCast (vtkObjectBase *o)

static vtkParametricKlein *	New ()

Static Public Member Functions inherited from vtkParametricFunction
static int	IsTypeOf (const char *type)

static vtkParametricFunction *	SafeDownCast (vtkObjectBase *o)

Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const

	vtkParametricKlein ()

	~vtkParametricKlein ()

Protected Member Functions inherited from vtkParametricFunction
	vtkParametricFunction ()

virtual	~vtkParametricFunction ()

Additional Inherited Members
Protected Attributes inherited from vtkParametricFunction
double	MinimumU

double	MaximumU

double	MinimumV

double	MaximumV

double	MinimumW

double	MaximumW

int	JoinU

int	JoinV

int	JoinW

int	TwistU

int	TwistV

int	TwistW

int	ClockwiseOrdering

int	DerivativesAvailable

Detailed Description

Generates a "classical" representation of a Klein bottle.

vtkParametricKlein generates a "classical" representation of a Klein bottle. A Klein bottle is a closed surface with no interior and only one surface. It is unrealisable in 3 dimensions without intersecting surfaces. It can be realised in 4 dimensions by considering the map $F:R^2 \rightarrow R^4$ given by:

The classical representation of the immersion in $R^3$ is returned by this function.

For further information about this surface, please consult the technical description "Parametric surfaces" in http://www.vtk.org/documents.php in the "VTK Technical Documents" section in the VTk.org web pages.

Thanks:: Andrew Maclean a.mac.nosp@m.lean.nosp@m.@cas..nosp@m.edu..nosp@m.au for creating and contributing the class.

Tests:: vtkParametricKlein (Tests)

Definition at line 48 of file vtkParametricKlein.h.

Member Typedef Documentation

typedef vtkParametricFunction vtkParametricKlein::Superclass

Definition at line 51 of file vtkParametricKlein.h.

Constructor & Destructor Documentation

vtkParametricKlein::vtkParametricKlein ( )

protected

vtkParametricKlein::~vtkParametricKlein ( )

protected

Member Function Documentation

static int vtkParametricKlein::IsTypeOf ( const char * type )

static

virtual int vtkParametricKlein::IsA ( const char * type )

virtual

Reimplemented from vtkParametricFunction.

static vtkParametricKlein* vtkParametricKlein::SafeDownCast ( vtkObjectBase * o )

static

virtual vtkObjectBase* vtkParametricKlein::NewInstanceInternal ( ) const

protectedvirtual

Reimplemented from vtkParametricFunction.

vtkParametricKlein* vtkParametricKlein::NewInstance ( ) const

void vtkParametricKlein::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)

static vtkParametricKlein* vtkParametricKlein::New ( )

static

Construct a Klein Bottle with the following parameters: MinimumU = 0, MaximumU = 2*Pi, MinimumV = -Pi, MaximumV = Pi, JoinU = 0, JoinV = 1, TwistU = 0, TwistV = 0, ClockwiseOrdering = 1, DerivativesAvailable = 1,

virtual int vtkParametricKlein::GetDimension ( )

inlinevirtual

Initialise the parameters for the Klein bottle.

Return the parametric dimension of the class.

Implements vtkParametricFunction.

Definition at line 61 of file vtkParametricKlein.h.

virtual void vtkParametricKlein::Evaluate	(	double	uvw[3],
		double	Pt[3],
		double	Duvw[9]
	)

virtual

A Klein bottle. This function performs the mapping $f(u,v) \rightarrow (x,y,x)$ , returning it as Pt. It also returns the partial derivatives Du and Dv. $Pt = (x, y, z), Du = (dx/du, dy/du, dz/du), Dv = (dx/dv, dy/dv, dz/dv)$ . Then the normal is $N = Du X Dv$ .

Implements vtkParametricFunction.

virtual double vtkParametricKlein::EvaluateScalar	(	double	uvw[3],
		double	Pt[3],
		double	Duvw[9]
	)

virtual

Calculate a user defined scalar using one or all of uvw, Pt, Duvw. uvw are the parameters with Pt being the the cartesian point, Duvw are the derivatives of this point with respect to u, v and w. Pt, Duvw are obtained from Evaluate(). This function is only called if the ScalarMode has the value vtkParametricFunctionSource::SCALAR_FUNCTION_DEFINED If the user does not need to calculate a scalar, then the instantiated function should return zero.

Implements vtkParametricFunction.

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

dox/Common/ComputationalGeometry/vtkParametricKlein.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation