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vtkParametricFigure8Klein Class Reference

Generate a figure-8 Klein bottle. More...

#include <vtkParametricFigure8Klein.h>

Inheritance diagram for vtkParametricFigure8Klein:
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Collaboration diagram for vtkParametricFigure8Klein:
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Public Types

typedef vtkParametricFunction Superclass
 
- Public Types inherited from vtkParametricFunction
typedef vtkObject Superclass
 

Public Member Functions

virtual int IsA (const char *type)
 
vtkParametricFigure8KleinNewInstance () const
 
void PrintSelf (ostream &os, vtkIndent indent)
 
virtual int GetDimension ()
 
virtual void Evaluate (double uvw[3], double Pt[3], double Duvw[9])
 
virtual double EvaluateScalar (double uvw[3], double Pt[3], double Duvw[9])
 
virtual void SetRadius (double)
 
virtual double GetRadius ()
 
- Public Member Functions inherited from vtkParametricFunction
vtkParametricFunctionNewInstance () 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 vtkParametricFigure8KleinSafeDownCast (vtkObjectBase *o)
 
static vtkParametricFigure8KleinNew ()
 
- Static Public Member Functions inherited from vtkParametricFunction
static int IsTypeOf (const char *type)
 
static vtkParametricFunctionSafeDownCast (vtkObjectBase *o)
 

Protected Member Functions

virtual vtkObjectBase * NewInstanceInternal () const
 
 vtkParametricFigure8Klein ()
 
 ~vtkParametricFigure8Klein ()
 
- Protected Member Functions inherited from vtkParametricFunction
 vtkParametricFunction ()
 
virtual ~vtkParametricFunction ()
 

Protected Attributes

double Radius
 
- 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

Generate a figure-8 Klein bottle.

vtkParametricFigure8Klein generates a figure-8 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:

This representation of the immersion in $R^3$ is formed by taking two Mobius strips and joining them along their boundaries, this is the so called "Figure-8 Klein Bottle"

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:
vtkParametricFigure8Klein (Tests)

Definition at line 48 of file vtkParametricFigure8Klein.h.

Member Typedef Documentation

Definition at line 51 of file vtkParametricFigure8Klein.h.

Constructor & Destructor Documentation

vtkParametricFigure8Klein::vtkParametricFigure8Klein ( )
protected
vtkParametricFigure8Klein::~vtkParametricFigure8Klein ( )
protected

Member Function Documentation

static int vtkParametricFigure8Klein::IsTypeOf ( const char *  type)
static
virtual int vtkParametricFigure8Klein::IsA ( const char *  type)
virtual

Reimplemented from vtkParametricFunction.

static vtkParametricFigure8Klein* vtkParametricFigure8Klein::SafeDownCast ( vtkObjectBase *  o)
static
virtual vtkObjectBase* vtkParametricFigure8Klein::NewInstanceInternal ( ) const
protectedvirtual

Reimplemented from vtkParametricFunction.

vtkParametricFigure8Klein* vtkParametricFigure8Klein::NewInstance ( ) const
void vtkParametricFigure8Klein::PrintSelf ( ostream &  os,
vtkIndent  indent 
)
static vtkParametricFigure8Klein* vtkParametricFigure8Klein::New ( )
static

Construct a figure-8 Klein Bottle with the following parameters: MinimumU = -Pi, MaximumU = Pi, MinimumV = -Pi, MaximumV = Pi, JoinU = 1, JoinV = 1, TwistU = 0, TwistV = 0, ClockwiseOrdering = 1, DerivativesAvailable = 1, Radius = 1

virtual void vtkParametricFigure8Klein::SetRadius ( double  )
virtual

Set/Get the radius of the bottle.

virtual double vtkParametricFigure8Klein::GetRadius ( )
virtual

Set/Get the radius of the bottle.

virtual int vtkParametricFigure8Klein::GetDimension ( )
inlinevirtual

Return the parametric dimension of the class.

Implements vtkParametricFunction.

Definition at line 67 of file vtkParametricFigure8Klein.h.

virtual void vtkParametricFigure8Klein::Evaluate ( double  uvw[3],
double  Pt[3],
double  Duvw[9] 
)
virtual

A Figure-8 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 vtkParametricFigure8Klein::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.

Member Data Documentation

double vtkParametricFigure8Klein::Radius
protected

Definition at line 91 of file vtkParametricFigure8Klein.h.


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