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vtkParametricFigure8Klein Class Reference

#include <vtkParametricFigure8Klein.h>

Inheritance diagram for vtkParametricFigure8Klein:

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Collaboration diagram for vtkParametricFigure8Klein:

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List of all members.

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.maclean@cas.edu.au for creating and contributing the class.
Tests:
vtkParametricFigure8Klein (Tests)

Definition at line 47 of file vtkParametricFigure8Klein.h.
virtual void SetRadius (double)
virtual double GetRadius ()
static vtkParametricFigure8Klein * New ()

Public Types

typedef vtkParametricFunction Superclass

Public Member Functions

virtual const char * GetClassName ()
virtual int IsA (const char *type)
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])

Static Public Member Functions

static int IsTypeOf (const char *type)
static vtkParametricFigure8Klein * SafeDownCast (vtkObject *o)

Protected Member Functions

 vtkParametricFigure8Klein ()
 ~vtkParametricFigure8Klein ()

Protected Attributes

double Radius

Member Typedef Documentation

typedef vtkParametricFunction vtkParametricFigure8Klein::Superclass
 

Reimplemented from vtkParametricFunction.

Definition at line 50 of file vtkParametricFigure8Klein.h.

Constructor & Destructor Documentation

vtkParametricFigure8Klein::vtkParametricFigure8Klein (   )  [protected]
 

vtkParametricFigure8Klein::~vtkParametricFigure8Klein (   )  [protected]
 

Member Function Documentation

virtual const char* vtkParametricFigure8Klein::GetClassName (   )  [virtual]
 

Reimplemented from vtkParametricFunction.

static int vtkParametricFigure8Klein::IsTypeOf (  const char *  type  )  [static]
 

Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeRevisionMacro found in vtkSetGet.h.

Reimplemented from vtkParametricFunction.

virtual int vtkParametricFigure8Klein::IsA (  const char *  type  )  [virtual]
 

Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeRevisionMacro found in vtkSetGet.h.

Reimplemented from vtkParametricFunction.

static vtkParametricFigure8Klein* vtkParametricFigure8Klein::SafeDownCast (  vtkObject *  o  )  [static]
 

Reimplemented from vtkParametricFunction.

void vtkParametricFigure8Klein::PrintSelf (  ostream &  os,
vtkIndent  indent
)  [virtual]
 

Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkParametricFunction.

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

Reimplemented from vtkObject.

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 (   )  [inline, virtual]
 

Return the parametric dimension of the class.

Implements vtkParametricFunction.

Definition at line 66 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 90 of file vtkParametricFigure8Klein.h.

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