FreeMat: vtkParametricKlein

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vtkParametricKlein

Section: Visualization Toolkit Common Classes

# Usage

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 given by:

The classical representation of the immersion in 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.

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

To create an instance of class vtkParametricKlein, simply invoke its constructor as follows

      obj = vtkParametricKlein

# Methods

The class vtkParametricKlein has several methods that can be used. They are listed below. Note that the documentation is translated automatically from the VTK sources, and may not be completely intelligible. When in doubt, consult the VTK website. In the methods listed below, `obj` is an instance of the vtkParametricKlein class.

- `string = obj.GetClassName ()`
- `int = obj.IsA (string name)`
- `vtkParametricKlein = obj.NewInstance ()`
- `vtkParametricKlein = obj.SafeDownCast (vtkObject o)`

- `int = obj.GetDimension ()` - A Klein bottle.

  This function performs the mapping , returning it as Pt. It also returns the partial derivatives Du and Dv. . Then the normal is .

- `obj.Evaluate (double uvw[3], double Pt[3], double Duvw[9])` - A Klein bottle.

  This function performs the mapping , returning it as Pt. It also returns the partial derivatives Du and Dv. . Then the normal is .

- `double = obj.EvaluateScalar (double uvw[3], double Pt[3], double Duvw[9])` - 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.