
 Usage

vtkWindowedSincPolyDataFiler adjust point coordinate using a
windowed sinc function interpolation kernel. The effect is
to "relax" the mesh, making the cells better shaped and the
vertices more evenly distributed. Note that this filter
operates the lines, polygons, and triangle strips composing
an instance of vtkPolyData. Vertex or poly-vertex cells are
never modified.
The algorithm proceeds as follows. For each vertex v, a
topological and geometric analysis is performed to determine
which vertices are connected to v, and which cells are
connected to v. Then, a connectivity array is constructed
for each vertex. (The connectivity array is a list of lists
of vertices that directly attach to each vertex.) Next, an
iteration phase begins over all vertices. For each vertex v,
the coordinates of v are modified using a windowed sinc
function interpolation kernel. Taubin describes this
methodology is the IBM tech report RC-20404 (#90237, dated
3/12/96) "Optimal Surface Smoothing as Filter Design" G.
Taubin, T. Zhang and G. Golub. (Zhang and Golub are at
Stanford University).
This report discusses using standard signal processing low-
pass filters (in particular windowed sinc functions) to
smooth polyhedra. The transfer functions of the low-pass
filters are approximated by Chebyshev polynomials. This
facilitates applying the filters in an iterative diffusion
process (as opposed to a kernel convolution). The more
smoothing iterations applied, the higher the degree of
polynomial approximating the low-pass filter transfer
function. Each smoothing iteration, therefore, applies the
next higher term of the Chebyshev filter approximation to
the polyhedron. This decoupling of the filter into an
iteratively applied polynomial is possible since the
Chebyshev polynomials are orthogonal, i.e. increasing the
order of the approximation to the filter transfer function
does not alter the previously calculated coefficients for
the low order terms.
Note: Care must be taken to avoid smoothing with too few
iterations. A Chebyshev approximation with too few terms is
an poor approximation. The first few smoothing iterations
represent a severe scaling and translation of the data.
Subsequent iterations cause the smoothed polyhedron to
converge to the true location and scale of the object. We
have attempted to protect against this by automatically
adjusting the filter, effectively widening the pass band.
This adjustment is only possible if the number of iterations
is greater than 1. Note that this sacrifices some degree of
smoothing for model integrity. For those interested, the
filter is adjusted by searching for a value sigma such that
the actual pass band is k_pb + sigma and such that the
filter transfer function evaluates to unity at k_pb, i.e. f
(k_pb) = 1
To improve the numerical stability of the solution and
minimize the scaling the translation effects, the algorithm
can translate and scale the position coordinates to within
the unit cube [-1, 1], perform the smoothing, and translate
and scale the position coordinates back to the original
coordinate frame. This mode is controlled with the
NormalizeCoordinatesOn() / NormalizeCoordinatesOff()
methods. For legacy reasons, the default is
NormalizeCoordinatesOff.
This implementation is currently limited to using an
interpolation kernel based on Hamming windows. Other windows
(such as Hann, Blackman, Kaiser, Lanczos, Gaussian, and
exponential windows) could be used instead.
There are some special instance variables used to control
the execution of this filter. (These ivars basically control
what vertices can be smoothed, and the creation of the
connectivity array.) The BoundarySmoothing ivar enables/
disables the smoothing operation on vertices that are on the
"boundary" of the mesh. A boundary vertex is one that is
surrounded by a semi-cycle of polygons (or used by a single
line).
Another important ivar is FeatureEdgeSmoothing. If this ivar
is enabled, then interior vertices are classified as either
"simple", "interior edge", or "fixed", and smoothed
differently. (Interior vertices are manifold vertices
surrounded by a cycle of polygons; or used by two line
cells.) The classification is based on the number of feature
edges attached to v. A feature edge occurs when the angle
between the two surface normals of a polygon sharing an edge
is greater than the FeatureAngle ivar. Then, vertices used
by no feature edges are classified "simple", vertices used
by exactly two feature edges are classified "interior edge",
and all others are "fixed" vertices.
Once the classification is known, the vertices are smoothed
differently. Corner (i.e., fixed) vertices are not smoothed
at all. Simple vertices are smoothed as before . Interior
edge vertices are smoothed only along their two connected
edges, and only if the angle between the edges is less than
the EdgeAngle ivar.
The total smoothing can be controlled by using two ivars.
The NumberOfIterations determines the maximum number of
smoothing passes. The NumberOfIterations corresponds to the
degree of the polynomial that is used to approximate the
windowed sinc function. Ten or twenty iterations is all the
is usually necessary. Contrast this with
vtkSmoothPolyDataFilter which usually requires 100 to 200
smoothing iterations. vtkSmoothPolyDataFilter is also not an
approximation to an ideal low-pass filter, which can cause
the geometry to shrink as the amount of smoothing increases.
The second ivar is the specification of the PassBand for the
windowed sinc filter. By design, the PassBand is specified
as a doubleing point number between 0 and 2. Lower PassBand
values produce more smoothing. A good default value for the
PassBand is 0.1 (for those interested, the PassBand (and
frequencies) for PolyData are based on the valence of the
vertices, this limits all the frequency modes in a
polyhedral mesh to between 0 and 2.)
There are two instance variables that control the generation
of error data. If the ivar GenerateErrorScalars is on, then
a scalar value indicating the distance of each vertex from
its original position is computed. If the ivar
GenerateErrorVectors is on, then a vector representing
change in position is computed.
To create an instance of class
vtkWindowedSincPolyDataFilter, simply invoke its constructor
as follows

    obj = vtkWindowedSincPolyDataFilter



 Methods

The class vtkWindowedSincPolyDataFilter 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 vtkWindowedSincPolyDataFilter
class.

* string = obj.GetClassName ()
* int = obj.IsA (string name)
* vtkWindowedSincPolyDataFilter = obj.NewInstance ()
* vtkWindowedSincPolyDataFilter = obj.SafeDownCast
  (vtkObject o)
* obj.SetNumberOfIterations (int ) - Specify the number of
  iterations (or degree of the polynomial approximating the
  windowed sinc function).
* int = obj.GetNumberOfIterationsMinValue () - Specify the
  number of iterations (or degree of the polynomial
  approximating the windowed sinc function).
* int = obj.GetNumberOfIterationsMaxValue () - Specify the
  number of iterations (or degree of the polynomial
  approximating the windowed sinc function).
* int = obj.GetNumberOfIterations () - Specify the number of
  iterations (or degree of the polynomial approximating the
  windowed sinc function).
* obj.SetPassBand (double ) - Set the passband value for the
  windowed sinc filter
* double = obj.GetPassBandMinValue () - Set the passband
  value for the windowed sinc filter
* double = obj.GetPassBandMaxValue () - Set the passband
  value for the windowed sinc filter
* double = obj.GetPassBand () - Set the passband value for
  the windowed sinc filter
* obj.SetNormalizeCoordinates (int ) - Turn on/off
  coordinate normalization. The positions can be translated
  and scaled such that they fit within a [-1, 1] prior to
  the smoothing computation. The default is off. The
  numerical stability of the solution can be improved by
  turning normalization on. If normalization is on, the
  coordinates will be rescaled to the original coordinate
  system after smoothing has completed.
* int = obj.GetNormalizeCoordinates () - Turn on/off
  coordinate normalization. The positions can be translated
  and scaled such that they fit within a [-1, 1] prior to
  the smoothing computation. The default is off. The
  numerical stability of the solution can be improved by
  turning normalization on. If normalization is on, the
  coordinates will be rescaled to the original coordinate
  system after smoothing has completed.
* obj.NormalizeCoordinatesOn () - Turn on/off coordinate
  normalization. The positions can be translated and scaled
  such that they fit within a [-1, 1] prior to the smoothing
  computation. The default is off. The numerical stability
  of the solution can be improved by turning normalization
  on. If normalization is on, the coordinates will be
  rescaled to the original coordinate system after smoothing
  has completed.
* obj.NormalizeCoordinatesOff () - Turn on/off coordinate
  normalization. The positions can be translated and scaled
  such that they fit within a [-1, 1] prior to the smoothing
  computation. The default is off. The numerical stability
  of the solution can be improved by turning normalization
  on. If normalization is on, the coordinates will be
  rescaled to the original coordinate system after smoothing
  has completed.
* obj.SetFeatureEdgeSmoothing (int ) - Turn on/off smoothing
  along sharp interior edges.
* int = obj.GetFeatureEdgeSmoothing () - Turn on/off
  smoothing along sharp interior edges.
* obj.FeatureEdgeSmoothingOn () - Turn on/off smoothing
  along sharp interior edges.
* obj.FeatureEdgeSmoothingOff () - Turn on/off smoothing
  along sharp interior edges.
* obj.SetFeatureAngle (double ) - Specify the feature angle
  for sharp edge identification.
* double = obj.GetFeatureAngleMinValue () - Specify the
  feature angle for sharp edge identification.
* double = obj.GetFeatureAngleMaxValue () - Specify the
  feature angle for sharp edge identification.
* double = obj.GetFeatureAngle () - Specify the feature
  angle for sharp edge identification.
* obj.SetEdgeAngle (double ) - Specify the edge angle to
  control smoothing along edges (either interior or
  boundary).
* double = obj.GetEdgeAngleMinValue () - Specify the edge
  angle to control smoothing along edges (either interior or
  boundary).
* double = obj.GetEdgeAngleMaxValue () - Specify the edge
  angle to control smoothing along edges (either interior or
  boundary).
* double = obj.GetEdgeAngle () - Specify the edge angle to
  control smoothing along edges (either interior or
  boundary).
* obj.SetBoundarySmoothing (int ) - Turn on/off the
  smoothing of vertices on the boundary of the mesh.
* int = obj.GetBoundarySmoothing () - Turn on/off the
  smoothing of vertices on the boundary of the mesh.
* obj.BoundarySmoothingOn () - Turn on/off the smoothing of
  vertices on the boundary of the mesh.
* obj.BoundarySmoothingOff () - Turn on/off the smoothing of
  vertices on the boundary of the mesh.
* obj.SetNonManifoldSmoothing (int ) - Smooth non-manifold
  vertices.
* int = obj.GetNonManifoldSmoothing () - Smooth non-manifold
  vertices.
* obj.NonManifoldSmoothingOn () - Smooth non-manifold
  vertices.
* obj.NonManifoldSmoothingOff () - Smooth non-manifold
  vertices.
* obj.SetGenerateErrorScalars (int ) - Turn on/off the
  generation of scalar distance values.
* int = obj.GetGenerateErrorScalars () - Turn on/off the
  generation of scalar distance values.
* obj.GenerateErrorScalarsOn () - Turn on/off the generation
  of scalar distance values.
* obj.GenerateErrorScalarsOff () - Turn on/off the
  generation of scalar distance values.
* obj.SetGenerateErrorVectors (int ) - Turn on/off the
  generation of error vectors.
* int = obj.GetGenerateErrorVectors () - Turn on/off the
  generation of error vectors.
* obj.GenerateErrorVectorsOn () - Turn on/off the generation
  of error vectors.
* obj.GenerateErrorVectorsOff () - Turn on/off the
  generation of error vectors.


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