/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkWindowedSincPolyDataFilter.h

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
// .NAME vtkWindowedSincPolyDataFilter - adjust point positions using a windowed sinc function interpolation kernel
// .SECTION Description
// 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.
//
// .SECTION Caveats
// The smoothing operation reduces high frequency information in the
// geometry of the mesh. With excessive smoothing important details may be
// lost. Enabling FeatureEdgeSmoothing helps reduce this effect, but cannot
// entirely eliminate it.
//
// .SECTION See Also
// vtkSmoothPolyDataFilter vtkDecimate vtkDecimatePro


#ifndef vtkWindowedSincPolyDataFilter_h
#define vtkWindowedSincPolyDataFilter_h


#include "vtkFiltersCoreModule.h" // For export macro
#include "vtkPolyDataAlgorithm.h"

class VTKFILTERSCORE_EXPORT vtkWindowedSincPolyDataFilter : public vtkPolyDataAlgorithm
{
public:
  vtkTypeMacro(vtkWindowedSincPolyDataFilter,vtkPolyDataAlgorithm);
  void PrintSelf(ostream& os, vtkIndent indent);

  // Description:
  // Construct object with number of iterations 20; passband .1;
  // feature edge smoothing turned off; feature
  // angle 45 degrees; edge angle 15 degrees; and boundary smoothing turned
  // on. Error scalars and vectors are not generated (by default). The
  // convergence criterion is 0.0 of the bounding box diagonal.
  static vtkWindowedSincPolyDataFilter *New();

  // Description:
  // Specify the number of iterations (or degree of the polynomial
  // approximating the windowed sinc function).
  vtkSetClampMacro(NumberOfIterations,int,0,VTK_INT_MAX);
  vtkGetMacro(NumberOfIterations,int);

  // Description:
  // Set the passband value for the windowed sinc filter
  vtkSetClampMacro(PassBand,double, 0.0, 2.0);
  vtkGetMacro(PassBand,double);

  // Description:
  // 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.
  vtkSetMacro(NormalizeCoordinates, int);
  vtkGetMacro(NormalizeCoordinates, int);
  vtkBooleanMacro(NormalizeCoordinates, int);

  // Description:
  // Turn on/off smoothing along sharp interior edges.
  vtkSetMacro(FeatureEdgeSmoothing,int);
  vtkGetMacro(FeatureEdgeSmoothing,int);
  vtkBooleanMacro(FeatureEdgeSmoothing,int);

  // Description:
  // Specify the feature angle for sharp edge identification.
  vtkSetClampMacro(FeatureAngle,double,0.0,180.0);
  vtkGetMacro(FeatureAngle,double);

  // Description:
  // Specify the edge angle to control smoothing along edges (either interior
  // or boundary).
  vtkSetClampMacro(EdgeAngle,double,0.0,180.0);
  vtkGetMacro(EdgeAngle,double);

  // Description:
  // Turn on/off the smoothing of vertices on the boundary of the mesh.
  vtkSetMacro(BoundarySmoothing,int);
  vtkGetMacro(BoundarySmoothing,int);
  vtkBooleanMacro(BoundarySmoothing,int);

  // Description:
  // Smooth non-manifold vertices.
  vtkSetMacro(NonManifoldSmoothing,int);
  vtkGetMacro(NonManifoldSmoothing,int);
  vtkBooleanMacro(NonManifoldSmoothing,int);

  // Description:
  // Turn on/off the generation of scalar distance values.
  vtkSetMacro(GenerateErrorScalars,int);
  vtkGetMacro(GenerateErrorScalars,int);
  vtkBooleanMacro(GenerateErrorScalars,int);

  // Description:
  // Turn on/off the generation of error vectors.
  vtkSetMacro(GenerateErrorVectors,int);
  vtkGetMacro(GenerateErrorVectors,int);
  vtkBooleanMacro(GenerateErrorVectors,int);

 protected:
  vtkWindowedSincPolyDataFilter();
  ~vtkWindowedSincPolyDataFilter() {}

  int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *);

  int NumberOfIterations;
  double PassBand;
  int FeatureEdgeSmoothing;
  double FeatureAngle;
  double EdgeAngle;
  int BoundarySmoothing;
  int NonManifoldSmoothing;
  int GenerateErrorScalars;
  int GenerateErrorVectors;
  int NormalizeCoordinates;
private:
  vtkWindowedSincPolyDataFilter(const vtkWindowedSincPolyDataFilter&);  // Not implemented.
  void operator=(const vtkWindowedSincPolyDataFilter&);  // Not implemented.
};

#endif
