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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricKuen.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.
=========================================================================*/
/**
* @class vtkParametricKuen
* @brief Generate Kuens' surface.
*
* vtkParametricKuen generates Kuens' surface. This surface has a constant
* negative gaussian curvature. For more information about this surface, see
* Dr. O'Niell's page at the
* <a href="http://www.math.ucla.edu/~bon/kuen.html">UCLA Mathematics Department</a>.
* @par Thanks:
* Tim Meehan
*/
#ifndef vtkParametricKuen_h
#define vtkParametricKuen_h
#include "vtkCommonComputationalGeometryModule.h" // For export macro
#include "vtkMath.h" // for vtkMath::Pi()
#include "vtkParametricFunction.h"
VTK_ABI_NAMESPACE_BEGIN
class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricKuen : public vtkParametricFunction
{
public:
vtkTypeMacro(vtkParametricKuen, vtkParametricFunction);
void PrintSelf(ostream& os, vtkIndent indent) override;
/**
* Construct Kuen's surface with the following parameters:
* (MinimumU, MaximumU) = (-4.5, 4.5),
* (MinimumV, MaximumV) = (DeltaV0, pi),
* JoinU = 0, JoinV = 0,
* TwistU = 0, TwistV = 0;
* ClockwiseOrdering = 0,
* DerivativesAvailable = 1,
*/
static vtkParametricKuen* New();
/**
* Return the parametric dimension of the class.
*/
int GetDimension() override { return 2; }
///@{
/**
* Set/Get the value to use when V == 0.
* Default is 0.05, giving the best appearance with the default settings.
* Setting it to a value less than 0.05 extrapolates the surface
* towards a pole in the -z direction.
* Setting it to 0 retains the pole whose z-value is -inf.
*/
vtkSetMacro(DeltaV0, double);
vtkGetMacro(DeltaV0, double);
///@}
/**
* Kuen's surface.
* This function performs the mapping \f$f(u,v) \rightarrow (x,y,x)\f$, returning it
* as Pt. It also returns the partial derivatives Du and Dv.
* \f$Pt = (x, y, z), D_u\vec{f} = (dx/du, dy/du, dz/du), D_v\vec{f} = (dx/dv, dy/dv, dz/dv)\f$ .
* Then the normal is \f$N = D_u\vec{f} \times D_v\vec{f}\f$ .
*/
void Evaluate(double uvw[3], double Pt[3], double Duvw[9]) override;
/**
* Calculate a user defined scalar using one or all of uvw, Pt, Duvw.
* This method simply returns 0.
*/
double EvaluateScalar(double uvw[3], double Pt[3], double Duvw[9]) override;
protected:
vtkParametricKuen();
~vtkParametricKuen() override;
private:
vtkParametricKuen(const vtkParametricKuen&) = delete;
void operator=(const vtkParametricKuen&) = delete;
double DeltaV0;
};
VTK_ABI_NAMESPACE_END
#endif
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