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/*=========================================================================
Program: Visualization Toolkit
Module: vtkParametricCatalanMinimal.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 vtkParametricCatalanMinimal
* @brief Generate Catalan's minimal surface.
*
* vtkParametricCatalanMinimal generates Catalan's minimal surface
* parametrically. This minimal surface contains the cycloid as a geodesic.
* More information about it can be found at
* <a href="https://en.wikipedia.org/wiki/Catalan%27s_minimal_surface">Wikipedia</a>.
* @par Thanks:
* Tim Meehan
*/
#ifndef vtkParametricCatalanMinimal_h
#define vtkParametricCatalanMinimal_h
#include "vtkCommonComputationalGeometryModule.h" // For export macro
#include "vtkParametricFunction.h"
VTK_ABI_NAMESPACE_BEGIN
class VTKCOMMONCOMPUTATIONALGEOMETRY_EXPORT vtkParametricCatalanMinimal
: public vtkParametricFunction
{
public:
vtkTypeMacro(vtkParametricCatalanMinimal, vtkParametricFunction);
void PrintSelf(ostream& os, vtkIndent indent) override;
/**
* Construct Catalan's minimal surface with the following parameters:
* (MinimumU, MaximumU) = (-4.*pi, 4.*pi),
* (MinimumV, MaximumV) = (-1.5, 1.5),
* JoinU = 0, JoinV = 0,
* TwistU = 0, TwistV = 0;
* ClockwiseOrdering = 0,
* DerivativesAvailable = 1,
*/
static vtkParametricCatalanMinimal* New();
/**
* Return the parametric dimension of the class.
*/
int GetDimension() override { return 2; }
/**
* Catalan's minimal 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:
vtkParametricCatalanMinimal();
~vtkParametricCatalanMinimal() override;
private:
vtkParametricCatalanMinimal(const vtkParametricCatalanMinimal&) = delete;
void operator=(const vtkParametricCatalanMinimal&) = delete;
};
VTK_ABI_NAMESPACE_END
#endif
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