/*========================================================================= Program: Visualization Toolkit Module: vtkParametricCatalanMinimal.cxx 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. =========================================================================*/ #include "vtkParametricCatalanMinimal.h" #include "vtkObjectFactory.h" #include "vtkMath.h" vtkStandardNewMacro(vtkParametricCatalanMinimal); //----------------------------------------------------------------------------// vtkParametricCatalanMinimal::vtkParametricCatalanMinimal() { // Preset triangulation parameters this->MinimumU = -4.*vtkMath::Pi(); this->MaximumU = 4.*vtkMath::Pi(); this->MinimumV = -1.5; this->MaximumV = 1.5; this->JoinU = 0; this->JoinV = 0; this->TwistU = 0; this->TwistV = 0; this->ClockwiseOrdering = 0; this->DerivativesAvailable = 1; } //----------------------------------------------------------------------------// vtkParametricCatalanMinimal::~vtkParametricCatalanMinimal() = default; //----------------------------------------------------------------------------// void vtkParametricCatalanMinimal::Evaluate(double uvw[3], double Pt[3], double Duvw[9]) { // Copy the parameters out of the vector, for the sake of convenience. double u = uvw[0]; double v = uvw[1]; // We're only going to need the u and v partial derivatives. // The w partial derivatives are not needed. double *Du = Duvw; double *Dv = Duvw + 3; // Location of the point. This parametrization was taken from: // https://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/catalan.html Pt[0] = u - cosh(v) * sin(u); Pt[1] = 1. - cos(u) * cosh(v); Pt[2] = 4.*sin(u / 2.) * sinh(v / 2.); // The derivative with respect to u: Du[0] = 1. - cosh(v) * cos(u); Du[1] = cosh(v) * sin(u); Du[2] = 2.*cos(u / 2.) * sinh(v / 2.); // The derivative with respect to v: Dv[0] = sin(u) * sinh(v); Dv[1] = -cos(u) * sinh(v); Dv[2] = 2.*sin(u / 2.) * cosh(v / 2.); } //----------------------------------------------------------------------------// double vtkParametricCatalanMinimal::EvaluateScalar(double *, double *, double *) { return 0; } //----------------------------------------------------------------------------// void vtkParametricCatalanMinimal::PrintSelf(ostream& os, vtkIndent indent) { this->Superclass::PrintSelf(os, indent); }