/*========================================================================= Program: Visualization Toolkit Module: vtkParametricBour.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 "vtkParametricBour.h" #include "vtkObjectFactory.h" #include "vtkMath.h" vtkStandardNewMacro(vtkParametricBour); //----------------------------------------------------------------------------// vtkParametricBour::vtkParametricBour() { // Preset triangulation parameters this->MinimumU = 0.; this->MaximumU = 1.0; this->MinimumV = 0.; this->MaximumV = 4.*vtkMath::Pi(); this->JoinU = 0; this->JoinV = 0; this->TwistU = 0; this->TwistV = 0; this->ClockwiseOrdering = 0; this->DerivativesAvailable = 1; } //----------------------------------------------------------------------------// vtkParametricBour::~vtkParametricBour() = default; //----------------------------------------------------------------------------// void vtkParametricBour::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://en.wikipedia.org/wiki/Bour%27s_minimal_surface Pt[0] = u * cos(v) - u * u * cos(2.*v) / 2.; Pt[1] = -u * sin(v) * (u * cos(v) + 1.); Pt[2] = 4. / 3.*pow(u, 1.5) * cos(1.5 * v); // The derivative with respect to u: Du[0] = cos(v) - u * cos(2 * v); Du[1] = -sin(v) * (1. + 2.*u * cos(v)); Du[2] = 2 * sqrt(u) * cos(1.5 * v); // The derivative with respect to v: Dv[0] = u * (2.*u * cos(v) - 1.) * sin(v); Dv[1] = -u * (cos(v) + u * cos(2.*v)); Dv[2] = -2.*pow(u, 1.5) * sin(1.5 * v); } //----------------------------------------------------------------------------// double vtkParametricBour::EvaluateScalar(double *, double *, double *) { return 0; } //----------------------------------------------------------------------------// void vtkParametricBour::PrintSelf(ostream& os, vtkIndent indent) { this->Superclass::PrintSelf(os, indent); }