Function_torus_in_R3.h

/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
 *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
 *    Author(s):       Siargey Kachanovich
 *
 *    Copyright (C) 2019 Inria
 *
 *    Modification(s):
 *      - YYYY/MM Author: Description of the modification
 */
 
#ifndef FUNCTIONS_FUNCTION_TORUS_IN_R3_H_
#define FUNCTIONS_FUNCTION_TORUS_IN_R3_H_
 
#include <cstdlib>  // for std::size_t
#include <cmath>    // for std::sqrt
 
#include <Eigen/Dense>
 
namespace Gudhi {
 
namespace coxeter_triangulation {
 
struct Function_torus_in_R3 {
  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
    double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
    Eigen::VectorXd result(cod_d());
    result(0) = (z * z + (std::sqrt(x * x + y * y) - r_) * (std::sqrt(x * x + y * y) - r_) - R_ * R_);
    return result;
  }
 
  std::size_t amb_d() const { return 3; };
 
  std::size_t cod_d() const { return 1; };
 
  Eigen::VectorXd seed() const {
    Eigen::Vector3d result(R_ + r_ + off_[0], off_[1], off_[2]);
    return result;
  }
 
  Function_torus_in_R3(double R = 1, double r = 0.5, Eigen::Vector3d off = Eigen::Vector3d::Zero())
      : R_(R), r_(r), off_(off) {}
 
 private:
  double R_, r_;
  Eigen::Vector3d off_;
};
 
}  // namespace coxeter_triangulation
 
}  // namespace Gudhi
 
#endif