Function_lemniscate_revolution_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_LEMNISCATE_REVOLUTION_IN_R3_H_
#define FUNCTIONS_FUNCTION_LEMNISCATE_REVOLUTION_IN_R3_H_
 
#include <cstdlib>  // for std::size_t
#include <cmath>    // for std::sqrt
 
#include <Eigen/Dense>
 
namespace Gudhi {
 
namespace coxeter_triangulation {
 
struct Function_lemniscate_revolution_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());
    double x2 = x * x, y2 = y * y, z2 = z * z, a2 = a_ * a_;
    double t1 = x2 + y2 + z2;
    result(0) = t1 * t1 - 2 * a2 * (x2 - y2 - z2);
    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(std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
    return result;
  }
 
  Eigen::VectorXd seed2() const {
    Eigen::Vector3d result(-std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
    return result;
  }
 
  Function_lemniscate_revolution_in_R3(double a = 1, Eigen::Vector3d off = Eigen::Vector3d::Zero())
      : a_(a), off_(off) {}
 
 private:
  double a_;
  Eigen::Vector3d off_;
};
 
}  // namespace coxeter_triangulation
 
}  // namespace Gudhi
 
#endif