/*    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 {

/**
 * \class Function_lemniscate_revolution_in_R3
 * \brief A class that encodes the function, the zero-set of which is a surface of revolution
 * around the x axis based on the lemniscate of Bernoulli embedded in R^3.
 */
struct Function_lemniscate_revolution_in_R3 {
  /**
   * \brief Value of the function at a specified point.
   * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
   */
  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;
  }

  /** \brief Returns the (ambient) domain dimension.*/
  std::size_t amb_d() const { return 3; };

  /** \brief Returns the codomain dimension. */
  std::size_t cod_d() const { return 1; };

  /** \brief Returns a point on the surface. This seed point is only one of
   * two necessary seed points for the manifold tracing algorithm.
   * See the method seed2() for the other point.
   */
  Eigen::VectorXd seed() const {
    Eigen::Vector3d result(std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
    return result;
  }

  /** \brief Returns a point on the surface. This seed point is only one of
   * two necessary seed points for the manifold tracing algorithm.
   * See the method seed() for the other point.
   */
  Eigen::VectorXd seed2() const {
    Eigen::Vector3d result(-std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
    return result;
  }

  /**
   * \brief Constructor of the function that defines a surface of revolution
   * around the x axis based on the lemniscate of Bernoulli embedded in R^3.
   *
   * @param[in] a A numerical parameter.
   * @param[in] off Offset vector.
   */
  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