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/* 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_IRON_IN_R3_H_
#define FUNCTIONS_FUNCTION_IRON_IN_R3_H_
#include <cstdlib> // for std::size_t
#include <cmath> // for std::pow
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_iron_in_R3
* \brief A class that encodes the function, the zero-set of which is a surface
* embedded in R^3 that ressembles an iron.
*/
struct Function_iron_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), y = p(1), z = p(2);
Eigen::VectorXd result(cod_d());
result(0) = -std::pow(x, 6) / 300. - std::pow(y, 6) / 300. - std::pow(z, 6) / 300. + x * y * y * z / 2.1 + y * y +
std::pow(z - 2, 4) - 1;
return result;
}
/** \brief Returns the domain (ambient) 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. */
Eigen::VectorXd seed() const {
Eigen::Vector3d result(std::pow(4500, 1. / 6), 0, 0);
return result;
}
/**
* \brief Constructor of the function that defines a surface embedded in R^3
* that ressembles an iron.
*
* @param[in] off Offset vector.
*/
Function_iron_in_R3(Eigen::Vector3d off = Eigen::Vector3d::Zero()) : off_(off) {}
private:
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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