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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_WHITNEY_UMBRELLA_IN_R3_H_
#define FUNCTIONS_FUNCTION_WHITNEY_UMBRELLA_IN_R3_H_
#include <cstdlib> // for std::size_t
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_whitney_umbrella_in_R3
* \brief A class that encodes the function, the zero-set of which is the Whitney umbrella
* surface embedded in R^3.
*/
struct Function_whitney_umbrella_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());
result(0) = x * x - y * y * z;
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(1 + off_[0], 1 + off_[1], 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(-1 + off_[0], -1 + off_[1], 1 + off_[2]);
return result;
}
/**
* \brief Constructor of the function that defines the Whitney umbrella in R^3.
*
* @param[in] off Offset vector.
*/
Function_whitney_umbrella_in_R3(Eigen::Vector3d off = Eigen::Vector3d::Zero()) : off_(off) {}
private:
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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