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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* 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 <gudhi/Functions/Function.h>
#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.
*
* \ingroup coxeter_triangulation
*/
struct Function_lemniscate_revolution_in_R3 : public Function {
/**
* \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(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(-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) {}
protected:
double a_;
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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