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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_CHAIR_IN_R3_H_
#define FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_
#include <cstdlib>
#include <gudhi/Functions/Function.h>
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_chair_in_R3
* \brief A class that encodes the function, the zero-set of which is a so-called
* "chair" surface embedded in R^3.
*
* \ingroup coxeter_triangulation
*/
struct Function_chair_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());
result(0) = std::pow(x*x + y*y + z*z - a_*k_*k_, 2) - b_*((z-k_)*(z-k_) - 2*x*x)*((z+k_)*(z+k_) - 2*y*y);
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 {
double t1 = a_-b_;
double discr = t1*t1 - (1.0 - b_)*(a_*a_ - b_);
double z0 = k_*std::sqrt((t1+std::sqrt(discr))/(1-b_));
Eigen::Vector3d result(off_[0], off_[1], z0+off_[2]);
return result;
}
/**
* \brief Constructor of the function that defines the 'chair' surface
* embedded in R^3.
*
* @param[in] a A numerical parameter.
* @param[in] b A numerical parameter.
* @param[in] k A numerical parameter.
* @param[in] off Offset vector.
*/
Function_chair_in_R3(double a = 0.8,
double b = 0.4,
double k = 1.0,
Eigen::Vector3d off = Eigen::Vector3d::Zero()) :
a_(a), b_(b), k_(k), off_(off) {}
protected:
double a_, b_, k_;
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
// (x^2 + y^2 + z^2 - a*k^2)^2 - b*((z-k)^2 - 2*x^2)*((z+k)^2 - 2*y^2)
// sqrt(k/(1-b))*sqrt(a-b + sqrt((a-b)^2 - (1-b)*(a^2 - b)*k^2))
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