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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_SM_IN_RD_H_
#define FUNCTIONS_FUNCTION_SM_IN_RD_H_
#include <cstdlib> // for std::size_t
#include <gudhi/Functions/Function.h>
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_Sm_in_Rd
* \brief A class for the function that defines an m-dimensional implicit sphere embedded
* in the d-dimensional Euclidean space.
*
* \ingroup coxeter_triangulation
*/
struct Function_Sm_in_Rd: 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.
*/
virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
Eigen::VectorXd x = p;
for (std::size_t i = 0; i < d_; ++i)
x(i) -= center_[i];
Eigen::VectorXd result = Eigen::VectorXd::Zero(k_);
for (std::size_t i = 0; i < m_+1; ++i)
result(0) += x(i)*x(i);
result(0) -= r_*r_;
for (std::size_t j = 1; j < k_; ++j)
result(j) = x(m_+j);
return result;
}
/** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
virtual std::size_t amb_d() const override {return d_;};
/** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
virtual std::size_t cod_d() const override {return k_;};
/** \brief Returns a point on the sphere. */
virtual Eigen::VectorXd seed() const override {
Eigen::VectorXd result = Eigen::VectorXd::Zero(d_);
result(0) += r_;
for (std::size_t i = 0; i < d_; ++i)
result(i) += center_[i];
return result;
}
/**
* \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
* in the d-dimensional Euclidean space.
*
* @param[in] r The radius of the sphere.
* @param[in] m The dimension of the sphere.
* @param[in] d The ambient dimension of the sphere.
* @param[in] center The center of the sphere.
*/
Function_Sm_in_Rd(double r,
std::size_t m,
std::size_t d,
Eigen::VectorXd center)
: m_(m), k_(d-m), d_(d), r_(r), center_(center) {}
/**
* \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
* in the d-dimensional Euclidean space centered at the origin.
*
* @param[in] r The radius of the sphere.
* @param[in] m The dimension of the sphere.
* @param[in] d The ambient dimension of the sphere.
*/
Function_Sm_in_Rd(double r,
std::size_t m,
std::size_t d)
: m_(m), k_(d-m), d_(d), r_(r), center_(Eigen::VectorXd::Zero(d_)) {}
/**
* \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
* in the (m+1)-dimensional Euclidean space.
*
* @param[in] r The radius of the sphere.
* @param[in] m The dimension of the sphere.
* @param[in] center The center of the sphere.
*/
Function_Sm_in_Rd(double r,
std::size_t m,
Eigen::VectorXd center)
: m_(m), k_(1), d_(m_+1), r_(r), center_(center) {}
/**
* \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
* in the (m+1)-dimensional Euclidean space centered at the origin.
*
* @param[in] r The radius of the sphere.
* @param[in] m The dimension of the sphere.
*/
Function_Sm_in_Rd(double r,
std::size_t m)
: m_(m), k_(1), d_(m_+1), r_(r), center_(Eigen::VectorXd::Zero(d_)) {}
Function_Sm_in_Rd(const Function_Sm_in_Rd& rhs)
: Function_Sm_in_Rd(rhs.r_, rhs.m_, rhs.d_, rhs.center_) {}
private:
std::size_t m_, k_, d_;
double r_;
Eigen::VectorXd center_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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