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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_AFFINE_PLANE_IN_RD_H_
#define FUNCTIONS_FUNCTION_AFFINE_PLANE_IN_RD_H_
#include <cstdlib> // for std::size_t
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_affine_plane_in_Rd
* \brief A class for the function that defines an m-dimensional implicit affine plane
* embedded in d-dimensional Euclidean space.
*/
struct Function_affine_plane_in_Rd {
/**
* \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 {
Eigen::VectorXd result = normal_matrix_.transpose() * (p - off_);
return result;
}
/** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
std::size_t amb_d() const { return d_; };
/** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
std::size_t cod_d() const { return k_; };
/** \brief Returns a point on the affine plane. */
Eigen::VectorXd seed() const {
Eigen::VectorXd result = off_;
return result;
}
/**
* \brief Constructor of the function that defines an m-dimensional implicit affine
* plane in the d-dimensional Euclidean space.
*
* @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
* correspond to the ambient dimension, the number of columns should correspond to
* the size of the normal basis (codimension).
* @param[in] offset The offset vector of the affine plane.
* The dimension of the vector should be the ambient dimension of the manifold.
*/
Function_affine_plane_in_Rd(const Eigen::MatrixXd& normal_matrix, const Eigen::VectorXd& offset)
: normal_matrix_(normal_matrix), d_(normal_matrix.rows()), k_(normal_matrix.cols()), off_(offset) {
normal_matrix_.colwise().normalize();
}
/**
* \brief Constructor of the function that defines an m-dimensional implicit affine
* plane in the d-dimensional Euclidean space that passes through origin.
*
* @param[in] normal_matrix A normal matrix of the affine plane. The number of rows should
* correspond to the ambient dimension, the number of columns should correspond to
* the size of the normal basis (codimension).
*/
Function_affine_plane_in_Rd(const Eigen::MatrixXd& normal_matrix)
: normal_matrix_(normal_matrix),
d_(normal_matrix.rows()),
k_(normal_matrix.cols()),
off_(Eigen::VectorXd::Zero(d_)) {
normal_matrix_.colwise().normalize();
}
private:
Eigen::MatrixXd normal_matrix_;
std::size_t d_, k_;
Eigen::VectorXd off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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