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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_AFFINE_PLANE_IN_RD_H_
#define FUNCTIONS_FUNCTION_AFFINE_PLANE_IN_RD_H_
#include <gudhi/Functions/Function.h>
#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.
*
* \ingroup coxeter_triangulation
*/
struct Function_affine_plane_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 result = normal_matrix_.transpose() * (p - off_);
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 affine plane. */
virtual Eigen::VectorXd seed() const override {
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 corespond 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()),
m_(d_ - k_),
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 corespond 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()),
m_(d_ - k_),
off_(Eigen::VectorXd::Zero(d_)) {
normal_matrix_.colwise().normalize();
}
protected:
Eigen::MatrixXd normal_matrix_;
std::size_t d_, k_, m_;
Eigen::VectorXd off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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