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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_WHITNEY_UMBRELLA_IN_R3_H_
#define FUNCTIONS_FUNCTION_WHITNEY_UMBRELLA_IN_R3_H_
#include <cstdlib> // for std::size_t
#include <gudhi/Functions/Function.h>
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \class Function_whitney_umbrella_in_R3
* \brief A class that encodes the function, the zero-set of which is the Whitney umbrella
* surface embedded in R^3.
*
* \ingroup coxeter_triangulation
*/
struct Function_whitney_umbrella_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.
*/
virtual Eigen::VectorXd operator()(const Eigen::VectorXd& p) const override {
double x = p(0)-off_[0], y = p(1)-off_[1], z = p(2)-off_[2];
Eigen::VectorXd result(cod_d());
result(0) = x*x - y*y*z;
return result;
}
/** \brief Returns the (ambient) domain dimension.*/
virtual std::size_t amb_d() const override {return 3;};
/** \brief Returns the codomain dimension. */
virtual std::size_t cod_d() const override {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.
*/
virtual Eigen::VectorXd seed() const override {
Eigen::Vector3d result(1+off_[0], 1+off_[1], 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(-1+off_[0], -1+off_[1], 1+off_[2]);
return result;
}
/**
* \brief Constructor of the function that defines the Whitney umbrella in R^3.
*
* @param[in] off Offset vector.
*/
Function_whitney_umbrella_in_R3(Eigen::Vector3d off = Eigen::Vector3d::Zero())
: off_(off) {}
private:
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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