Loading...
Searching...
No Matches
Function_lemniscate_revolution_in_R3.h
/* 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_LEMNISCATE_REVOLUTION_IN_R3_H_
#define FUNCTIONS_FUNCTION_LEMNISCATE_REVOLUTION_IN_R3_H_
#include <cstdlib> // for std::size_t
#include <cmath> // for std::sqrt
#include <Eigen/Dense>
namespace Gudhi {
namespace coxeter_triangulation {
struct Function_lemniscate_revolution_in_R3 {
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());
double x2 = x * x, y2 = y * y, z2 = z * z, a2 = a_ * a_;
double t1 = x2 + y2 + z2;
result(0) = t1 * t1 - 2 * a2 * (x2 - y2 - z2);
return result;
}
std::size_t amb_d() const { return 3; };
std::size_t cod_d() const { return 1; };
Eigen::VectorXd seed() const {
Eigen::Vector3d result(std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
return result;
}
Eigen::VectorXd seed2() const {
Eigen::Vector3d result(-std::sqrt(2 * a_) + off_[0], off_[1], off_[2]);
return result;
}
Function_lemniscate_revolution_in_R3(double a = 1, Eigen::Vector3d off = Eigen::Vector3d::Zero())
: a_(a), off_(off) {}
private:
double a_;
Eigen::Vector3d off_;
};
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
Gudhi
Gudhi namespace.
Definition SimplicialComplexForAlpha.h:14
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::Function_lemniscate_revolution_in_R3
Function_lemniscate_revolution_in_R3(double a=1, Eigen::Vector3d off=Eigen::Vector3d::Zero())
Constructor of the function that defines a surface of revolution around the x axis based on the lemni...
Definition Function_lemniscate_revolution_in_R3.h:73
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::seed
Eigen::VectorXd seed() const
Returns a point on the surface. This seed point is only one of two necessary seed points for the mani...
Definition Function_lemniscate_revolution_in_R3.h:52
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::cod_d
std::size_t cod_d() const
Returns the codomain dimension.
Definition Function_lemniscate_revolution_in_R3.h:46
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::seed2
Eigen::VectorXd seed2() const
Returns a point on the surface. This seed point is only one of two necessary seed points for the mani...
Definition Function_lemniscate_revolution_in_R3.h:61
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::operator()
Eigen::VectorXd operator()(const Eigen::VectorXd &p) const
Value of the function at a specified point.
Definition Function_lemniscate_revolution_in_R3.h:33
Gudhi::coxeter_triangulation::Function_lemniscate_revolution_in_R3::amb_d
std::size_t amb_d() const
Returns the (ambient) domain dimension.
Definition Function_lemniscate_revolution_in_R3.h:43