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Function_chair_in_R3.h
1/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
2 * See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
3 * Author(s): Siargey Kachanovich
4 *
5 * Copyright (C) 2019 Inria
6 *
7 * Modification(s):
8 * - YYYY/MM Author: Description of the modification
9 */
10
11#ifndef FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_
12#define FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_
13
14#include <cstdlib> // for std::size_t
15#include <cmath> // for std::pow
16
17#include <Eigen/Dense>
18
19namespace Gudhi {
20
21namespace coxeter_triangulation {
22
33 Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
34 double x = p(0) - off_[0], y = p(1) - off_[1], z = p(2) - off_[2];
35 Eigen::VectorXd result(cod_d());
36 result(0) = std::pow(x * x + y * y + z * z - a_ * k_ * k_, 2) -
37 b_ * ((z - k_) * (z - k_) - 2 * x * x) * ((z + k_) * (z + k_) - 2 * y * y);
38 return result;
39 }
40
42 std::size_t amb_d() const { return 3; }
43
45 std::size_t cod_d() const { return 1; }
46
48 Eigen::VectorXd seed() const {
49 double t1 = a_ - b_;
50 double discr = t1 * t1 - (1.0 - b_) * (a_ * a_ - b_);
51 double z0 = k_ * std::sqrt((t1 + std::sqrt(discr)) / (1 - b_));
52 Eigen::Vector3d result(off_[0], off_[1], z0 + off_[2]);
53 return result;
54 }
55
65 Function_chair_in_R3(double a = 0.8, double b = 0.4, double k = 1.0, Eigen::Vector3d off = Eigen::Vector3d::Zero())
66 : a_(a), b_(b), k_(k), off_(off) {}
67
68 protected:
69 double a_, b_, k_;
70 Eigen::Vector3d off_;
71};
72
73} // namespace coxeter_triangulation
74
75} // namespace Gudhi
76
77#endif
78
79// (x^2 + y^2 + z^2 - a*k^2)^2 - b*((z-k)^2 - 2*x^2)*((z+k)^2 - 2*y^2)
80// sqrt(k/(1-b))*sqrt(a-b + sqrt((a-b)^2 - (1-b)*(a^2 - b)*k^2))
A class that encodes the function, the zero-set of which is a so-called "chair" surface embedded in R...
Definition: Function_chair_in_R3.h:28
Function_chair_in_R3(double a=0.8, double b=0.4, double k=1.0, Eigen::Vector3d off=Eigen::Vector3d::Zero())
Constructor of the function that defines the 'chair' surface embedded in R^3.
Definition: Function_chair_in_R3.h:65
std::size_t cod_d() const
Returns the codomain dimension.
Definition: Function_chair_in_R3.h:45
Eigen::VectorXd seed() const
Returns a point on the surface.
Definition: Function_chair_in_R3.h:48
std::size_t amb_d() const
Returns the domain (ambient) dimension.
Definition: Function_chair_in_R3.h:42
Eigen::VectorXd operator()(const Eigen::VectorXd &p) const
Value of the function at a specified point.
Definition: Function_chair_in_R3.h:33