11#ifndef FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_
12#define FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_
21namespace coxeter_triangulation {
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);
42 std::size_t
amb_d()
const {
return 3; }
45 std::size_t
cod_d()
const {
return 1; }
48 Eigen::VectorXd
seed()
const {
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]);
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) {}
Gudhi namespace.
Definition: SimplicialComplexForAlpha.h:14
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