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Diffstat (limited to 'src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h')
-rw-r--r-- | src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h | 80 |
1 files changed, 80 insertions, 0 deletions
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h new file mode 100644 index 00000000..620446da --- /dev/null +++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_chair_in_R3.h @@ -0,0 +1,80 @@ +/* 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_CHAIR_IN_R3_H_ +#define FUNCTIONS_FUNCTION_CHAIR_IN_R3_H_ + +#include <cstdlib> // for std::size_t +#include <cmath> // for std::pow + +#include <Eigen/Dense> + +namespace Gudhi { + +namespace coxeter_triangulation { + +/** + * \class Function_chair_in_R3 + * \brief A class that encodes the function, the zero-set of which is a so-called + * "chair" surface embedded in R^3. + */ +struct Function_chair_in_R3 { + /** + * \brief Value of the function at a specified point. + * @param[in] p The input point. The dimension needs to coincide with the ambient dimension. + */ + 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()); + result(0) = std::pow(x * x + y * y + z * z - a_ * k_ * k_, 2) - + b_ * ((z - k_) * (z - k_) - 2 * x * x) * ((z + k_) * (z + k_) - 2 * y * y); + return result; + } + + /** \brief Returns the domain (ambient) dimension. */ + std::size_t amb_d() const { return 3; } + + /** \brief Returns the codomain dimension. */ + std::size_t cod_d() const { return 1; } + + /** \brief Returns a point on the surface. */ + Eigen::VectorXd seed() const { + double t1 = a_ - b_; + double discr = t1 * t1 - (1.0 - b_) * (a_ * a_ - b_); + double z0 = k_ * std::sqrt((t1 + std::sqrt(discr)) / (1 - b_)); + Eigen::Vector3d result(off_[0], off_[1], z0 + off_[2]); + return result; + } + + /** + * \brief Constructor of the function that defines the 'chair' surface + * embedded in R^3. + * + * @param[in] a A numerical parameter. + * @param[in] b A numerical parameter. + * @param[in] k A numerical parameter. + * @param[in] off Offset vector. + */ + Function_chair_in_R3(double a = 0.8, double b = 0.4, double k = 1.0, Eigen::Vector3d off = Eigen::Vector3d::Zero()) + : a_(a), b_(b), k_(k), off_(off) {} + + protected: + double a_, b_, k_; + Eigen::Vector3d off_; +}; + +} // namespace coxeter_triangulation + +} // namespace Gudhi + +#endif + +// (x^2 + y^2 + z^2 - a*k^2)^2 - b*((z-k)^2 - 2*x^2)*((z+k)^2 - 2*y^2) +// sqrt(k/(1-b))*sqrt(a-b + sqrt((a-b)^2 - (1-b)*(a^2 - b)*k^2)) |