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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_TORUS_IN_R3_H_
+#define FUNCTIONS_FUNCTION_TORUS_IN_R3_H_
+
+#include <cstdlib> // for std::size_t
+#include <cmath> // for std::sqrt
+
+#include <Eigen/Dense>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+/**
+ * \class Function_torus_in_R3
+ * \brief A class that encodes the function, the zero-set of which is a torus
+ * surface embedded in R^3.
+ */
+struct Function_torus_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) = (z * z + (std::sqrt(x * x + y * y) - r_) * (std::sqrt(x * x + y * y) - r_) - R_ * R_);
+ 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 {
+ Eigen::Vector3d result(R_ + r_ + off_[0], off_[1], off_[2]);
+ return result;
+ }
+
+ /**
+ * \brief Constructor of the function that defines a torus embedded in R^3.
+ *
+ * @param[in] R The outer radius of the torus.
+ * @param[in] r The inner radius of the torus.
+ * @param[in] off Offset vector.
+ */
+ Function_torus_in_R3(double R = 1, double r = 0.5, Eigen::Vector3d off = Eigen::Vector3d::Zero())
+ : R_(R), r_(r), off_(off) {}
+
+ private:
+ double R_, r_;
+ Eigen::Vector3d off_;
+};
+
+} // namespace coxeter_triangulation
+
+} // namespace Gudhi
+
+#endif