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Diffstat (limited to 'src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h')
-rw-r--r-- | src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h | 85 |
1 files changed, 85 insertions, 0 deletions
diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h new file mode 100644 index 00000000..beb41e00 --- /dev/null +++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_lemniscate_revolution_in_R3.h @@ -0,0 +1,85 @@ +/* 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 { + +/** + * \class Function_lemniscate_revolution_in_R3 + * \brief A class that encodes the function, the zero-set of which is a surface of revolution + * around the x axis based on the lemniscate of Bernoulli embedded in R^3. + */ +struct Function_lemniscate_revolution_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()); + 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; + } + + /** \brief Returns the (ambient) domain 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. This seed point is only one of + * two necessary seed points for the manifold tracing algorithm. + * See the method seed2() for the other point. + */ + Eigen::VectorXd seed() const { + Eigen::Vector3d result(std::sqrt(2 * a_) + off_[0], off_[1], off_[2]); + return result; + } + + /** \brief Returns a point on the surface. This seed point is only one of + * two necessary seed points for the manifold tracing algorithm. + * See the method seed() for the other point. + */ + Eigen::VectorXd seed2() const { + Eigen::Vector3d result(-std::sqrt(2 * a_) + off_[0], off_[1], off_[2]); + return result; + } + + /** + * \brief Constructor of the function that defines a surface of revolution + * around the x axis based on the lemniscate of Bernoulli embedded in R^3. + * + * @param[in] a A numerical parameter. + * @param[in] off Offset vector. + */ + 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 |