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// Copyright (c) 2013-2015 The University of Western Sydney, Australia. // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h $ // $Id: include/CGAL/Compute_cone_boundaries_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Authors: Weisheng Si, Quincy Tse /*! \file Compute_cone_boundaries_2.h * * This header implements the functor for computing the directions of cone boundaries with a given * cone number and a given initial direction either exactly or inexactly. */ #ifndef CGAL_COMPUTE_CONE_BOUNDARIES_2_H #define CGAL_COMPUTE_CONE_BOUNDARIES_2_H #include #include #include #include #include #include // included compiler_config.h, defining CGAL_USE_CORE, etc. #include #include // CGAL_PI is defined there #include #if defined(CGAL_USE_LEDA) || defined(CGAL_USE_CORE) #include #endif #include namespace CGAL { /*! \ingroup PkgConeSpanners2Ref * * \brief The functor for computing the directions of cone boundaries with a given * cone number and a given initial direction. * * This computation can be either inexact by simply dividing an approximate \f$ \pi \f$ by the cone number * (which is quick), or exact by using roots of polynomials (requiring number types such as `CORE::Expr` or `leda_real`, * which are slow). The inexact computation is done by the general functor definition, * while the exact computation is done by a specialization of this functor. * * In the construction of cone-based spanners such as Yao graph and Theta graph implemented by this package, * this functor is called first to compute the cone boundaries. * Of course, this functor can also be used in other applications where the plane needs to be divided * into equally-angled cones. * * \tparam Traits_ Must be either `CGAL::Exact_predicates_exact_constructions_kernel_with_root_of` * or `CGAL::Exact_predicates_inexact_constructions_kernel`. * */ template class Compute_cone_boundaries_2 { public: /*! the geometric traits class. */ typedef Traits_ Traits; /*! the direction type. */ typedef typename Traits::Direction_2 Direction_2; private: typedef typename Traits::Aff_transformation_2 Transformation; public: /* Note: No member variables in this class, so a custom constructor is not needed. */ /*! \brief The operator(). * * \details The direction of the first ray can be specified by the parameter `initial_direction`, * which allows the first ray to start at any direction. * This operator first places the `initial_direction` at the * position pointed by `result`. Then, it calculates the remaining directions (cone boundaries) * and output them to `result` in the counterclockwise order. * Finally, the past-the-end iterator for the resulting directions is returned. * * \tparam DirectionOutputIterator an `OutputIterator` with value type `Direction_2`. * \param cone_number The number of cones * \param initial_direction The direction of the first ray * \param result The output iterator */ template DirectionOutputIterator operator()(const unsigned int cone_number, const Direction_2& initial_direction, DirectionOutputIterator result) { if (cone_number<2) { std::cout << "The number of cones must be larger than 1!" << std::endl; CGAL_assertion(false); } *result++ = initial_direction; const double cone_angle = 2*CGAL_PI/cone_number; double sin_value, cos_value; Direction_2 ray; for (unsigned int i = 1; i < cone_number; i++) { sin_value = std::sin(i*cone_angle); cos_value = std::cos(i*cone_angle); ray = Transformation(cos_value, -sin_value, sin_value, cos_value)(initial_direction); *result++ = ray; } return result; } // end of operator }; #if defined(CGAL_USE_LEDA) || defined(CGAL_USE_CORE) /* The specialized functor for computing the directions of cone boundaries exactly with a given cone number and a given initial direction. */ template <> class Compute_cone_boundaries_2 { public: /* Indicate the type of the cgal kernel. */ typedef Exact_predicates_exact_constructions_kernel_with_root_of Kernel_type; private: typedef Kernel_type::FT FT; typedef Kernel_type::Direction_2 Direction_2; typedef Kernel_type::Aff_transformation_2 Transformation; public: /* Note: No member variables in this class, so a Constructor is not needed. */ /* The operator(). The direction of the first ray can be specified by the parameter initial_direction, which allows the first ray to start at any direction. The remaining directions are calculated in counterclockwise order. \param cone_number The number of cones \param initial_direction The direction of the first ray \param result The output iterator */ template DirectionOutputIterator operator()(const unsigned int cone_number, const Direction_2& initial_direction, DirectionOutputIterator result) { if (cone_number<2) { std::cout << "The number of cones must be larger than 1!" << std::endl; std::exit(1); } // Since CGAL::root_of() gives the k-th smallest root, // here -x is actually used instead of x. // But we want the second largest one with no need to count. Polynomial x(CGAL::shift(Polynomial(-1), 1)); Polynomial double_x(2*x); Polynomial a(1), b(x); for (unsigned int i = 2; i <= cone_number; ++i) { Polynomial c = double_x*b - a; a = b; b = c; } a = b - 1; unsigned int m, i; bool is_even; if (cone_number % 2 == 0) { is_even = true; m = cone_number/2; // for even number of cones } else { m= cone_number/2 + 1; // for odd number of cones is_even = false; } FT cos_value, sin_value; // for storing the intermediate result Direction_2 ray; // For saving the first half number of rays when cone_number is even std::vector ray_store; // add the first half number of rays in counter clockwise order for (i = 1; i <= m; i++) { cos_value = - root_of(i, a.begin(), a.end()); sin_value = sqrt(FT(1) - cos_value*cos_value); ray = Transformation(cos_value, -sin_value, sin_value, cos_value)(initial_direction); *result++ = ray; if (is_even) ray_store.push_back(ray); } // add the remaining half number of rays in ccw order if (is_even) { for (i = 0; i < m; i++) { *result++ = -ray_store[i]; } } else { for (i = 0; i < m-1; i++) { cos_value = - root_of(m-i, a.begin(), a.end()); sin_value = - sqrt(FT(1) - cos_value*cos_value); ray = Transformation(cos_value, -sin_value, sin_value, cos_value)(initial_direction); *result++ = ray; } } return result; } // end of operator() }; // end of functor specialization: Compute_cone_..._2 #endif } // namespace CGAL #endif