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// Copyright (c) 2024 // INRIA Nancy (France), and Université Gustave Eiffel Marne-la-Vallee (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Triangulation_on_hyperbolic_surface_2/include/CGAL/Hyperbolic_fundamental_domain_factory_2.h $ // $Id: include/CGAL/Hyperbolic_fundamental_domain_factory_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Vincent Despré, Loïc Dubois, Marc Pouget, Monique Teillaud #ifndef CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H #define CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H #include #include #include #include #include namespace CGAL { /* Factory class, whose only purpose is to construct random fundamental domains of closed orientable hyperbolic surfaces. The function `make_hyperbolic_fundamental_domain_g2()` constructs such a domain for a surface of genus 2. */ template class Hyperbolic_fundamental_domain_factory_2 { private: typedef typename Traits::FT FT; typedef typename Traits::Complex Cmplx; typedef typename Traits::Hyperbolic_point_2 Point; Random random_; public: Hyperbolic_fundamental_domain_factory_2(); Hyperbolic_fundamental_domain_2 make_hyperbolic_fundamental_domain_g2(unsigned int seed); private: float random_positive_float(); // returns number in [0,1] float random_float(); // returns number in [-1,1] Complex_number random_complex_float(); // returns complex z such that modulus(z) < 1 and imag(z) > 0 FT exact_number_from_float(float x); Cmplx exact_complex_from_float_complex(const Complex_number& z); bool try_to_compute_inexact_z0_from_z1_z2_z3(Complex_number& z0, Complex_number& z1, Complex_number& z2, Complex_number& z3); bool try_to_compute_exact_z3_from_z0_z1_z2(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3); bool sanity_check(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3); const int CGAL_DENOMINATOR_FOR_GENERATION = 10000; }; //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////// template Hyperbolic_fundamental_domain_factory_2::Hyperbolic_fundamental_domain_factory_2() {} //////////////////////////////////////////////////////////////////////////////// template Hyperbolic_fundamental_domain_2 Hyperbolic_fundamental_domain_factory_2:: make_hyperbolic_fundamental_domain_g2(unsigned int seed) { random_ = Random(seed); bool is_domain_generated = false; Cmplx exact_z0, exact_z1, exact_z2, exact_z3; while (!is_domain_generated) { // 1. Generate inexact z0,z1,z2,z3 Complex_number z0, z1, z2, z3; z1 = random_complex_float(); z2 = random_complex_float(); z3 = random_complex_float(); while (! try_to_compute_inexact_z0_from_z1_z2_z3(z0,z1,z2,z3)) { z1 = random_complex_float(); z2 = random_complex_float(); z3 = random_complex_float(); } // 2. Compute exact z0,z1,z2,z3 nearby exact_z0 = exact_complex_from_float_complex(z0); exact_z1 = exact_complex_from_float_complex(z1); exact_z2 = exact_complex_from_float_complex(z2); exact_z3 = exact_complex_from_float_complex(z3); // 3. Modify z3 to fix the area... is_domain_generated = try_to_compute_exact_z3_from_z0_z1_z2(exact_z0, exact_z1, exact_z2, exact_z3); if (is_domain_generated) { // ... and perform a sanity check is_domain_generated = sanity_check(exact_z0, exact_z1, exact_z2, exact_z3); } } Cmplx exact_zero(FT(0), FT(0)); std::vector vertices; vertices.push_back(Point(exact_z0.real(), exact_z0.imag())); vertices.push_back(Point(exact_z1.real(), exact_z1.imag())); vertices.push_back(Point(exact_z2.real(), exact_z2.imag())); vertices.push_back(Point(exact_z3.real(), exact_z3.imag())); vertices.push_back(Point(-exact_z0.real(), -exact_z0.imag())); vertices.push_back(Point(-exact_z1.real(), -exact_z1.imag())); vertices.push_back(Point(-exact_z2.real(), -exact_z2.imag())); vertices.push_back(Point(-exact_z3.real(), -exact_z3.imag())); std::vector pairings; for (int k=0; k<8; ++k) { pairings.push_back((k+4)%8); } Hyperbolic_fundamental_domain_2 domain(vertices, pairings); return domain; } //////////////////////////////////////////////////////////////////////////////// template float Hyperbolic_fundamental_domain_factory_2::random_positive_float() { return random_.uniform_01(); } template float Hyperbolic_fundamental_domain_factory_2::random_float() { return random_.uniform_01() * 2 - 1; } template Complex_number Hyperbolic_fundamental_domain_factory_2:: random_complex_float() { Complex_number result (random_float(), random_positive_float()); while (norm(result) >= 1) { result.real(random_float()); result.imag(random_positive_float()); } return result; } //////////////////////////////////////////////////////////////////////////////// template typename Traits::FT Hyperbolic_fundamental_domain_factory_2:: exact_number_from_float(float x) { if (x < 0) { return FT(0)-exact_number_from_float(-x); } return FT(int(x*CGAL_DENOMINATOR_FOR_GENERATION)%CGAL_DENOMINATOR_FOR_GENERATION)/FT(CGAL_DENOMINATOR_FOR_GENERATION); } template typename Traits::Complex Hyperbolic_fundamental_domain_factory_2:: exact_complex_from_float_complex(const Complex_number& z) { return Cmplx(exact_number_from_float(z.real()), exact_number_from_float(z.imag())); } //////////////////////////////////////////////////////////////////////////////// template bool Hyperbolic_fundamental_domain_factory_2:: try_to_compute_inexact_z0_from_z1_z2_z3(Complex_number& z0, Complex_number& z1, Complex_number& z2, Complex_number& z3) { if (((z2/z1).imag()<=0) || ((z3/z2).imag()<=0)) { return false; } Complex_number one(1.0f, 0.0f); Complex_number u = (one - conj(z1*z2)) * (one - conj(z2*z3)); float a = -(conj(u*z1)*z3).imag(); float b = (u*(conj(z3-z1))).imag(); float c = u.imag(); const float COMPUTATION_TRESHOLD = 0.00001f; if (a+b+c> 0 - COMPUTATION_TRESHOLD) { return false; } z0.real(2.0f * c / (std::sqrt(b * b - 4.0f * a * c) - b)); z0.imag(0.0f); return true; } template bool Hyperbolic_fundamental_domain_factory_2:: try_to_compute_exact_z3_from_z0_z1_z2(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3) { FT zero_number (0); FT one_number (1); if ((z0.real()<=zero_number) || (z1.imag()<=zero_number) || (z2.imag()<=zero_number) || (z3.imag()<=zero_number)) { return false; } if ((norm(z0)>=one_number) || (norm(z1)>=one_number) || (norm(z2)>=one_number) || (norm(z3)>=one_number)) { return false; } if (((z1/z0).imag()<=zero_number) || ((z2/z1).imag()<=zero_number) || ((z3/z2).imag()<=zero_number)) { return false; } Cmplx one_cmplx (FT(1), FT(0)); Cmplx two_cmplx(FT(2), FT(0)); Cmplx f_of_z0 = two_cmplx * z0 / (z0*z0 + one_cmplx); Cmplx f_of_z1 = (z0 + z1) / (z0*z1 + one_cmplx); Cmplx f_of_z2 = (z0 + z2) / (z0*z2 + one_cmplx); Cmplx f_of_z3 = (z0 + z3) / (z0*z3 + one_cmplx); Cmplx intermediate = (one_cmplx - f_of_z0*conj(f_of_z1)) * (one_cmplx - f_of_z1*conj(f_of_z2)); FT P_of_zero = intermediate.imag(); FT P_of_one = (intermediate * (one_cmplx-f_of_z2*conj(f_of_z3))).imag(); if (P_of_one == P_of_zero) { return false; } FT lbda = P_of_zero / (P_of_zero - P_of_one); Cmplx V (lbda*(f_of_z3.real()), lbda*(f_of_z3.imag())); if ((V.imag()<=zero_number) || (norm(V)>=one_number) || ((V/f_of_z2).imag()<=zero_number)) { return false; } z3 = (V - z0) / (one_cmplx - z0*V); return true; } //////////////////////////////////////////////////////////////////////////////// template bool Hyperbolic_fundamental_domain_factory_2:: sanity_check(Cmplx& z0, Cmplx& z1, Cmplx& z2, Cmplx& z3) { FT zero_number(0); FT one_number(1); // 1. Check the positions if ((z0.imag()!=zero_number) || (z0.real()<=zero_number) || (z1.imag()<=zero_number) || (z2.imag()<=zero_number) || (z3.imag()<=zero_number)) { return false; } if ((norm(z0)>=one_number) || (norm(z1)>=one_number) || (norm(z2)>=one_number) || (norm(z3)>=one_number)) { return false; } if (((z2/z1).imag()<=zero_number) || ((z3/z2).imag()<=zero_number)) { return false; } // 2. Check the area Cmplx one_cmplx (one_number, zero_number); Cmplx Z = (one_cmplx-z0*conj(z1)) * (one_cmplx-z1*conj(z2)) *(one_cmplx-z2*conj(z3)) *(one_cmplx+z3*conj(z0)); if (Z.imag()!=zero_number) { return false; } return true; } } // namespace CGAL #endif // CGAL_HYPERBOLIC_FUNDAMENTAL_DOMAIN_FACTORY_2_H