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// Copyright (c) 2012-2013, IGN France. // Copyright (c) 2012-2024, Oslandia. // Copyright (c) 2024-2025, SFCGAL team. // SPDX-License-Identifier: LGPL-2.0-or-later #ifndef SFCGAL_NUMERIC_H_ #define SFCGAL_NUMERIC_H_ #include #include #include "SFCGAL/export.h" #include "SFCGAL/Kernel.h" namespace SFCGAL { constexpr double EPSILON = 1e-8; #if defined(__clang__) #pragma clang diagnostic push #pragma clang diagnostic ignored "-Wfloat-equal" #elif defined(__GCC__) #pragma gcc diagnostic push #pragma gcc diagnostic ignored "-Wfloat-equal" #endif inline auto almostEqual(const double a, const double b, const double epsilon) -> bool { // shortcut and handles inf values if (a == b) { return true; } if (std::isnan(a) || std::isnan(b)) { return std::isnan(a) && std::isnan(b); } const double absA = std::fabs(a); const double absB = std::fabs(b); const double diff = std::fabs(a - b); // fixed epsilon if (diff <= epsilon) { return true; } return diff <= epsilon * std::max(absA, absB); // adaptative epsilon } inline auto almostEqual(const Kernel::FT &a, const Kernel::FT &b, const Kernel::FT &epsilon) -> bool { // shortcut and handles inf values if (a == b) { return true; } const Kernel::FT absA = abs(a); const Kernel::FT absB = abs(b); const Kernel::FT diff = abs(a - b); // fixed epsilon if (diff <= epsilon) { return true; } return diff <= epsilon * std::max(absA, absB); // adaptative epsilon } #if defined(__clang__) #pragma clang diagnostic pop #elif defined(__GCC__) #pragma gcc diagnostic pop #endif /** * shortcut to get NaN for double */ inline double NaN() { return std::numeric_limits::quiet_NaN(); } /** * @brief round a double to the nearest integer */ inline double round(const double &v) { if (v < 0.0) { return ::ceil(v - 0.5); } else { return ::floor(v + 0.5); } } #ifdef CGAL_USE_GMPXX /** * @brief floor a rational to an integer */ SFCGAL_API ::mpz_class floor(const ::mpq_class &v); /** * @brief ceil a rational to an integer */ SFCGAL_API ::mpz_class ceil(const ::mpq_class &v); /** * @brief round a rational to an integer */ SFCGAL_API ::mpz_class round(const ::mpq_class &v); #endif /** * @brief floor a rational to an integer */ SFCGAL_API CGAL::Gmpz floor(const CGAL::Gmpq &v); /** * @brief ceil a rational to an integer */ SFCGAL_API CGAL::Gmpz ceil(const CGAL::Gmpq &v); /** * @brief round a rational to an integer */ SFCGAL_API CGAL::Gmpz round(const CGAL::Gmpq &v); /** * @brief Normalizes a vector * @param v The vector to normalize * @return The normalized vector */ inline Kernel::Vector_3 normalizeVector(const Kernel::Vector_3 &vec) { Kernel::FT length = CGAL::sqrt(CGAL::to_double(vec.squared_length())); return (length > 0) ? vec / length : vec; } } // namespace SFCGAL #endif